%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: tensor.dvi %%Pages: 42 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: XYATIP10 XYBTIP10 XYDASH10 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips tensor.dvi -o tensor.ps %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2000.05.02:1439 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} def end %%EndProcSet %%BeginProcSet: special.pro %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N /@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X /yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet %%BeginFont: XYDASH10 %!PS-AdobeFont-1.1: XYDASH10 001.104 %%CreationDate: 1997 Jul 20 21:19:18 %%RevisionDate: 1997 Aug 28 05:34:12 %%RevisionDate: 1997 Sep 18 10:23:31 % % XYDASH10: line segments for Xy-pic at 10 point % % Original Metafont design Copyright (C) 1991-1997 Kristoffer H. Rose. % PostScript adaptation Copyright (C) 1994-1997 Ross Moore. % Hinting and ATM compatibility Copyright (C) 1997 Y&Y, Inc. % % This file is part of the Xy-pic macro package. % Xy-pic Copyright (c) 1991-1997 Kristoffer H. Rose % % The Xy-pic macro package is free software; you can redistribute it % and/or modify it under the terms of the GNU General Public License % as published by the Free Software Foundation; either version 2 % of the License, or (at your option) any later version. % % The Xy-pic macro package is distributed in the hope that it will % be useful, but WITHOUT ANY WARRANTY; without even the implied % warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. % See the GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this macro package; if not, write to the % Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. 11 dict begin /FontInfo 9 dict dup begin /version (001.104) readonly def /Notice (Copyright (C) 1996, 1997 Ross Moore and Y&Y, Inc.) readonly def /FullName (XYDASH10) readonly def /FamilyName (XYDASH) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -300 def /UnderlineThickness 150 def end readonly def /FontName /XYDASH10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 28 /d28 put dup 34 /d34 put dup 67 /d67 put dup 68 /d68 put dup 73 /d73 put dup 77 /d77 put dup 79 /d79 put dup 80 /d80 put dup 82 /d82 put dup 85 /d85 put dup 105 /d105 put dup 106 /d106 put dup 110 /d110 put dup 111 /d111 put dup 113 /d113 put dup 117 /d117 put dup 123 /d123 put dup 124 /d124 put readonly def /FontBBox{-40 -520 503 520}readonly def /UniqueXX 5092844 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d743b8793c40476b99911a1be6c93ca a7ffc9533764a6a2a3ebcf0bebc6668e399d80ad8b0e5e21d556d8fa71b95a1e 01e6689c74f977a4bbec6795aec114d8507f237839f414ee4fbf8162c865260f 923a63721852c7bff69703f7e0ab99c3b85e83c62c13ea99442890e370376cce 7133ce8f3de2f4c1dc78fb55dff4eb737c195d266281adef5d56fbbc3b785b1b 59d6efeab3b93e713f4b9105cf1594c83472177c0f2b04c840760c92c094a0b9 2a720e4c7b03708d225531ac69324547d65009965f1c52d2be3112c67b6002b1 3d5f2c82505b7f0136cc926ff2bda0b53691b13e816817e913048ad033e0ff31 9d18776c4be80936c7449f316ff7f9026e5eeb9984867fc558bb18773e9a5390 d4490fb8e63a0ce175f52732043cba9d379d01ef25fc4be056d3206186b53195 63ee3d03fa580efa0ad7d3162f77878d348a841432fabedfebc8559530f6cbc1 59df0a77aacfa9f0974542a736680e064ac101c646442b0ca133c4701c206de9 6b70d341f9558a800520c2d32be3628b6df05a19538ec2596d2334f05d54e742 a1a18ebbc12f04c45b899f667d9e6f3a4eaa1854562506d0da4057c4bbfbbacc c1c208cc47b76226ef6d4d3da7d976b7a21a2cc7aa7cf0602fbd2a46022f7894 c0667e19a31cc10ca33811f882ca5cc140bd49eb62545ffe3f418e8cb9b223e3 b2630b486a3b948c74751c414e84334424a1eee8f20b1bd4eab9a0e0545c9bf2 f8cda548feb88b89e369f29f5318ee43b25672b275b05016b635dc656bca5b14 a28e91c516e3f5e99609f5a37a696fbb39379b8374a044e2fe6d4a193d5360d4 31229d74455ff8645ba7462da11460be68629c6a2b1b4b4f409c806cdaec4d3f 941ec5e5a1a6aaaf2c72de027d73b6d446b29f4a0504dfa9e100f273e0b8f54f 707a5a7e1e5f5f3734783960d641ff957f220cdff18bb2d536a406abc54e557f a1e9728df44ca1a17c233e052e050fcd4d771fc5fa346a7707cd9f99d84d5117 03cc24d00bc9a07facc9d43e8ed8d24492443c69222cc444820fd282106b145d e827cd39334d12ac5ce75341e831caae76283c49935c4fd9dd0326d3abe5afe1 0e8f5279592d753f14ac5d342bd3d6bf32ca10068eda0ca6b4efa56c2aa4681e 6797e2301c9311cf83ff35250362b64b1c39b154b40020a56ee060e7b7740ce7 0a3547ac633756e2968875c226b5c476dd58e66037fca3949219349fa3bd7b03 06010bc612531bc1b732e88fb974a48f0b5193cd09e2adf32e587bfc1c0cfdb9 d9dc516b06dc94649a36152f602bbf3ac10d0a293111339893881f9e864db3d3 7939f8506094e16286fa810f1753921226c9a12a7523c2f189952fe6d920b2d3 bcbc901a5a849b1e15c9735f67169a1e9e382e024b50d2f209b13fb837a6e6e1 5a5e553fe4b462e5120e45b49e1ff99a03f62f350f4942f6f263119d36bcf828 0d17951f18a151e2ceb5091a5b7fef845bc8ee8b6c0cb59ba58cb354eb4b70bb e1aac5c7e333b7ed8e3089160d3054c48abab3ed77a64523f2780c06cba2b32c 1cfc1616b10e05d466a73e4f9d0282ea0998c1a73ba60bea6405030924a89325 4f2c371e95f7c555a96d9fdf038ac12b8319fe6be5fce36176c23dbe6f7c70ea f8195c3425b205b0a52836fd569df967c57015a5e527d49aaee26c0eb365a4da 15ec6c927a62d03431de447bf2c22e250d3bed7d68ea452f31df04330937fe94 69cc064a8d21a2e1fdcce04074577ce791b195559b8a13fafe150ad72f7e7ff2 5b474dcff6711021a476e0c8c2fad2c2ba4eac3709008419893044802ddce7e2 2aa3c69fe7ceb71d43aa3aa90a03414679eac03ca824e08f0d8bb36224c514ea ce3b15ec4881604f8a2ff536109fd896bd852cf92ccfc8b3ee4ba98aa8100a57 5ff41502ffd7ea42673296a9e6efb7521ea0c609877ff9c68b55d76d5325ca2a 57992dc5c35b4f36c54a237dca3ff572abec4b11b8c82e803d4d7d87fe80aba5 009c9742fb1eaebc7540f1f9663f832a2828072a03537c428124595c561d416e 3d500fb2d469583b509a05c63ef231b185ea1d3fd8d6d799b667383c0d4c2d44 2952fabbad72e27d408ec9c4869cde11b72b8f06e0dc732f6802fe2d7f3ca724 1eb3f5568868b6cb4b15b6f168126956393a411cee268050d2a54a7036fd7779 45c6bd96e6e9abe09ee7fef295344226e54f0b0aacd2fbac480d227074a9d2a9 faafe76527d34c5d79c2c2f854cc533cd76de1084d05921d9d8bd2ff7389c638 9e525562625d290be869d9a2e5da4bb88fae5a22c66d8d39c4f28313a052d7e2 b2d4d40bc512e9e6715babe38ea067f3012033f5d5d0d6dd588120a427359638 cea6f9f7ce2ebc82b39ea58d2e955d2f9a6ed7db7f5155949a1c262edaa59aff 25038dfec75f093af2e33f46a0a56fed47179a3824c8514a32cbcea7e9183145 02a80859bc5d5e0f4290ef95514edad5997695e999f7e8919bf474040bd0d879 17532bf89d5982ba7e073e569ecfaff74991e2b5b78f8ebe71790b4f803c6e8b 59cb7e0a03e8f30e961ee414da0e4614dbf6c11ec255e9a716276e1b2fb3d422 123c88c513b1ee248c99cdd48efc2464985fa7ab01dd3717369974d59d7ebc32 29a2124398aebb1bf68d1d7a0ac89aa432c808dcf1e6ab4144aae5a256978be7 f74f09043d699eb65bc7c8e1745db0a0fc7be240120515ef2c097ac0197cf782 922d94ad9f4173a7be421d3aef569a3eff6e724ca5a7c0ece0f6d8a38d3a6d86 ef1acfba6f228cf09cbb1beb2d054eb70bd6848d03cb311a41dcc1bb24c6a052 8ad9fffc9ab458133b488a195483ab46e75672f37d55af3174e3d303cced8801 4cc3763c18a764b5be44b3b28c5b0262a9ee204ac66ddad9388bbee8a4cac3d5 5332ffbec65eb9c6bb3f9dfea5be766b30d1fa5d2ab1bad9840e60606103038b 9befaa2a8823873b981ab33777655d362eb956d55464b6a3e02f69256219c432 02968951f1a7d1014f187c3057b250fd580ecb8ffe11a86614a985b3d9560b97 764621deb7a6ab9c7414134c27737e3cd20c9c4a5ac469f6db595763a2b568c6 ea95e79e5b03e7dc6c4d46d7bac22e0a503d558d72d0b6190756179d141bb4fd 03baa95a77906d32cdf149f643ccf98ab6967f29ba543b674bd19661107281c5 e52bfd2120d96f8e933a861bec284b58b9130a73953734a64580406e10a5a3fc c4661e2c40300def60e01a5324c6d8fb0d7840cc59f78f1db77a1f458c38a99a 9c9df4e4142f5e82567481f4068789819e86087ffd03cf0fe49cfcd5fa21e72b f8b617afa99e91eeb3f6ff64c59bca52985604e5f9f4634a65bc87972fe02d00 20a285ac50e63f5f6baab788d428460ef0639dd16f2cda3ab643a91f38b5b545 ed3521be5a3df7e3a4c96f43ba93b66508ac9a5ae7d01964ac31c52a477b25e1 b39b7913836e2a3dd9c35d62dc0841d6abd837c889ad7bd96c30eae92ceeaa36 78678b4a2542a26283f0cb57274516a23f9de5648d10d915bff016118ab3d1db 8bf4da2151fc1568574b9b18bb82344fc2abd967f0dbda5f75657ebc14fd7bf1 1ac6cf81a8eb952a043b1340a7fc883b28638897d15bb4c394d70df7df3d1312 2629b5a8c236d9e91fe466b264d6e5018581bb79e23dd527875cb97ef7962d44 2fb47682afcf9a3869ef323af9fec2d18e8a3613c10d546970216927e6740be8 0e272580db4cdc1b8fece17f94fc78640294a0 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: XYBTIP10 %!PS-AdobeFont-1.1: XYBTIP10 001.104 %%CreationDate: 1997 Jul 20 21:19:18 %%RevisionDate: 1997 Sep 14 19:58:47 % % XYBTIP10: lower arrow tips for Xy-pic at 10 point "technical style". % % Original Metafont design Copyright (C) 1991-1997 Kristoffer H. Rose. % PostScript adaptation Copyright (C) 1994-1997 Ross Moore. % Hinting and ATM compatibility Copyright (C) 1997 Y&Y, Inc. % % This file is part of the Xy-pic macro package. % Xy-pic Copyright (c) 1991-1997 Kristoffer H. Rose % % The Xy-pic macro package is free software; you can redistribute it % and/or modify it under the terms of the GNU General Public License % as published by the Free Software Foundation; either version 2 % of the License, or (at your option) any later version. % % The Xy-pic macro package is distributed in the hope that it will % be useful, but WITHOUT ANY WARRANTY; without even the implied % warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. % See the GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this macro package; if not, write to the % Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. 11 dict begin /FontInfo 9 dict dup begin /version (001.104) readonly def /Notice (Copyright (C) 1996, 1997 Ross Moore and Y&Y, Inc.) readonly def /FullName (XYBTIP10) readonly def /FamilyName (XYBTIP) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -276 def /UnderlineThickness 138 def end readonly def /FontName /XYBTIP10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 14 /d14 put dup 15 /d15 put dup 16 /d16 put dup 33 /d33 put dup 34 /d34 put dup 36 /d36 put dup 38 /d38 put dup 39 /d39 put dup 40 /d40 put dup 41 /d41 put dup 42 /d42 put dup 46 /d46 put dup 47 /d47 put dup 52 /d52 put dup 55 /d55 put dup 58 /d58 put dup 61 /d61 put dup 79 /d79 put dup 97 /d97 put dup 110 /d110 put dup 111 /d111 put dup 116 /d116 put dup 118 /d118 put dup 119 /d119 put dup 120 /d120 put dup 125 /d125 put dup 126 /d126 put readonly def /FontBBox{-542 -542 542 542}readonly def /UniqueXX 5092839 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d78041987a409a2d06b6b3057738213cee08cd789eeaa 097caceb2738a78b2f437638f0d63dd9e45ce613ae94486e726c4ed202501d61 51965c5c865a24933f21e0b1c67ff0d74bea0b8003496a2b1c9e3cde218dfa02 7343f1561243c5419412a440b6d4682c4dd92bf310718d73d28f47559a653346 c8fa6a8e3ec0a68d6661b293a71328a0bd0521249f1263070e67d0c20ca4a48d 221bcd864852e33289496155416b7cc05e73dd2b7f9ba0977ab328be862ac7e0 139c8eef1237e57525cbc853d7cbe3c9a8b54c378e8af02257a8daa736c3d9ae fb18fd198a33681c334984d81e2d783d32adf54549f5bea0bf351b1016032908 81685bde8d44703654d97063c8ebfb896e029b2383f5754d467163ec07f3398a d88196c720fd98b9a2260de8d7d3aa6453f831ce18233cfbf6cb098bc3ca2cd1 495386a279ced386537228ec08f3b3e400cc040ab2e763b0cd93c9a2c5ee0436 f0a2f033ba5d3e4231aacc9b0aa820f7ad72a3cec593a1153ee5527693ad3bc8 eaef55ac2f52fdf27146c04dcc825181a275e632e75a94cb9b3d3f7d17c1c08b 83bbf5c681f864e234d10b0f7c64839aa1671931f39a001e4134030b91d9a473 6c7d5e101e04feb20a04907ab46ab24902c1844b018beefd9014c8b629674e57 f1f0d63ad79dfa8ce4d1fffabeb4315386d494a3ab66cc9f291a714ef0ee4f9f 1687f0ecbcd2acea0e98dd5f94dfd700e546599e58d1f25bc54ef6ec0f12b91e 6690287b7c527a51724cea71da655f2b2974633ba5484cc6c2300ba28dff89e2 0c37542986ec1e4613cc8a16521e5c2720d88fa18111a1083dcee82b011400a2 8b4124ab1a5bdde460e2589f2872b0436396df646b0eb176e75de9af54d7c4ab f628a596d7e1ead5815ec6bb58786913f0125dbe4a6328ea358185ce03fdf5b2 8d3e5cee90066a67f548590d69d197b1503ae8f993a1a7aa4248f0be3be623c0 fe29e1772ade5b00f22b228152d197d6b3e1ddf4dece5c7cbadfec3e7bb38696 91becf5079caf4c910b4a25a1b19e3c64eeb79e5223d56f7aae7411259fda2b2 2e2a4652323e63b97e76d22ca5fa800398fb0b4636201037f11794493ce10d4a 80fc85a0a26686c096d560a3a77cb2cf4fdcd105e98e7e88454412c6a107c5dc 7605eef7932c093879753c20b5397cdeba78d0a798f789304d63956f0f471a10 ad93e8ade240e9185f8028420ecc26e436fcff5421bcd39aeb8ac91800241d34 133cc54e557b68947337eb889fb494948d932519e0e19f3dd891220c04935f13 96f8196a907180e760be47484d144c1039ee7934d0f08397e9b640062ffd670c 1c7fc029acbe5f5c7982e68820e9140313eb390f785901879c614f5461f3e0e6 908f053b64f7f0ec48d567b4125934d21158a2ba50e361b6966e857922618b72 06d412a748706d7eac5fff41ee5c52f4142fce1ce9ba67a3c97ec186b187b80c 41b8ee73ba38e3bf2bc6741de19ef652832faba07c55e7bd7ae5fb49d86b1808 8bb5e80ed536552a211ce36d2961583aff648edd54f1de84ae741b98bbd57e37 577e55ca0f97c4ac1fed15732a0a072a176b0c5f14dbcee98f6d60fe3b3df180 2d93213c7eb7a37ff92ff4f97619596aa0771d0cbc82c5cf55b5be4f44fba75e 631ae71cbc9afbc42312cecdd86b7aec3152ddcf7fa1c6f5e051581597864746 2e975089ad928df03a4073bf06bfe1e262a551f24a12bca29408aacf7ed2e43a 3b7f7ff8e40af2ad2b131622058405cdf249568c2653b0be457fed5352e113fc 1107d6ed67a6ffeef5608109c13e5d5bc2432e65b82d3c3fe6d012e7a84e7730 13ae1201e1ad5ac9c2c11163be1d85f342956954f92651fcde7efbd58975fd01 37afbc60f68065b6b4af9856ef3a425a57a25b3ce8e5375aeccfc1146b78fb7e 6aa315ea438e2826d160cb12ae97fbd9c4704114f4269ae8ed6a114882c3fe34 9aa90531189c9e3b9fd1bb8f1772fdd681245ccfcb8b42165e018ad8af8f2440 954f0390129495317eab98a4d43da3e8b81c4269b19e4069c61c0ecb28a57873 610c578517a8e08f9762dce236f12bdb99718602cba86a56166ddcd42497ebf9 5b52ebedd9f09a6109ae30158fbe7d998aff28df96cb38f706e1b05b685c7df4 8410ed3d5558666c7c85dbae18e6e50330f7fd850d55e2c7a2277fa9fc2372b5 5e8102cd124121243810279c8d7773e43cc5233bdab4d5379ae5bf2f2ef82d78 9621ea5c345dba373f989f82a3f1d6edeb69dc7c9abb0de83996d732589a642c b63d80a8dd4420f3593380d56dabe56ffbf30f6d1bc7b8e3d8da03de5eb33aca 4b1dd4b2ae4b385c05b16d65d336149a68d790bfe240b23f6d38c19945037652 4b54fc9e0a60df4b23b9054d0c05b7081ed97195ef3fa26beecf5ea3fe6cae8b ebea88ed339f7e59494275fa923c8e6d1f6d34d82dd65764941e4578de48351c b2bdd01bcb8f95fbd8adc59d14b5212aa0f4243d1284c6c9325eb8331f11a031 c3c72668b913f9dc2b818ffa189229145614d11cc645beb56e006f2eddb395be f40407977ed4c2018231bdb1b3975e3471c917838f156ce50b6b7881cd5a924e f908a4246961874932ef7694a89836e8b2bdccf9d5e37465d72a051b28eacaa9 0c0499a2caf6f048e16a2d538f93db84d5aa1f5ca2bf5f59e688483eb6f7b76b 86fa39f5bb91ac2cb449490d02cacfae6eeda6cc9f81dd1f23f75dfaa147ed8a 8409b1df8fc6ab93b5e0faa71e6ccd142f1d922463b33e72adb48edb72841e71 6e736726f7502bb9acc792946494e722e21bf0fd127e18a5a841c4eb8e5da923 4b33a1ca992a972d9e9be9ab9ac03490a1ac894a14d0d968505d2e85e031c7ba 214a73d474109de5438f3d6c6fcf7d7c3328c23bb891d9a032b826499fef9f6a 6d2f4b931dac8a9e52f0cdc71237f90c0cc8d3ea2b77300e8eaf805a1c96a531 29116f4d980e6b5d2255be1b414827ec5f1c704957686a2a15eb97163c52aa2e 7ff983316875f3254b75360a5eb964fbbe2512639537c9d747ec797438cc6a1f c29c4ece2df509aca9f4432f2802404525ec3ccdd00c16d5e4b1d988e05a32d0 b3109c438bb4d96461ec7a01f31397d05613041ce4e7a058c76db266c85186ea c120fc8ded67831b7b6eaedc2697dbe21aa0be8c23376566c5c2368571454153 c6376da88f348eba5f988877fe62b7173a34031cf1a438f1d0681e252ba36789 ff08228ba054542b40c4d51023bbcc575acd9b5e48212cbdd008e48b5b455ae4 5e8f7abaac5079262c2f68dab05f1a2bfaf0c701cd9f6212786d56080b547abe de0a0c45b69b6735611e712287a2a2dd7c48bd41b61d5a521465d0056ad19950 f3b69224cceb5e44f4434014634678fad7c159c53fe7f1641358a043c397a25d dfcaaa727be1061288fd97407d8ca2e249e551e25cd28a4013136d80e56a9f03 7b1cf2a97c9d3e555c87c7442f038cda997d27c059816266af66e5af51445134 21ba39ffb81e96b689e4b1e8e6a31a64146f292793e8eef0390cb8cb8ef6ee21 95ffc8dc3707c1b5edd3e55958bafd54976526eaa15c355b4ff695b5dea821e4 78100344d5aa80c8968e88f8084a6c3d4f8498773f922ca08b95e293f39a66c0 7cf7a6471e41f1d213e63b2fc4ed95aaaff8523974de592f8781313988ee1fa1 da857e896e84708b791ce58ef30be9ab9d02ced5d8d6a72833dffeb44db429e3 a9c41e2c05da263b966233f2f52870aff1f5814a7460361ebc8146d9addcde2a 44347bd9eaeffcc9761fdc17a89ea5e8f445f95006e017e9276e079f74c8df0e c40a1c57cd36402eca43f744fa2586a1159bebcb5cdfb5cc7d85a50dcfa3a62d 3ee6c5bfb1867e002e8aa07a2acf3e66b535885f1e226169f48a0128d65481cf dcb8c0c147570b40a573595e69a63d1b7ea70ea2512bf2a3ec433d10ccbd63fb 692e642cb7397d926de8e29fa5320505e0023dc37be3ed06cc5d08b0efd62382 92c8a6fafb49304e2bb94b5a9603c34c7f30fe91bc74b9ba972013ac477ccfac 93541acea4d89fd121931f93bedede6bca4bb76959c2bae0655474de2364b0f2 3f0837b0dfb1ffd40fef2cad7cbd9f4e483227ec15a96a23badbf56d9c46a0b6 71771274545d4e81f830000c86c88934f4eda292bd7f13d93f158f446364831a 887ec603d4bb1308fed4f6effe728ed2460280640addf145df15c70d87970054 f86abf37ce50926a7d7f3a8dafb63ed484128a581d72a90c9ead1890f6551444 8fb113f29934bd2da3fc2a33a83bbcb5ea207c71cad63b05f82d1a55fc81280d 548451d254f5df3c97cd3bf42181bb306f365f419cf90ce7778ff5ffea51ea09 4fab9198f70afaac4dd6a703065f723b7d6e53db961c9699bfe7d79280e2f62f 4a05d7a1c0bbe55ae3be7e851f8bdc5206de3f6f1ea55f26248ca6fbdb061417 eb7689dd9d59d4a6d2e42d8a40b606ff7d4ff5fe0b6f6bf498528e0693b398f6 c74708bcec71b15d2cea5140321727a091677ac067f787001ea089276558c727 51a1e8644e499199d2f896154a8275d8b9b01aa32dec10a0f0196e4474e4b188 ab9a89e29a8edf5c449d7c25ea1091646d2c246599e5dcc4f0167f7ee1081ad8 c267205b3b256b96a3b54281236eb39a700fa43acf8517abc72a845bc110e1ec 153fc374710975248e3401bc8d1e66458fa2198d8885374f1feb57e7f77bf4ab 5edec4d089a223380cdd01d9ce39fdaf30ea1e3512db78a713a40159e3f7f578 fc119c61b32b73c6de5dbdf2899d6e9ccfd5c563887bc57122bc0dbac2091844 6b1ab98b5786c8f18477cb06b0df72dddc8c343deea9161c526b7210c5397fe9 faf8d92b0f886b1cda38491d477c1c8d082a8b542e505c6a8bc5bed72b14f1c3 9f 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: XYATIP10 %!PS-AdobeFont-1.1: XYATIP10 001.104 %%CreationDate: 1997 Jul 20 21:19:17 %%RevisionDate: 1997 Sep 14 19:58:47 % % XYATIP10: upper arrow tips for Xy-pic at 10 point "technical style". % % Original Metafont design Copyright (C) 1991-1997 Kristoffer H. Rose. % PostScript adaptation Copyright (C) 1994-1997 Ross Moore. % Hinting and ATM compatibility Copyright (C) 1997 Y&Y, Inc. % % This file is part of the Xy-pic macro package. % Xy-pic Copyright (c) 1991-1997 Kristoffer H. Rose % % The Xy-pic macro package is free software; you can redistribute it % and/or modify it under the terms of the GNU General Public License % as published by the Free Software Foundation; either version 2 % of the License, or (at your option) any later version. % % The Xy-pic macro package is distributed in the hope that it will % be useful, but WITHOUT ANY WARRANTY; without even the implied % warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. % See the GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this macro package; if not, write to the % Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. 11 dict begin /FontInfo 9 dict dup begin /version (001.104) readonly def /Notice (Copyright (C) 1996, 1997 Ross Moore and Y&Y, Inc.) readonly def /FullName (XYATIP10) readonly def /FamilyName (XYATIP) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -276 def /UnderlineThickness 138 def end readonly def /FontName /XYATIP10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 14 /d14 put dup 15 /d15 put dup 16 /d16 put dup 33 /d33 put dup 34 /d34 put dup 36 /d36 put dup 38 /d38 put dup 39 /d39 put dup 40 /d40 put dup 41 /d41 put dup 42 /d42 put dup 47 /d47 put dup 52 /d52 put dup 55 /d55 put dup 58 /d58 put dup 61 /d61 put dup 79 /d79 put dup 97 /d97 put dup 102 /d102 put dup 111 /d111 put dup 116 /d116 put dup 118 /d118 put dup 119 /d119 put dup 120 /d120 put dup 125 /d125 put dup 126 /d126 put readonly def /FontBBox{-542 -542 542 542}readonly def /UniqueXX 5092838 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d78041987a409a2d06b6b3057738213cee08cd789eeaa 097caceb2738a78b2f437638f0d63dd9e45ce613ae94486e726c4ed202501d61 51965c5c865a24933f21e0b1c67ff0d74bea0b8003496a2b1c9e3cde218dfa02 7343f1561243c5419412a440b6d4682c4dd92bf310718d73d28f47559a653346 c8fa6a8e3ec0a68d6661b293a71328a0bd0521249f1263070e67d0c20ca4a48d 221bcd864852e33289496155416b7cc05e73dd2b7f9ba0977ab328be862ac7e0 139d5cb0db6f50b26bd8ab173859c9c94db82970311d7eb0a02bee1be5f0d126 f9079e67107eda14b460e46b03b0422eb45a4f4afa382841c35b0bc0c8639b73 43c819afc69838ce781c2de7d22bf503ef6eec27c83cfd52a77bbc754b4f2050 55341700991f3ef4b5b5a54c21283034b38c8b6a6e65abccc94c0c26836806ec 4df8d8c64f595841395072f8a2d289b7fe5497bc0e061810b16a1e48653bb092 42ffa3ef0bba4e37a5aa4ddc31f3138aaf10998fd66f3817b77012eac677ed2d 7447908c771fbaba4dfcfeca5374a6b87e5657809a82f0ae068c5384c12f4653 2a82645a512212140d815e80ec76b3370c382e9f6d29ec6afc178a622249fda7 775d4f6a554f04748ed4210257fa6e376188a175db3c00f88421820b063a985c 07ad665eff7e2d32a27015c528227c2805aa8df134f4abad9958b841aa4263ec 9ec6d907308b0a5a51049de002cfe60ef35bf33fc863ba14ff361749554abd65 47426fbf3958ddb506ea3e303c932edec2896d3017a57913cde60cbdafeddbd3 cd5ef6dd49299783a92fe9deafb24e7f74a6ca6c0198b2fcda46b51445a2800f d1dc6a092b3192cfb314892e52753b5c7b94edd34c8213b032f8aab5d08753cb 65bd1a1225ba43194efa625ee5dc6eec6d0353d06ef3bef9c0d7df78fe189482 779c9276e83ccd71b50e87ba92cf092d65498e5b43cdc89436019e306c0d628e c7d1470ab322ca2d6adc3e9ff4196c0f7792ca0b20f741ad7bbd4391b0218511 14f0e97a44fd7d03e7003d1fe2c70d6266740dad7b07b3794dc53871887c8eba 2910d6fa654346318753cc752a7d25c1ef970e7dda8d8bbe249e9edf2c8c2ae6 abb93bab2dd8560466a7d08ce3e200d7cc488c6045871a8033ec1dc3a53e7056 3fe265f58c6ac98754d399b47b817b7aed7ebbbb503268e7324d6c0a0931978b 51a7d37187a99f234ae4c46b585383938e7cf59d2dfd20717031966eaa4317e7 21c03e9363598030c707f2613d977fe82f5967e1781e158d5c9e376a1c79fa5f 9a90ddbcf4bc24f3bcda234fd4058b5012e85de7894c0745a24d91b21a38ebeb d918421472462f7dc83bb4c5dea61690d651eb9fa223871876375aa4974454e6 84fa4ce807a9e8819397c651905a743f356d8c237792bd51845a0a4aa21bf8c3 ed53d949adc90e8a30a8dd8ac9e1df77546c22473a4b7177fa4f23c728b7d114 f75aad3f3d4296c2229e4110a89596c5fa8f15a463aacd6195a0944873982a40 14489e6cdc91ce1bfe9c89d1280eed70d3ffdd76062ae2ac47a11f51bf7aa32a 324f0b190d173b31fb4561fe52d5ca51f2b3af2d669ce118191f3fc73d5d569c 042babcb5f4274b32451f58e9263c81b00fde9f3a04fbc3f92f75e08009c529b 2e208a633412ef2605b86d646f4756e2ad21fac5b6988f5b17eeba3969de4b74 6f39fda9e78fbf6b3d8c1e02696bdbe7c30986bfcf9ee9cdc913bfe7b1636fee ac3cd434f742666830f9b92b9a83c5720a9944d861517362f82bdf1d2af271a3 3f81000f5e326012c6354dac835d75bd06e5c55d53f83b29bc85f3ddc697d598 05ba9ab873f212210abbb05a0281e79a1f915ae212d87a9011eb8b32b2cbc95a a762953ae9ba7c09f4632cd0768fad198e628615bcd0bf68a99b237790e1209f c0a5e893a72026d5100b7a83691438a9ab33c666b435455cd9c93e747b2330cb a0d9509b9152baf9b50ba2e752ace11dbbe3b6c3cbb7ff609d8cbdfc84a84eb3 e414b8f766180fcf56e458907bef3770f3af102e79df71968e50648799555e95 be5f24c7a845994413509437682b0ab41818dd62083ca3807fefe98cabed2900 356bd8a9f0b25e43afbfd13fb318aaacad189f310102e5d1f6bfefadc109f971 a6cae196fb50c2f8a874a293e7bf9c3c096b617f1330e1e4a92ed453cdfac802 9b1057a187107b57ba1e6f8632b1e03f151e60c8706b5e179c5c3f1e1c4bb256 7d273ca9b0c2c54080d788190ae4b996df6f194419ca1ce698ca3d5bc9793af2 2f6ef6d11a3ac289b0354219ff71fd1987cce29aecca00fc99acf05a9c591f6c 354cef5be580f0f0edda224ae7a2ac9920b668f2488c8e7f76f5b0d15b55f029 83067c386c23abc0da400b158b2be1eed2b5fe6ebe12843bf20bdec8b276680d aa9410026d5f55335a1cdcbd722fe08f5e9e8051cd5bf9293f36da2a4bbc00b3 c18b601ae9a39bc5585c61dc74bd70817cbfa302902a4ee33e141556d4bb4a79 5fb7ed6b52d7ebfa65167b6f3baff8eb94cd41094829fc580ed5154802783d8b c05ec49e8133c8cc18f75c767eb5023c3e15993a9c5b6d25f4a5a81eb8a5245b 80a333f189217bd3f17037b658e3a7f329f02d3b5aa3dd8dc22db77510c6c487 41219d20f482ee812155b4fc631786cedad713feff2f5291f5b53f0e12c2809e b9f6358c15371ccba9efd8c799100812dbcd649925fed9f16beeab273fa277e5 16776a191ac0640aa7c7dc1cc06c5e1fa3cd45450f82069ac2bb524476b9a4d1 ac3fe653cced38cd3faa3ab4fdc2e01667cb0bb1353ab5f12505f148eb603fd7 15abadf2cf0fe8a68dc6d5bb39205e589135f4086eeab8ec1cb1724138f0db98 25cb18c59340302c5105af6f9fbeb5ae107cd2e288a4ede1b412f7d5fa4fe7d8 8ac7bf1b5c0d45052f9032106b1ec80c7d0018260650870f7fb016a98267125c a2f65069b152aeaf6a4fd334bda7e7770cc33dcecb5db182d90819f9f563b1e6 1defafeebf3d1a2d7ee3be019b4f879aaf0570ae310851588b8d3e29bff0ad1e 2889e533f404b0987861d7751a496375f10cb9a98015d57c316418be4710410c 3a3125e021e201e2ad01cee609409a06975001b543791c922fe60fca8987344b 14ca7ac266db5c3f0cbe203a89faea3398ee2a07403a50941ea92f972e678b53 1a2631e67d7756adcb8fd9d36f12ef8466cc0158632e987ad0ee3ee4a83f8d9c 5722e43a70fa1b65e1812ece8368924401f6bfc2f7e25ad032666ab364dfc6ce a0214b9423be11c165b6adef90ee172b93b3804d1ebb874c0bea37b6a83e80f2 aacf8dcbd745906dcba2086ac29271c57638d217a003beda81f1319ff8facff3 a4b57bf1d79446f72705058ddab5913dc05bf2139efd682416e5d9112a328211 9c11b306f01f2b211217f8617593e9d1f6a77c657a64ef19df535d2e8cc30b81 ae43cef766ba0808871a541741883573da1273d8897308b560d1b87dc5c0fba7 a265041bbb8028567c5b1674927b9b45bafa4a1241328aa21b99f3b87a39698f 508979202924e76d6e549f4b13f4122242e0519cbd6e6fb98da54921f886dc30 b5cc090b7a77eae8866c57e543a2ceb4537de00c327ef025781c2bfcc654a940 934d2515da059286a0b35c4639791ad74b0376979596a4cdb523655ce94e5e65 55c80ecbbe34eb41738c4637e8cbd5b656520516401788dbc136f3033645792b 7ec54808e8d8fa2a9c044ce9a61573ea1c6eb7b01a39e0933fdced27a52bf6b5 42cb378a770b063219fbd305f63dd006ad3bc406967e51588356ede72c4a4d10 a7c2291e94cbd6adb33647e81e2c0f2892f66a7dfcc5164e1f40ca50fbd72c16 4262ba4a22258f8cbbf315701736a6ff696b9206bb05fd85534b0cc1f91db4b3 9226ce66a9a7e2d3d26584018dadb04d462405dfd34182905c2cafd833f06f57 eed56f4896a452b4d74436497141f13b5e1f742f1d2ae467e28d37467019a29f acc7c54052888e28330147b68951bee8da395c9441de4e0a74a2c60bc8e931b7 130339672f0630adc462642bc9f516859a40c92e7a7298cec345e62fc9d9b79e d34ec4c21d81e1b73df628d6f9429e928db06716730a702a045c1f8d8e224ead 3fc8ebbc2285da9175732bc83d570eb1a2d42b3a05487954006ae813b0998784 8a626dcdaad74eeb9aeca6e5492c720adbe281d4e925559d0f2f1b475846d7ff 628185f28fc84bf1d68d21f63e91126979f32411c4902203a262d43417928205 2ab2430e886609046fd7f876dba3558348200f07246f86654c019d12c926f8bd 7cf2f5883e1fa9a9eef2665c95053a42460e221455520d947be7e1a73ce77f77 506bfe20f08f0ea8af0271115f45985979be39065900b9f15bb5183c5bba02ae e002dae0faea51e7a323db1afa7d2a3b7b7ed93e6cdeb7e5c48f01e29e630b3c 2724eeded01b6fc74423cbea86b4037fe312fced0d5b5ad9e6c0e75d27c9dd3b ff10d470072a99021b9f1132a35aaaae587d92dbd18e8126b15e9b5669f4e696 9745f3af17bb2e0ba7eb1b92c06f97347a958a481e9863d2b436a97f3a166957 bbc24f9adcc2af310593c6d23ca5898ad1d84095d540c8ce0fb9c8a2a328667f 9966fe42c60b9ee51a24266dc013462f31e8556f13895c0449ac34071199d9cc 01d754441769d980cd63bd56d8c143df1506d97d8651652cdd1192459d1a6023 a0c57616184f8235f3889a39927d112118e7e0549b3e1e83df5ac426fbd1984d 61fdfad0 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 600 600 (tensor.dvi) @start %DVIPSBitmapFont: Fa cmex8 8 6 /Fa 6 113 df2 DI<92380FFF8092B512F8020714FF 021F15C0027F15F0902701FFF8F813FC490180EB0FFE902607FC00EB01FFD91FF0913800 7FC0D93FC0ED1FE049486F7E49C76E7ED801FCEE01FC4916004848177E484883A24848EF 1F8049170F001F19C090C815074819E0003E1803007E19F0007C1801A300FC19F8481800 A2BBFCA500F8C800F8C8FCA36C1801007C19F0A3007E1803003E19E0003F18076C19C06D 170F000F19806D171F6C6CEF3F00A26C6C177E6C6C5F6D16016CB4EE07F86D6C4B5A6D6C 4B5AD91FF0ED7FC0D907FC4A48C7FC902603FF80EB0FFE6D01F8EBFFFC6D6CB612F0021F 15C0020792C8FC020014F8030F138045427C7F4E>76 D80 D<143014FCEB03FF010F13C0013F 13F090387F03F83901FC00FED807E0EB1F80D81F80EB07E0007EC7EA01F800F0EC003C00 C0150C260C80B027>98 D<19031907190F190E191E191C193C19381978197019F019E018 0119C0180319801807190060180E181E181C183C18381878187018F06017016017036017 0795C7FC5F170E171E171C173C5F0140157001E015F000015ED807F01401000F5E001F15 03D871F85D00E11507D840FC92C8FC00005D017E140E161E6D141C163C6D6C1338167816 706D6C13F05E903807E0015E903803F0035E903801F80793C9FC5D903800FC0E151EEC7E 1C153CEC3F3815786E5AA26E5AA25D14075D14034050788247>112 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb eufm8 8 1 /Fb 1 104 df<903801800C903807F03890381FFEF8EB7FFF90B5FCD803E713F0EA07E0 1403EBC001120F1403ADEBE0079038F01FF8EBF83BEBFCF33807FFC16CEB81FC1401EA01 FCEA00F813709038E000F8D8038013F0486C13E0487E391FF001C0D87FFC138039EFFF07 00000713FE00015B6C6C5AEB1FF0EB00801E2D7F9E23>103 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc msam6 6 1 /Fc 1 3 df2 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd msam8 8 1 /Fd 1 3 df2 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe msbm8 8 6 /Fe 6 124 df<91390FFC018091B5FC903903FC07E390390F7001FF90393CE0007FD9F1 C013392601C380131DD80383C7120D4848140FD80E061407D80C0E1403EA1C0C00381501 EA301C13181270006092C7FC1338EAE03012C0AA12E0EA6038131812701230A2EA381CEA 1C0CD80C0E1570D80E0615F0D80707EC01E026038380EB03C0D801C114072600F1E0EB0F 00D93C70133E90390F3E01FC0103B512F0010014C0DA0FFEC7FC2C307EAE21>67 D78 D82 D<001FB612FCA23A183E00701801F0EB6038D81BC0EBE030001FC7EAC070003E010113E0 003C90380380C01501003801071380EC0603003090380E0700EC1C06EC180EC7EA380CEC 301CEC7038ECE030ECC07001015B4A5AEB03819038070180EB0603D90E07C7FCEB0C06EB 1C0EEB380CEB301CD970381303EBE030EBC070000101601307EB80E0260381C013062607 0180130ED80603141E000E90C7FCD80C07143ED81C0E1476D8380C14E6D8301CEB01CED8 7018EB078CD86038EB3E0CB712FCA2282E7EAD38>90 D<95261FFFF01D70051FB66CF303 F00407B700F01B3F93B800FC973803FFE0030F91C7D80FFF083F130092B50080020001C0 953803FFF0021F01F0C9D81FF0063F90C7FCDAFFFECAD803FC943807FFF0010F01C09426 00FF8093B51280D9FFFCCCD83FF0031F01F0C8FC000F01C0DF0FFF020FB5C9FCD87FFCCD 000390B712F0D8FFC008004CCAFC00FCCF001F158000E00A000280CBFCA40F80BBA5>94 D123 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmsy6 6 9 /Ff 9 96 df0 D<0060143000E014706C14F00078EB01E06CEB 03C06CEB07806CEB0F003807801E6C6C5A6C6C5A6C6C5AEB79E0EB3FC06D5A6DC7FC497E 497EEB79E0EBF0F03801E07848487E48487E48487E001EEB078048EB03C048EB01E048EB 00F0481470006014301C1D779A30>2 D<136013701360A20040132000E0137038F861F0 387E67E0381FFF803807FE00EA00F0EA07FE381FFF80387E67E038F861F038E060700040 132000001300A21370136014157B9620>I<14301438B1B712FCA3C70038C7FCAFB712FC A326277CA430>6 D 24 D<01FEEC0FE02603FFC0EB3FF8000F01F0EBFE3E3B1F0FF801F0073C3C01FC07C003 803B3000FE0F00010070D93F1EEB00C00060EB1F9C00E0D90FF81460485C14076E7E6E7E 81020315E00060D9073F14C091390F1F80016C90261E0FE01380003890397C07F0073C1C 01F003FE1F003B0F8FE001FFFE3B03FF80007FF8C648C7EA0FE033177C953D>49 D67 D<157CEC03FEEC0FFF5CEC787F4A7EEB01E00103133E903807C03CEC8010010F90C7FC49 C8FCA25B133EA25BA213FCA25BA212015BA212035B1620484814E015033A0FFF8007C002 FC13804890B512004814FCD8700F5B39C0007FC023247DA22B>76 D<00E0140315076C140F0070140E0078141E0038141C003C143C001C1438001E1478000E 1470000F14F06C14E0EB8001000314C0EBC00300011480EBE007000014006D5AEB700EEB 781EEB381CEB3C3CEB1C38EB1E78EB0E70EB0FF06D5AA26D5AA26D5A20207C9E2A>95 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmsy8 8 22 /Fg 22 117 df0 D<123C127E12FFA4127E123C08087A9414>I< EC3FF0903801FFFE903907C00F8090391E0001E00178EB007801E0141C48488048488048 6CEC0F80D80EE0EC1DC0D80C701438D81C38EC70E0D8181CECE060D8380E903801C070D8 300790380380303B700380070038276001C00E13186D6C5A00E0D97038131C486D48130C 6E5AEC0FC06E5A6EC7FC4A7E4A7EEC1CE0EC38706C496C131C0060496C131849487E2770 03800713383B300700038030D8380E903801C070D8181C903800E060D81C38EC70E0D80C 70EC38C0D80EE0141D6C48EC0F806C48EC07006C6C140E6C6C5C01781478011EEB01E090 3907C00F80902601FFFEC7FC9038003FF02E2F7CA737>10 D17 D<91B612C01307131FD97F80C8FC01FCC9 FCEA01F0EA03C0485A48CAFC121E121C123C123812781270A212F05AA97E1270A2127812 38123C121C121E7E6C7E6C7EEA01F0EA00FCEB7F80011FB612C0130713002A2B7AA537> 26 D<170EA3170F8384170384170184717E1878187C84180FF007C0BA12F819FC19F8CB EA07C0F00F00183E601878604D5A60170360170795C7FC5F170EA33E237CA147>33 D67 D<91383FFFF00107B6FC011F15E0017F 812701F83E0313FCD803C09038003FFED80F00EC07FF001E017E6D1380481500007CEE7F C00078163F48EE1FE048137CC7150FA202FC1407A25CA3010116C05CA2EF0F8013034A15 005F171E49485C177C177849485C4C5A4C5A49C7485A040EC7FC163C013E14F0ED03E001 3CEB0F80017C01FEC8FC90387FFFF848B512E04849C9FC4813E0332D7EAC37>I76 D<0378172003F81760020118E01A01A26FEE03C01A071A0F 0203171F1A3F037E167FF2FF80A2DA073EED01EFDA063FED03DFF1079FF10F1FDA0E1F15 1E020C6D023E1300197C19F84A6C6C49485A19E0F003C0DA3007EC078070EB0F00181E02 604B133E6F6C137C02E05D02C04A48137E6F6C485AD901804A5A70485A0103010049C7FC 91C7EAFE3E49EC7EFC0106EC7FF8010E6E5A010C5DD8301C6E5AD83C385DD87FF86EC8EA 7F0849020C16F8484891C913E01BC06C48F03E006C4895C7FC000FCEFC4D317FAD54>I< 0206EB3F8091391E01FFF0DA78077FDAF01F7F903A03C03C1FFE903A0700F003FF90391E 01E0014948486C1380494848137FD9F00F143FD801E090C713C00003011E141FEBC03E38 07803C000F017C140FEB00784813E0001E1380003E90C8FCA2007E1780127CA2171F00FC 1700A2171E173E173C177C6C16785F16016C5E6C4B5A6D4A5A4CC7FC6C6C141E6D5C6C6C 14706D495AD80FFEEB07802707FFC03FC8FC6CEBFFFC6C14F06C6C1380D90FF8C9FC322F 7CAD38>79 D<91383FFFFC0107B612C0011F15F0017F15FC2701F83E007FD803C0EC0FFF D80F001403001E017E0100138048167F007C163F127848017C141F5AC7160014FC171E17 3E4A143C177C177801015D4A495A4C5A4CC7FC0103141E4A137CED03F09138E1FFC0D907 E790C8FCECCFF8ECDF8002C0C9FC495AA349CAFCA3133EA2133C137CA25BA25B485A1380 31307EAC31>I<023FB57E0107B612F8011F15FE017F813A01F83E001FD803C002017FD8 0F00EC007F001E017E143F5A007C161F12784894C7FC48137CC7FC173E02FC143C177C4A 14785F4C5A01014A5A4A010FC8FC167EED1FF80103EB7FE09138E0FF8002E17FECE07F49 486C7E6F7E150F010F80EC80076F7E1400496D7EF00180013E6D6CEB07006093387F801E 49EDC03893383FE0F00178EDFFC001F86E5B01E06E48C7FC4848EC07F0392E7EAC3C>82 DI<181C183C0107B712F8011F16F090B812C0481700270780 007CC8FC48C712FC121E123E007E495A127C12FC12F048495AC7FCA34A5AA44A5AA44A5A A4143F92C9FCA4147EA3147C14FCA25C1301A25C13035CA2495A5C49CAFC130836347DAE 27>I86 D<141F14FFEB03F0EB0FC0 EB1F8014005B133EB3A2137E137C13FC485A485AEA7FC048C7FCEA7FC0EA03F06C7E6C7E 137C137E133EB3A2133F7F1480EB0FC0EB03F0EB00FF141F18437BB123>102 D<12FCB47EEA0FE0EA01F0EA00FC137C137E133EB3A37F1480130FEB07E0EB01FEEB007F EB01FEEB07E0EB0F80131F1400133EB3A3137E137C13FCEA01F0EA0FE0EAFF8000FCC7FC 18437BB123>I<13031307130F130EA2131E131C133C1338A21378137013F013E0A21201 13C01203138012071300A25A120E121E121CA2123C123812781270A212F05A7E1270A212 781238123C121CA2121E120E120F7EA21380120313C0120113E01200A213F01370137813 38A2133C131C131E130EA2130F1307130310437AB11B>I<12E0A27E1270A21278123812 3C121CA2121E120E120F7EA21380120313C0120113E01200A213F0137013781338A2133C 131C131E130EA2130F1307130F130EA2131E131C133C1338A21378137013F013E0A21201 13C01203138012071300A25A120E121E121CA2123C123812781270A212F05AA210437CB1 1B>I<12E0B3B3B3AD034378B114>I<00E0151CB3B3B712FCA27E26287CA72F>116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmbx8 8 14 /Fh 14 84 df48 DIII<15F814011403A2140714 0F141F143F147FA214F7EB01E7EB03C71307EB0F87EB1F07131E133C137813F01201EA03 E013C0EA0780EA0F00121E123E5A5AB712F0A4C7380FF800A7010FB512F0A4242C7EAB29 >I<00181438391FC003F890B5FC15F015E015C01580ECFE005C14E091C7FC90C8FCA5EB 1FF8EB7FFF90B512C09038F01FE09038C00FF090380007F8001E14FC001CEB03FEC7FCA2 15FFA2120C123FEA7F8012FF13C0A215FE13801407D87E0013FCEC0FF86C131F391FC07F F06CB512C06C14800001EBFC0038003FE0202D7CAB29>II<123C123F90B612E0A44815C0168016005D5D397C0001F80078495A00F8 495A485C140F4A5AC748C7FC147E5CA2495A13035C1307A2495AA2131FA3495AA4137FA9 6D5A6DC8FC232E7CAC29>III< B712E016FE707E17E0000190C77FEE3FF8161F707EA2707EA5160F5FA24C5A4C5AEEFFE0 0307138091B548C7FC707E17E091C7EA1FF8707E707E707E18808218C0A618805EA24C13 00EE1FFEEE7FFCB85A17E0178004FCC7FC322E7DAD3A>66 D 76 D81 D<90391FF8038090B512070003 14CF4814FF381FF00FEBC001393F80007F48C7123F007E141FA200FE140FA215077E7F6D 90C7FC13F06CB4FC14F0ECFF806C14E06C14F86C14FE6C806C1580C615C0131F010114E0 EB000F020013F0153F151F150F12F01507A37E16E06C140F6C15C06C141F01C0EB3F8001 FCEBFF0090B55A00F95CD8F03F13F0D8E003138024307CAE2D>83 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmti8 8 69 /Fi 69 128 df<92397F8007C0913A01FFE01FF0913A07E0787C78DA0F8013F891261F00 F813F8923801F9F1143EA2923900E3F0E04A903803E000A402FC13074A5CA4017FB71280 A2903B01F0000F8000A313034A131F94C7FCA401075C4A133EA4010F147E4A137CA4011F 14FC91C75AA4491301013E5CA3137E017C495AA3003890383807C038FCF8FC5E01F0130F 4BC8FC39F1E0F03E39F3C0707C397F803FF0391E000FC0353D81AE2C>11 DIII<127012F87EA27E127E7E7EEA0F80120713C01203EA01000A0D6CAD24>18 D<1338137C13FC1201EA03F8EA07E0EA0FC0EA1F80EA3E005A5A12E012400E0D69AD24> I<3807803C380FC07E381FE0FFEA3FE1A3EA1FE0000F137F3800C006A20001130EEB800C 0003131CEB0018481338000E13704813E0383801C03870038038E00700EAC006181574AD 25>34 D39 D44 D<387FFFC0A2B5FCA26C13 0012057A901A>I<121C127F12FFA412FE12380808788716>I<14031407140F141E143E14 7E14FEEB03FCEB1F7CEB7CFC1360EB00F8A21301A214F0A21303A214E0A21307A214C0A2 130FA21480A2131FA21400A25BA2133EA2137EA2137CA213FCB512F8A2182C79AB24>49 D<147F903801FFC0903807C1F090380F00F8011E137C13380178133E13F3EBE380D801E1 133F13C1120313810183137F0007EB007E5B1306010E13FE4913FC3903F801F83901E003 F0C7EA07E0EC0FC0EC1F80EC3F0014FC495AEB07E0EB0F80013EC7FC5BEA01F04848131C 4848133C49133848C7FC001E14784814F0383FC001397FFE03E00078B512C0EA703FD8F0 0F130038E003FEEB00F8202D7AAB24>II<13F0EA01F812031207A3EA03F0EA01C0C7FCAD121C127F5AA45A12 380D1D789C16>58 D<16E01501821503A21507150FA2151FA2153B157B157315E382EC01 C114031581EC0701A2140EA2141C143C143802707F15005C13015C49B5FCA249C7FCA213 0E131E131C4980167E5B13F0485AA21203D80FF014FFD8FFFC011F13F0A22C2F7CAE35> 65 D<011FB512FCEEFF80903A00FE000FC0EE03E04AEB01F017F80101140017FC5CA213 0317F84A1301A20107EC03F017E04AEB07C0EE0F80010FEC3F0016FE9138C007F891B512 E04914F89138C0007C4A7F82013F1580A291C7120FA25BA2017E141FA213FEEE3F005B16 7E00015D4B5A49495A4B5A0003EC3F80B600FEC7FC15F82E2D7BAC32>II<011FB512FCEEFF80903A00FE000FC0EE03E04A EB01F0EE00F80101157C173C4A143E171E0103151FA25CA21307A25CA2130FA24A143FA2 131F173E4A147EA2013F157C17FC91C8FC17F849EC01F0A2017EEC03E0A201FEEC07C0EE 0F8049EC1F00163E00015D5E49495AED07C00003023FC7FCB612FC15E0302D7BAC36>I< 011FB612FEA2903900FE0001EE007E4A143EA20101151E171C5CA21303A25C16E0010713 01170002E05B1503130F15074A485A91B5FC5BECC01F4A6CC7FCA2133FA2DA000E13E0A2 491401030013C0017E1403178001FE14071700495C161E12015E49147CED01FC0003EC0F F8B7FC5E2F2D7CAC30>I<011FB612F8A2903900FE000716014A13001778130117705CA2 1303A25C16E001071301170002E05B1503130F15074A485A91B5FC5BECC01F4A6CC7FCA2 133FA2EC000EA25B92C8FC137EA213FEA25BA21201A25BA21203B512F0A22D2D7CAC2E> I<03FF1318020FEBC03891393F00F07802F8EB38F8D903F0131CD907C0EB0FF0EB1F8049 C71207137E49EC03E0485A485AA2484815C0485AA2485A178048CAFCA25A127EA312FE5A A292B512E0A2923801FE006F5A15015EA3007C14035E127E123E001E1407001F5D6C6C13 0F6C6C133F6C6C13793A00F803F1C090383FFF80D907FCC8FC2D2F75AD37>I<903B1FFF F81FFFF8A2D900FEC7EAFE00A24A5CA2010114015F5CA2010314035F5CA2010714075F5C A2010F140F5F5C91B6FC5B9139C0001F805CA2013F143F94C7FC91C7FCA2495C167E137E A201FE14FE5E5BA2000114015E5BA200031403B500C0B512C0A2352D7BAC35>I<90381F FFF8A2903800FE00A25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2 133FA291C7FCA25BA2137EA213FEA25BA21201A25BA21203B512C0A21D2D7CAC1B>I<91 387FFFE0A2913800FE00A25DA214015DA314035DA314075DA3140F5DA3141F5DA3143F92 C7FCA35CA2147EA2003C13FE127E00FE5BA2495AEAFC0300F05B48485A38700FC0D8781F C8FCEA1FFCEA07F0232E7AAC25>I<90261FFFF8EBFFFEA2D900FEC7EA1FE018804AEC3E 005F01015DEE01E04A495AEE0F8001034AC7FC163C4A5B4B5A0107EB03C04B5A4A48C8FC 153E010F137E15FEECC1FF14C790381FCF3F02DE7FECFC1F02F87FEB3FE04A6C7E1480EC 000749801503017E80A201FE6D7EA2491300820001157E167F5B831203B539C007FFF8A2 372D7BAC37>I<90381FFFFEA2D900FEC7FCA25CA21301A25CA21303A25CA21307A25CA2 130FA25CA2131FA25CA2133FA291C7121CA249143C1638017E1478167001FE14F0A249EB 01E0A200011403ED07C049130FED3F80000314FFB7FC1600262D7BAC2D>III<4AB4FC020F13C091383E03F09138F8007CD903E07FD9 07807F011FC77E013E15804914074915C0485AEE03E0485A485AA2485A121F90C8FC5AA2 003E1507127EA348ED0FC0A3EE1F80A217005E163E167E167C16FC4B5A007C5D4B5A6C4A 5A4B5A6C4AC7FC6C6C133E6D13F83903E003F03901F80FC026007FFFC8FCEB0FF02B2F75 AD37>I<011FB512FCEEFF80903A00FE000FE0EE03F04AEB00F8A20101157CA25C177E13 0317FC5CA20107EC01F8A24AEB03F017E0010FEC07C0EE0F804AEB3F00ED01FC91B512F0 4991C7FC0280C8FCA3133F91C9FCA35B137EA313FE5BA312015BA21203B512C0A22F2D7C AC30>I<4AB4FC020F13C091383E03F09138F800FCD903E0133E49487F011FC7FC013EEC 0F804914074915C012014915E04848140312075B120F485AA248C8FC1607123E127EA348 ED0FC0A3EE1F80A21700485D163E167E6C157C16FC4B5A007C01F05B903903FC03E03A3E 070E07C0903906060F80271F0E071FC7FC390F0C033E018C13F8D803EC5B3901FE0FC03A 007FFF0018EB0FF7D90007133816301670ED80F0ED81E015C3EDFFC0A25E93C7FC6E5AEC 00F82B3B75AD37>I<011FB512E016FC903900FE003FEE0FC04AEB07E016030101EC01F0 A24A14F8A21303EE03F05CA20107EC07E017C04AEB0F80EE1F00010F143E16FC9138C007 F091B512805B9138C00FE091388003F06F7E133F6F7E91C7FCA2491301A2017E5CA201FE 1303A2495C17080001163C17384914E0EEF07800031670B5D8C00113E09238007FC0C9EA 1F002E2E7BAC34>I<91380FF00C91383FFC1C9138F80F3C903903C007BC9039078003FC 90390F0001F8131E491300A24914F0A313F816E0A216007F7F6D7EEB7FF8ECFF806D13E0 6D13F801077F01017FEB001FEC01FF6E7E8181A281121CA35D003C141EA25DA2007E5C5D 007F495A6D485A26F1F01FC7FC38E07FFC38C00FF0262F7BAD28>I<000FB712F0A23A1F E00FE00701001401001E02C013E0481500141F12380078EC8001A20070013F14C012F048 1400A25CC791C7FC147EA214FEA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2 131FA25CA2133F003FB57EA22C2D74AC33>I<3B3FFFF007FFF0A2D801FCC7EA7F00163C 5B16380003157816705BA2000715F05E5BA2000F14015E5BA2001F14035E5BA2003F1407 93C7FC90C7FCA2485C150E127EA2151E00FE141C5A153C153815781570007C5C1401007E 495A003E495A6C49C8FC6C133C3807C0F83801FFE06C6CC9FC2C2E72AC35>III89 D<010FB612C0A2903A1FF8003F8002C0 14004A5B49C712FE013E495A013C495A49495A5E0170130F01F0495A49495A4BC7FC15FE 90C75A14014A5A4A5A4A5A4A5A5D143F4AC8FC14FE495A495A5C49481370130F494813F0 49485B49C7FC017E1301495C00011403485A4848495A485A49130F4848131F003F027FC7 FC397F0003FFB7FC5D2A2D7AAC2C>I92 D97 D<13F8121FA21201A25BA21203A25BA21207A25BA2120FEBC7C0EB9FF0EBF878381F F03CEBE03EEBC01EEB801FEA3F00A2123EA2007E133FA2127CA2147F00FC137E5AA214FC A214F8130114F0EB03E0EA780714C0383C0F80381E3E00EA0FF8EA03E0182F78AD21>I< EB01F8EB0FFE90383E0780EBFC03D801F013C03803E0070007130FEA0FC001801380121F 48C8FCA25A127EA312FE5AA5EC0180007CEB03C0EC0780EC0F006C131E001E137C380F83 F03807FFC0C648C7FC1A1F799D21>I<153EEC07FEA2EC007EA2157CA215FCA215F8A214 01A215F0A21403EB07C390381FF3E0EB7C3BEBF81FEA01F03903E00FC0EA07C0120FEA1F 801580EA3F00141F5A007E1400A25C12FE48133EA2EC7E18153848137CA214FCD8780113 78397C03F870A2393C0F78E0381E1E3D390FF81FC03903E00F001F2F79AD24>III<14F8EB03FE90380F873890381F03F8137EEB7C0113F81201EA03F0 15F0EA07E01403120F01C013E0A21407121F018013C0A2140FA21580141F120F143FEC7F 006C6C5AEA03C33801FFBF38007E3E1300147EA2147CA214FC00385BEAFC015C495A4848 5A38F01F80D87FFEC7FCEA1FF01D2C7C9D21>I<131FEA03FFA2EA003FA2133EA2137EA2 137CA213FCA25BA21201147E9038F3FF809038F787C03903FE03E013FC13F8A2EA07F013 E0A213C0000F130715C01380A2001F130F15801300141F481406150E003E133F143E007E 141EEC7E1C007C137CEC3C3812FC157048EB1FE00070EB07801F2F7BAD24>I<130E131F EB3F80A2EB1F00130E90C7FCA9EA03E0EA0FF0EA1E78EA1C7C12381278127013FCEAF0F8 12E012E1EAC1F0120112035B12075BA2120F13831387121F13075BEA3F0E123EEA1E1C13 3C1338EA0FF0EA03C0112E7AAC16>II<131FEA03FFA2EA003FA2133EA2137EA2137CA213 FCA25BA21201EC01E09038F007F0EC1E380003EB3878EC71F8EBE0E1EBE1C13807E381EC 00E049130013CEEA0FFC13F0A213FF381F9FC0EB87E0EB03F01301003F14301570123EA2 007E14F015E0007C13E014E100FC14C0903800F38048EB7F000070131E1D2F7BAD21>I< 137CEA0FFCA21200A213F8A21201A213F0A21203A213E0A21207A213C0A2120FA21380A2 121FA21300A25AA2123EA2127EA2127CA2EAFC30137012F8A213F013E012F012F113C012 FBEA7F80EA1E000E2F7AAD12>I<3B07801FC007F03B1FE07FF01FFC3B3DF1E0F8783E3B 38F3C078F01E3B78FF007DC01FD870FEEB7F80A2D8F1FC1400D8E1F8137EA249137C00C3 02FC5B0003163E495BA200070101147E177C01C05B17FC000F0103ECF83018700180EBE0 0117F0001F010715F0040313E0010001C013E0EFE1C048010F1301EFE380003E91398000 FF00001C6DC7123C341F7A9D3A>I<3907801FC0391FE07FF0393DF1E0F83938F3C07839 78FF007CEA70FEA2EAF1FCEAE1F8A25B00C314FC00035C5BA2000713015D13C01403000F ECE0C015E1EB800715C1001F14C3020F13800100138391380787005A158E003EEB03FC00 1CEB00F0221F7A9D28>II<90383C01 F09038FF07FC3901E79E1E9038C7BC0F000301F81380903887F00702E013C038078FC013 0F1480A2D8061F130F12001400A249131F1680133EA2017EEB3F00A2017C133E157E01FC 137C5DEBFE015D486C485AEC0F80D9F3FEC7FCEBF0F8000390C8FCA25BA21207A25BA212 0FA2EAFFFCA2222B7F9D24>I<903807C06090381FF0E0EB7C39EBF81FEA01F03903E00F C0EA07C0120FEA1F801580EA3F00A248131F007E1400A300FE5B48133EA3147E48137CA2 14FCEA7801387C03F8A2EA3C0FEA1E1F380FF9F0EA03E1EA000113035CA313075CA2130F A23801FFFCA21B2B799D21>I<3807803E391FE0FF80393CF3C1C03938F781E03878FF07 EA70FE13FC12F139E1F8038091C7FC5B12C312035BA21207A25BA2120FA25BA2121FA290 C8FCA25AA2123E121C1B1F7A9D1E>II< 131C133EA2137EA2137CA213FCA25BA21201A2B512E0A23803F000A25BA21207A25BA212 0FA25BA2121FA290C7FCA24813C01301123E130314801307003C1300130E131E6C5AEA0F F0EA07C0132B7AA918>II<3903C001C0390FF003E0391E7807F0EA1C7C123800781303007013 0113FCD8F0F813E012E000E1130038C1F001000114C0120313E014030007148013C0A2EC 0700120F1380140EA25C12076D5A00035B6D5AC6B45A013FC7FC1C1F7A9D21>II<90383E01F090 38FF87F83903C7DE1E380783DC903803F87EEA0E01001E13F0EA1C03003C14380038EBE0 00A2EA300700005BA3130F5CA3011F1318153814001238D87C3F137012FC15E0EB7F0139 F0FF03C03970E78780393FC3FE00381F00F81F1F7C9D21>II<010F13E0EB3F80EBFFC1ECE3C048EBF3803803E0FF 9038C03F00EB801E00075BC7123814785C495A495A495A49C7FC131E5B5B9038F0018038 01E003EA03C038078007390F000F00EA1FE0EBF83E383C7FFE486C5A38701FF838F00FF0 38E007C01B1F7C9D1D>II<381C01C0387F07F0EAFF0FA400FE13E0 3838038014086EAD24>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmtt8 7 3 /Fj 3 111 df<1370EA01FCA5EA007090C7FCA5EA7FF8487EA2127FEA007CB1387FFFFC B5FCA27E16257CA41F>105 D<127F487EA2127F1207A7903883FFC0018713E0A2018313 C0903880FC00EB81F8EB83F0EB87E0EB8FC0EB9F8001BFC7FCEBFF80808013F3EBE1F0EB C1F8EB80FC147C80143F397FF87FE039FFFCFFF0A2397FF87FE01C247FA31F>107 D<387F83F838FFCFFC90B5FC7E3907FE1F8013F8EBF00F13E0A213C0AC397FFC3FF839FF FE7FFCA2397FFC3FF81E1980981F>110 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk eufm7 7 1 /Fk 1 104 df<0107134090381FC1C0EB7FFF48B51280EA03BFEA0F83EB800F381F0007 140FACEB801FEBC07F9038E0EFC0EBF38F380FFF07EA07FCD803F813E0EA01F013C03903 8003C0D807001380D81F801300383FC006387FF00438FFFC18380FFFF06C5B00015B6C6C 5A1B277D9A23>103 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmbxti10 10 6 /Fl 6 116 df101 D<143C147F495A15805B1500A25C6D5AEB007091C7FCAB133FEBFFC000037F3807C7F038 0F87F8EA1F07A2EA3E0FA2127C131F5C12FCEAF83F00005B137F5CA213FF5CA25A91C7FC 5A5BEC0F801207EBFC1F1500120F495A143E5C13F000075BEBF1F06CB45AC65B013EC7FC 193C79BA1E>105 D 108 DI<90390F C003FC903A3FF00FFF8090267FFC3F13E0903A7DFEFE0FF0903AF8FFF807F800019138F0 03FC4913C001F115FED803E113801500A2EA07E313C35CEA000301071407A25CA2010F14 0F17FC5CA2011F141F17F85CEE3FF0133F17E04AEB7FC0A2017FECFF806E4813004B5A6E 485A9039FFFC0FF091B512C0029F90C7FCEC87F8480180C8FCA291C9FCA25AA25BA21207 A25B387FFFE0B57EA25C2F367EA531>112 D115 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmmi8 8 49 /Fm 49 127 df11 D<131FD9FFC013304801F0137000076D13604815 E0D9807C13C0391E003C0148011E13800038EB0E03480107130000605CEC030612E0C713 8EEC018C159C159815B815B0A215F05DA35DA25DA21403A44AC7FCA4140EA45CA3141824 2C7F9D24>13 DI<1460A5EC7FF0EC3FF814FF903803CF E0903807800049C7FC131E5B5B5BA2485A485AA2485A48C8FCA25A121E123E123CA3127C 1278A412F8A4127CA2127E127F6C7E13E0EA1FFC6CB47E6C13F000017F38003FFCEB07FE 1300143F80A280141EA2EB601CEB7838EB1FF0EB07C01D3C7DAD1F>16 D<147C49B4FC903803C78090380783C090381F03E0EB1E01133E017C13F013F8A2EA01F0 120313E01207A2EA0FC01403A2EA1F80A21407003F14E0130090B5FCA2397F000FC0127E A2141F1580127C00FC14005CA2147EA248137C14FC00785B495AA2387C03E0383C07C049 5A001C90C7FCEA1E3EEA0FF8EA03E01C307DAE21>18 D<13FC13FFEB1FC0130F6D7EA36D 7EA2130180A26D7EA3147EA280A36E7EA2140F81A24A7E143F147FECF3F0EB01E3EB03C1 90380781F8130F49C67E133E5B49137E485A48487F1207485A4848EB1F8048C7FC127E48 EC0FC048EC07E000701403232F7DAD29>21 D<90B612F812035A4815F03A1E0380C00000 3C130000701301130700E05CEAC00638000E03A3131CA2133C140713381378A201F07FA2 1201A2D803E07FA20007130313C0A26C486C5A251E7E9C29>25 DI<0103B512F0 131F137F90B612E03A01FC1F80003903F00FC03807C00748486C7E121F1300123EA25AA2 140700FC5C5AA2140F5D141F92C7FC143E0078133C147C007C5B383C01E0381F07C0D807 FFC8FCEA01F8241E7D9C28>I<90B6128012035A481500261E00E0C7FC5A00705B130112 E012C0EA0003A25CA21307A349C8FCA35BA2131E133EA45BA21338211E7E9C1F>I34 D<123C127E12FFA4127E123C08087A8714>58 D<123C127EB4FCA21380A2127F123D1201A312031300A25A1206120E5A5A5A126009157A 8714>I<15C0140114031580A214071500A25C140EA2141E141CA2143C143814781470A2 14F05CA213015CA213035C130791C7FCA25B130EA2131E131CA2133C1338A21378137013 F05BA212015BA212035BA2120790C8FC5A120EA2121E121CA2123C1238A212781270A212 F05AA21A437CB123>61 D<1670A216F01501A24B7EA21507150DA2151915391531ED61FC 156015C0EC0180A2EC03005C14064A7F167E5C5CA25C14E05C4948137F91B6FC5B0106C7 123FA25B131C1318491580161F5B5B120112031207000FED3FC0D8FFF8903807FFFEA22F 2F7DAE35>65 D<013FB6FC17C0903A00FE0007F0EE01F84AEB00FC177E1301177F5CA213 03177E4A14FEA20107EC01FC17F84AEB03F0EE07E0010FEC1FC0EE7F009138C003FC91B5 5A4914FE9139C0003F804AEB0FC017E0013F140717F091C7FC16035BA2017E1407A201FE 15E0160F4915C0161F0001ED3F80EE7F004914FEED03F80003EC0FF0B712C003FCC7FC30 2D7CAC35>I<92387FC003913903FFF80791391FC03E0F91397E00071FD901F8EB03BF49 48EB01FED90FC013004948147E49C8FC017E157C49153C485A120348481538485AA2485A 173048481500A2127F90CAFCA35A5AA5EE018016031700A2007E5D1606160E6C5D5E6C6C 5C000F5D6C6C495A6C6CEB0780D801F8011EC7FCD8007E13F890381FFFE0010390C8FC30 2F7CAD32>I<013FB512FEEEFFC0903A00FE0007F0EE01F84AEB007E8301018118804A14 0F18C00103150718E05CA21307A25CA2130FA24A140FA2131F18C04A141FA2013F168017 3F91C81300A249157EA2017E5D5F01FE14014C5A494A5A4C5A00014BC7FC163E4914FCED 03F00003EC1FC0B7C8FC15F8332D7CAC3A>I<013FB71280A2D900FEC7127F170F4A1407 A20101150318005CA21303A25C16300107147094C7FC4A136016E0130F15019138C007C0 91B5FC5BECC0074A6C5AA2133FA20200EB000CA249151C92C71218017E1538173001FE15 705F5B4C5A000115034C5A49140F161F00034AB4C7FCB8FC5E312D7DAC34>I<92387FC0 03913903FFF80791391FC03E0F91397E00071FD901F8EB03BF4948EB01FED90FC0130049 48147E49C8FC017E157C49153C485A120348481538485AA2485A173048481500A2127F90 CAFCA35A5AA292381FFFFCA29238003FC0EE1F80163F1700A2127E5E167E7EA26C6C14FE 000F4A5A6C7E6C6C1307D801F8EB1E3CD8007EEBFC3890391FFFE018010390C8FC302F7C AD37>71 D<90273FFFFC0FB5FCA2D900FEC7EA3F80A24A1500A201015D177E5CA2010315 FE5F5CA2010714015F5CA2010F14035F5C91B6FC5B9139C00007E05CA2013F140F5F91C7 FCA249141F5F137EA201FE143F94C7FC5BA200015D167E5BA2000315FEB539E03FFFF8A2 382D7CAC3A>I<90263FFFFC90381FFF80A2D900FEC73803F80018E04AEC07804DC7FC01 01151C5F4A14E04C5A01034A5A040EC8FC4A5B5E010714E04B5A9138E00780030EC9FC01 0F131F157F4A487E14C190391FC71FC014CEEC9C0F02F07F90383FE00702C07FEC000382 5B6F7E137E6F7E13FE167F5B707E1201161F4981831203B539E001FFFEA2392D7CAC3C> 75 D77 DI<013FB6FC17E0903A00FE0007F0EE01FC4AEB007EA2010181A25C1880 010316005F5CA2010715FEA24A5C4C5A010F4A5A4C5A4AEB1F8004FFC7FC91B512F84914 C00280C9FCA3133F91CAFCA35B137EA313FE5BA312015BA21203B512E0A2312D7DAC2D> 80 D<013FB512F816FF903A00FE001FC0EE07E04A6D7E707E01016E7EA24A80A213034C 5A5CA201074A5A5F4A495A4C5A010F4A5A047EC7FC9138C003F891B512E04991C8FC9138 C007C04A6C7E6F7E013F80150091C77EA2491301A2017E5CA201FE1303A25BA20001EE03 8018005B5F0003913801FC0EB5D8E000133CEE7FF0C9EA0FC0312E7CAC35>82 D<913807F00691383FFE0E9138F80F9E903903E001FE903807800049C7127C131E49143C A2491438A313F81630A26D1400A27FEB7F8014F86DB47E15F06D13FC01077F01007F141F 02011380EC003F151F150FA215071218A3150F00381500A2151EA2007C5C007E5C007F5C 397B8003E039F1F00F8026E07FFEC7FC38C00FF0272F7CAD2B>I<000FB8FCA23B1FC003 F8003F0100151F001C4A130E123C003801071406123000704A130EA20060010F140C12E0 485CA2141FC715005DA2143FA292C8FCA25CA2147EA214FEA25CA21301A25CA21303A25C A21307A25C130F131F001FB512F0A2302D7FAC29>I<3B7FFFF801FFFEA2D801FCC7EA0F C0178049EC070016060003150E160C5BA20007151C16185BA2000F153816305BA2001F15 7016605BA2003F15E05E90C8FCA24814015E127EA2150300FE92C7FC5A5D1506150E007C 5C151815386C5C5D6CEB03C0260F800FC8FC3803E03C3801FFF038003FC02F2E7BAC30> III<0107B612F8A2903A0FFC0007F002E0EB0FE00280EB1FC049C71380011E143F 011CEC7F004914FE4B5A0130495A0170495A0160495A4B5A4B5A90C748C7FCA215FE4A5A 4A5A4A5A4A5A4A5A4A5A4AC8FC14FE5C130149481306495A4948130E4948130C495A49C7 121C01FE141848481438485A5E484814F048481301484813034848495A48C7127FB7FC5E 2D2D7CAC30>90 D 97 D99 D<151FEC03FFA2EC003FA2153EA2157EA215 7CA215FCA215F8A21401EB07E190381FF9F0EB7C1DEBF80FEA01F03903E007E0EA07C012 0FEA1F8015C0EA3F00140F5A007E1480A2141F12FE481400A2EC3F021506143E5AEC7E0E 007CEBFE0C14FC0101131C393E07BE18391F0E1E38390FFC0FF03903F003C0202F7DAD24 >II<157C4AB4FC91 3807C380EC0F87150FEC1F1FA391383E0E0092C7FCA3147E147CA414FC90383FFFF8A2D9 00F8C7FCA313015CA413035CA413075CA5130F5CA4131F91C8FCA4133EA3EA383C12FC5B A25B12F0EAE1E0EA7FC0001FC9FC213D7CAE22>I<14FCEB03FF90380F839C90381F01BC 013E13FCEB7C005B1201485A15F8485A1401120F01C013F0A21403121F018013E0A21407 A215C0A2000F130F141F0007EB3F80EBC07F3803E1FF3800FF9F90383E1F0013005CA214 3EA2147E0038137C00FC13FC5C495A38F807E038F00F80D87FFEC7FCEA1FF81E2C7E9D22 >I<131FEA03FFA2EA003FA2133EA2137EA2137CA213FCA25BA21201143F9038F1FFC090 38F3C1F03803FF0001FC7F5BA2485A5BA25B000F13015D1380A2001F13035D1300140748 ECC04016C0003E130F1580007E148191381F0180007C1403ED070000FCEB0F06151E48EB 07F80070EB01E0222F7DAD29>I<1307EB0F80EB1FC0A2EB0F80EB070090C7FCA9EA01E0 EA07F8EA0E3CEA1C3E123812301270EA607EEAE07C12C013FC485A120012015B12035BA2 1207EBC04014C0120F13801381381F01801303EB0700EA0F06131EEA07F8EA01F0122E7E AC18>I<131FEA03FFA2EA003FA2133EA2137EA2137CA213FCA25BA2120115F89038F003 FCEC0F0E0003EB1C1EEC387EEBE07014E03807E1C09038E3803849C7FC13CEEA0FDC13F8 A2EBFF80381F9FE0EB83F0EB01F81300481404150C123EA2007E141C1518007CEBF038EC F83000FC1470EC78E048EB3FC00070EB0F801F2F7DAD25>107 D<27078007F0137E3C1F E01FFC03FF803C18F0781F0783E03B3878E00F1E01263079C001B87F26707F8013B00060 010013F001FE14E000E015C0485A4914800081021F130300015F491400A200034A130760 49133E170F0007027EEC8080188149017C131F1801000F02FCEB3F03053E130049495C18 0E001F0101EC1E0C183C010049EB0FF0000E6D48EB03E0391F7E9D3E>109 D<3907C007E0391FE03FF83918F8783E393879E01E39307B801F38707F00126013FEEAE0 FC12C05B00815C0001143E5BA20003147E157C5B15FC0007ECF8081618EBC00115F0000F 1538913803E0300180147016E0001F010113C015E390C7EAFF00000E143E251F7E9D2B> I<90387C01F89038FE07FE3901CF8E0F3A03879C0780D907B813C0000713F000069038E0 03E0EB0FC0000E1380120CA2D8081F130712001400A249130F16C0133EA2017EEB1F80A2 017C14005D01FC133E5D15FC6D485A3901FF03E09038FB87C0D9F1FFC7FCEBF0FC000390 C8FCA25BA21207A25BA2120FA2EAFFFCA2232B829D24>112 D<903807E03090381FF870 90387C1CF0EBF80D3801F00F3903E007E0EA07C0000F1303381F800715C0EA3F00A24813 0F007E1480A300FE131F481400A35C143E5A147E007C13FE5C1301EA3E07EA1F0E380FFC F8EA03F0C7FC13015CA313035CA21307A2EBFFFEA21C2B7D9D20>I<3807C01F390FF07F C0391CF8E0E0383879C138307B8738707F07EA607E13FC00E0EB03804848C7FCA2128112 015BA21203A25BA21207A25BA2120FA25BA2121FA290C8FC120E1B1F7E9D20>II<130E131FA25BA2133EA2137EA2137CA2 13FCA2B512F8A23801F800A25BA21203A25BA21207A25BA2120FA25BA2001F1310143013 001470146014E0381E01C0EB0380381F0700EA0F0EEA07FCEA01F0152B7EA919>I<15C0 EC01E0140015F01570007FB512FCB6FC7EC7EA01F0EC03E0EC0780150014061E0D74AE23 >126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmmi6 6 18 /Fn 18 114 df21 D<127812FCA212FEA2127E1206 A3120CA2121C121812301260124007107A8513>59 D<140C141C143C1438A21478147014 F014E0130114C0A21303148013071400A25B130E131E131CA2133C13381378137013F05B A212015B12035BA2120790C7FC5A120EA2121E121C123C123812781270A212F05AA21631 7CA420>61 D<151815381578157C15FC1401A2EC037C14071406EC0C7EEC1C3E14181430 A21460ECC03FA249487EEB0300A213065B010FB512805B903838000F13305B13E05B4848 14C00003140790C7FCD80F80130FD8FFE0EBFFFE16FC27247DA32E>65 D<90B6FC16E0903907C003F8ED00FC4948133E161E161FEE0F8049C7FCA317C0133EA449 1580161FA21700495CA2163E5E485A5E4B5A4B5A4848495A4B5A033EC7FC0007EB01F8B6 12E092C8FC2A227CA132>68 D83 D85 DI<3CFF FC01FFF007FF5C270FC0003FC712F849166018C07F00074AEB018003DF13031800DA019F 13061403031F5B0206141CEE80189026E00C0F5B0003131C02185C023014E05F0260EB81 8014E002C00183C7FCD9E18013C601F11307D9F30013CCEA01F701F614D801FC14F0A249 5C5B5E495C15036C4891C8FC38237CA139>I<131FEBFF8C3801E0DE3803807E3807007C 48133C121E123E003C5B127CA3485BA215401560903801E0C012781303393807E180391C 1CF300380FF87F3807E03C1B177E9522>97 D101 D<140FEC3FC0EC71E014E3A2010113C0EC E180ECE000495AA5495AA2EBFFFEA2EB0780A249C7FCA5131EA65BA55BA31370A2EA38F0 EA78E012F8EAF9C0EA7180007FC8FC121E1B2F7CA31E>II<1338137CA2137813701300A7EA0780EA1FC0EA38E01230EA60F0EAC1E0A3 EA03C0A3EA0780A2EA0F0013041306EA1E0CA21318121CEA1E70EA0FE0EA07800F237DA1 16>105 D<1418143C147CA214381400A7EB0780EB1FE01338EB60F013C0A2EA0180A238 0001E0A4EB03C0A4EB0780A4EB0F00A4131EA21238EA783CEAF8381378EA70F0EA7FC000 1FC7FC162D81A119>I<13F8EA0FF0A21200A2485AA4485AA43807801E147FEB81C3EB83 87380F060F495A1318EB700E4848C7FCA213FCEA1E7EEA3C0F80EB0781158039780F0300 A21402EB070600F0138CEB03F8386000F019247CA221>I<000F13FC381FC3FF3931C707 803861EC0301F813C0EAC1F0A213E03903C00780A3EC0F00EA0780A2EC1E041506D80F00 130C143C15181538001EEB1C70EC1FE0000CEB07801F177D9526>110 D113 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmr8 8 91 /Fo 91 128 df0 D<156015F0A24A7E4A7EA24A7E1406EC0E7F14 0C91381C3F8014184A6C7E150F02607F150702C07F1503D901807F1501D903007F496D7E 1306010E147F130C011C6E7E131801386E7E1330496E7E160749811603484881160148C8 7F486F7E1206000E167F120C001CEE3F801218003FB812C0A24817E0A2B912F0342F7DAE 3B>II10 D<9138FF807E01079038E1 FF80903A1F807FC3C0D93E00EB87E049EBFF074913FE485A00039138FC018049017CC7FC AAB712FCA22703E0007CC7FCB3A6486C13FE3A7FFF0FFFF0A22B2F7FAE29>I<14FF0107 13E090381F80F090383E003849137C4913FC485A1203491378153092C7FCA7157CB612FC A23803E000157CB3A5486C13FE3A7FFF0FFFE0A2232F7FAE27>II<91397F800FF0903A03FFE07FFE903A1FC079F80F903B3E001F E003804990393FC007C04990387F800F48481400A24848017EEB0780033EEB030094C7FC A7EF07C0B9FCA23B03E0003E000F1707B3A5486C017FEB0FE03C7FFF07FFF0FFFEA2372F 7FAE3B>I<13E0EA01F01203A2EA07E0EA0FC0EA1F00121E5A5A12E012400C0C72AD23> 19 D<123C127E12FFA7127EA9123CAA1218A41200A7123C127E12FFA4127E123C082F7A AE14>33 D<003C13F0387E01F838FF03FCA2EB83FEA2EA7F81383D80F600011306A30003 130EEB000CA248131C00061318000E13384813704813E0387001C00060138017157EAD23 >I38 D<123C127EB4FCA21380A2127F123D1201A312031300A25A1206120E5A5A5A126009157A AD14>I<13031307130E131C1338137013F0EA01E013C01203EA0780A2EA0F00A2121EA3 5AA45AA512F8A25AAB7EA21278A57EA47EA37EA2EA0780A2EA03C0120113E0EA00F01370 1338131C130E1307130310437AB11B>I<12C07E12707E7E7E120FEA0780120313C0EA01 E0A2EA00F0A21378A3133CA4131EA5131FA2130FAB131FA2131EA5133CA41378A313F0A2 EA01E0A2EA03C013801207EA0F00120E5A5A5A5A5A10437CB11B>I43 D<123C127EB4FCA21380A2127F123D1201A31203 1300A25A1206120E5A5A5A126009157A8714>II<123C127E12FF A4127E123C08087A8714>I<15C0140114031580A214071500A25C140EA2141E141CA214 3C143814781470A214F05CA213015CA213035C130791C7FCA25B130EA2131E131CA2133C 1338A21378137013F05BA212015BA212035BA2120790C8FC5A120EA2121E121CA2123C12 38A212781270A212F05AA21A437CB123>II<130C133C137C EA03FC12FFEAFC7C1200B3B113FE387FFFFEA2172C7AAB23>III<140EA2141E143EA2147E14FEA2EB01BE1303143E1306130E130C1318 13381330136013E013C0EA0180120313001206120E120C5A123812305A12E0B612FCA2C7 EA3E00A9147F90381FFFFCA21E2D7EAC23>I<000CEB0180380FC01F90B512005C5C14F0 14C0D80C7EC7FC90C8FCA8EB1FC0EB7FF8380DE07C380F801F01001380000E130F000CEB 07C0C713E0A2140315F0A4127812FCA448EB07E012E0006014C00070130F6C14806CEB1F 006C133E380780F83801FFE038007F801C2D7DAB23>II<1230123C003FB512F8A215F05A15E039700001C000601480140348EB07 00140E140CC7121C5C143014705C495AA2495AA249C7FCA25B130E131EA2133EA3133C13 7CA413FCA913781D2E7CAC23>III<123C127E 12FFA4127E123C1200AD123C127E12FE12FFA3127F123F1203A312071206A2120E120C12 1C1218123812701260082A7A9C14>59 D61 D<4A7E4A7EA34A7EA24A7EA3EC1BF81419A2EC30FCA2EC70FEEC607EA24A7EA349486C7E A2010380EC000FA201066D7EA3496D7EA2011FB57EA29038180001496D7EA349147EA201 E0147F4980A20001ED1F801203000716C0D80FF0EC3FE0D8FFFC0103B5FCA2302F7EAE35 >65 DIIIIIIII<90387FFFF0A201001300147EB3AD123812FEA314FE5C1278 387001F86C485A381E07E03807FF80D801FCC7FC1C2E7DAC24>IIIIIIIII<90383F80303901FFF0703807C07C390F000E F0001E13074813034813011400127000F01470A315307EA26C1400127E127FEA3FE013FE 381FFFE06C13FC6C13FF00011480D8003F13E013039038003FF0EC07F81401140015FC15 7C12C0153CA37EA215787E6C14706C14F06CEB01E039F78003C039E3F00F0038E07FFE38 C00FF01E2F7CAD27>I<007FB712F8A29039000FC003007C150000701638A200601618A2 00E0161CA248160CA5C71500B3A94A7E011FB512E0A22E2D7EAC33>II< B500C090380FFFC0A2D807FCC73803FE006C48EC00F800015E5F6C7E5F6D1401017E5DA2 6D4AC7FCA26E5B011F140680010F5CA26D6C5BA26E133801031430A26D6C5BA26E13E001 005C8091387E0180A26E48C8FCA21583EC1F86A2EC0FCCA215FC6E5AA26E5AA36E5AA26E 5A322E7FAC35>II<3B7FFFE003FFF8A2000390C713806C48EC7E 000000157C017F14786D14706E5B6D6C5B6D6C485A15036D6C48C7FC903803F80601015B ECFC1C6D6C5AEC7F305DEC3FE06E5A140F816E7E81140DEC1DFCEC38FEEC307F14609138 E03F8049486C7EEC800FD903007F496D7E010E6D7E130C011C6D7E496D7E49147E167F01 F0EC3F80000316C0D80FF8EC7FE0D8FFFE0103B5FCA2302D7EAC35>II<003FB612C0A29038F000 1F0180EB3F80003EC7EA7F00123C003814FE4A5A5A4A5A4A5A12604A5A4A5AA2C7485A4A C7FCA214FE495AA2495A5C1307495AA2495A495A166049C7FC13FEA2485A484814E0A248 5A484814C01501485A48481303150748C7121F00FE14FFB7FCA2232D7CAC2B>II<0003130C48131C000E13384813704813E0 003013C0EA700100601380A2EAE00300C01300A300DE137800FF13FCEB83FEA2EA7F81A2 383F00FC001E1378171577AD23>II<13FF 000713C0380F01F0381C00F8003F137C80A2143F001E7FC7FCA4EB07FF137F3801FE1FEA 07F0EA1FC0EA3F80EA7F00127E00FE14065AA3143F7E007E137F007FEBEF8C391F83C7FC 390FFF03F83901FC01E01F207D9E23>97 DII<15F8141FA214011400ACEB0FE0EB7FF83801F81E3803E007 3807C003380F8001EA1F00481300123E127EA25AA9127C127EA2003E13017EEB8003000F 13073903E00EFC3A01F03CFFC038007FF090391FC0F800222F7EAD27>III<013F13F89038FFC3FE3903E1 FF1E3807807C000F140C391F003E00A2003E7FA76C133EA26C6C5A00071378380FE1F038 0CFFC0D81C3FC7FC90C8FCA3121E121F380FFFF814FF6C14C04814F0391E0007F8481300 48147C12F848143CA46C147C007C14F86CEB01F06CEB03E03907E01F803901FFFE003800 3FF01F2D7E9D23>III<130FEB1F80EB3FC0A4EB1F80EB0F0090C7FCA8EB07C013FFA2130F1307B3AD123012 7838FC0F80A21400485AEA783EEA3FF8EA07E0123C83AD16>II< EA07C012FFA2120F1207B3B3A3EA0FE0EAFFFEA20F2E7EAD14>I<2607C07FEB07F03BFF C3FFC03FFC903AC783F0783F3C0FCE01F8E01F803B07DC00F9C00F01F8D9FF8013C04990 387F000749137EA249137CB2486C01FEEB0FE03CFFFE0FFFE0FFFEA2371E7E9D3C>I<38 07C0FE39FFC3FF809038C703E0390FDE01F0EA07F8496C7EA25BA25BB2486C487E3AFFFE 1FFFC0A2221E7E9D27>II<3807C0FE39FFC7FF8090 38CF03E0390FDC01F03907F800FC49137E49133E49133FED1F80A3ED0FC0A8151F1680A2 ED3F00A26D137E6D137C5D9038FC01F09038CE07E09038C7FF80D9C1FCC7FC01C0C8FCA9 487EEAFFFEA2222B7E9D27>I<90380FE01890387FF8383801F81C3903E00E783807C007 390F8003F8001F1301EA3F00A2007E1300A212FE5AA8127EA36C13017EEB8003380FC007 3803E00E3801F03C38007FF0EB1FC090C7FCA94A7E91381FFFC0A2222B7E9D25>I<3807 81F838FF87FEEB8E3FEA0F9CEA07B813B0EBF01EEBE000A45BB0487EB5FCA2181E7E9D1C >I<3801FE183807FFB8381E01F8EA3C00481378481338A21418A27E7EB41300EA7FF06C B4FC6C13C06C13F0000113F838001FFC130138C0007E143EA26C131EA27EA26C133CA26C 137838FF01F038E3FFC000C0130017207E9E1C>I<1360A413E0A312011203A21207121F B512F0A23803E000AF1418A714383801F03014703800F860EB3FE0EB0F80152A7FA81B> II<3AFFFC01FFC0A23A0FE0007E000007147C 15380003143015706C6C1360A26C6C5BA390387C0180A26D48C7FCA2EB3F07EB1F06A2EB 0F8CA214DCEB07D8A2EB03F0A36D5AA26D5A221E7F9C25>I<3BFFFC3FFE07FFA23B0FE0 03F001F801C09038E000F00007010114E0812603E00314C0A2913807F8012701F0067813 80A29039F80E7C030000D90C3C1300A290397C181E06A2151F6D486C5AA2168C90391F60 0798A216D890390FC003F0A36D486C5AA36DC75A301E7F9C33>I<3AFFFC07FF80A23A0F F003FC000003EB01F0000114C06D485A000091C7FCEB7C06EB3E0E6D5A14B8EB0FB0EB07 E013036D7E497E1307EB067C497EEB1C1F01387FEB700F496C7E6E7ED803C07F00076D7E 391FE003FC3AFFF007FFC0A2221D7F9C25>I<3AFFFC01FFC0A23A0FE0007E000007147C 1538000314306D137000011460A26C6C5BA2EBFC01017C5BEB7E03013E90C7FCA2EB1F06 A2148EEB0F8CA2EB07D8A2EB03F0A36D5AA26D5AA2495AA2130391C8FC1278EAFC06A25B 131CEA7838EA7070EA3FE0EA0F80222B7F9C25>I<003FB51280A2EB003F003C14000038 137E00305BEA700100605B495A495A130F00005B495A49C7FC5B137E9038FC0180EA01F8 120313F03807E003EA0FC0001F1400138048485A007E5B00FE133FB6FCA2191D7E9C1F> III<38078008380FE01C381FF838383F FFF038707FE038E01FC03840078016077AAC23>126 D<001C13E0387F03F8A200FF13FC A2007F13F8A2381C00E016087AAD23>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmr6 6 16 /Fp 16 117 df<130C1338137013E0EA01C0EA038013005A120EA25AA25AA312781270A3 12F0AB1270A312781238A37EA27EA27E7E1380EA01C0EA00E013701338130C0E317AA418 >40 D<12C012707E7E7E7E7E1380EA01C0A2EA00E0A21370A313781338A3133CAB1338A3 13781370A313E0A2EA01C0A2EA038013005A120E5A5A5A12C00E317CA418>I<1438B2B7 12FEA3C70038C7FCB227277C9F2F>43 D<13FF000313C0380781E0380F00F0001E137848 133CA248131EA400F8131FAD0078131EA2007C133E003C133CA26C13786C13F0380781E0 3803FFC0C6130018227DA01E>48 D<13E01201120712FF12F91201B3A7487EB512C0A212 217AA01E>II<13FF000313C0380F03E0381C 00F014F8003E13FC147CA2001E13FC120CC712F8A2EB01F0EB03E0EB0FC03801FF00A238 0003E0EB00F01478147C143E143F1230127812FCA2143E48137E0060137C003813F8381E 03F0380FFFC00001130018227DA01E>I<14E01301A213031307A2130D131D1339133113 6113E113C1EA01811203EA07011206120C121C12181230127012E0B6FCA2380001E0A6EB 03F0EB3FFFA218227DA11E>I54 D<137F3803FFC0380781E0380E00704813380018131C1238A3123C003F133838 1FC078EBE0F0380FF9E03807FF80120114C0000713F0380F0FF8381C03FC383801FE3870 007E141F48130F1407A314060070130E0078130C6C1338001F13F03807FFC0C613001822 7DA01E>56 D61 D<120C123FA4120CC7FCA712 0FB4FCA2121F7EB0EAFFE0A20B237DA212>105 D<380F07F038FF1FFCEB703E381FC01E 6C487EA21300AE39FFF0FFF0A21C167D9522>110 D<137E3803FFC0380781E0380F00F0 001E137848133CA248131EA200F8131FA70078131E007C133E003C133C003E137C6C13F8 380F81F03803FFC0C6130018187D961E>I<380F07F038FF3FFCEB703F391FC00F80390F 8007C01300EC03E0A2EC01F0A7EC03E0A2EC07C0018013809038C01F00EB703EEB3FFCEB 07E090C8FCA7EAFFF0A21C207D9522>I<487EA41203A21207A2120F123FB51280A23807 8000AA14C0A63803C180EBE300EA01FEEA007C12207E9E18>116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmbx12 17.28 2 /Fq 2 64 df33 D<91380FFFF849B612C0010F15F8013F15FE496F7E2701FFF80080480180011F13F0D807 FCC700077FD80FF080484882003F8301F880486C827FB5178080A76C90C7FC4C14006C5A 6C5AD807F04A5BC95C5E4C5B604C5B4C138093B5C7FC4B13FC5F4B13E05F4B5B4B90C8FC 5E5E4B5A5E4B5AA25E4B5AA293C9FCA215FEA35DAE5D92CAFCABEC01FCEC07FF4A7F023F 13E0A24A7FA291B57EA76E5BA26E5BA2020F13806E90C9FCEC01FC396577E44C>63 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmbx5 5 1 /Fr 1 50 df<131C137CEA0FFC12FFA212F01200B3387FFFF8A3151C7B9B1F>49 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmbx7 7 1 /Fs 1 50 df49 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft msbm5 5 1 /Ft 1 124 df<1506D803F0133FD80FF813FF001FEB03FE9038F00FFC3900303FF0ECFF C001631300EB6FFEEBFFF614CC0003130C380FFC18393FF01FF8D8FFC013F0010013E000 FC1480006090C7FC20127B9127>123 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmex7 7 2 /Fu 2 99 df80 D<1440EB01F0EB07FCEB1FFF90387F BFC03901FE0FF03907F001FC391F80003F007EC7EA0FC000F0EC01E000C0EC0060230B7F AA26>98 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv msam7 7 1 /Fv 1 3 df2 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw msam10 10 3 /Fw 3 33 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fx cmsy5 5 6 /Fx 6 96 df0 D<13E0A438F0E1E0EAF843387E4FC0380F5E00 EA01F0A2EA0F5E387E4FC038F843E0EAF0E13800E000A413127B921F>3 D10 D48 D<14C01301B3A7007FB61280B7FC7E211D7B9C2D>63 D<00E0146015E06C1301007014C00078130300381480003C1307001C1400001E5B000E13 0E000F131E6C131CEB803C00031338EBC07800011370EBE0F000005B13F1EB71C0137BEB 3B80133F6DC7FCA2130EA21B1B7B9927>95 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fy cmex10 10 39 /Fy 39 126 df<1430147014E0EB01C01303EB0780EB0F00A2131E5BA25B13F85B12015B 1203A2485AA3485AA3121F90C7FCA25AA3123EA2127EA6127C12FCB3A2127C127EA6123E A2123FA37EA27F120FA36C7EA36C7EA212017F12007F13787FA27F7FA2EB0780EB03C013 01EB00E0147014301462738226>0 D<12C07E12707E123C7E7EA26C7E6C7EA26C7E7F12 007F1378137CA27FA37FA31480130FA214C0A31307A214E0A6130314F0B3A214E01307A6 14C0A2130FA31480A2131F1400A3133EA35BA2137813F85B12015B485AA2485A48C7FCA2 121E5A12385A5A5A14627C8226>I<151E153E157C15F8EC01F0EC03E01407EC0FC0EC1F 8015005C147E5CA2495A495AA2495AA2495AA2495AA249C7FCA2137EA213FE5B12015BA2 12035BA21207A25B120FA35B121FA45B123FA548C8FCA912FEB3A8127FA96C7EA5121F7F A4120F7FA312077FA21203A27F1201A27F12007F137EA27FA26D7EA26D7EA26D7EA26D7E A26D7E6D7EA2147E80801580EC0FC0EC07E01403EC01F0EC00F8157C153E151E1F947182 32>16 D<12F07E127C7E7E6C7E7F6C7E6C7E12017F6C7E137EA27F6D7EA26D7EA26D7EA2 6D7EA26D7EA26D7EA280147E147F80A21580141FA215C0A2140F15E0A3140715F0A41403 15F8A5EC01FCA9EC00FEB3A8EC01FCA9EC03F8A515F01407A415E0140FA315C0141FA215 80A2143F1500A25C147E14FE5CA2495AA2495AA2495AA2495AA2495AA249C7FC137EA25B 485A5B1203485A485A5B48C8FC123E5A5A5A1F947D8232>I<160F161F163E167C16F8ED 01F0ED03E0ED07C0150FED1F801600153E157E5D4A5A5D14034A5A5D140F4A5AA24AC7FC 143E147E5CA2495AA2495AA2495AA2130F5CA2495AA2133F91C8FCA25B137E13FEA25B12 01A25B1203A35B1207A35B120FA35BA2121FA45B123FA690C9FC5AAA12FEB3AC127FAA7E 7FA6121F7FA4120FA27FA312077FA312037FA312017FA212007FA2137E137F7FA280131F A26D7EA2801307A26D7EA26D7EA26D7EA2147E143E143F6E7EA26E7E1407816E7E140181 6E7E157E153E811680ED0FC01507ED03E0ED01F0ED00F8167C163E161F160F28C66E823D >I<12F07E127C7E7E6C7E6C7E6C7E7F6C7E1200137C137E7F6D7E130F806D7E1303806D 7EA26D7E147C147E80A26E7EA26E7EA26E7EA2811403A26E7EA2811400A281157E157FA2 811680A2151F16C0A3150F16E0A3150716F0A31503A216F8A4150116FCA6150016FEAA16 7FB3AC16FEAA16FC1501A616F81503A416F0A21507A316E0150FA316C0151FA31680153F A216005DA2157E15FE5DA214015DA24A5AA214075DA24A5AA24A5AA24AC7FCA2147E147C 14FC495AA2495A5C1307495A5C131F49C8FC137E137C5B1201485A5B485A485A48C9FC12 3E5A5A5A28C67E823D>III40 D<177C17FCEE01F8A2EE03F0EE07E0EE0FC0A2EE1F80 EE3F005E167E5E15015E15034B5A5E150F5E151F4B5AA24BC7FCA215FEA24A5AA24A5AA2 4A5AA2140F5D141F5D143F5DA2147F92C8FC5CA25C13015C1303A25C1307A3495AA3495A A3133F5CA3137F5CA313FF91C9FCA35A5BA31203A25BA31207A35BA3120FA45BA2121FA6 5BA2123FA85BA2127FAE5B12FFB3A62E95688149>48 D<12F87E127EA27E6C7E6C7EA26C 7E6C7E7F12016C7E7F137E137F6D7E131F80130F806D7EA26D7EA26D7EA26D7EA2147FA2 6E7EA281141F81140F811407A281140381A2140181140081A28182A36F7EA36F7EA38215 0FA3821507A3821503A3821501A382A281A31780A3167FA317C0A4163FA217E0A6161FA2 17F0A8160FA217F8AE160717FCB3A62E957E8149>I<12F0B3B3B00434678037>63 DII76 D<95387FFF80050FB512FC94B712C0040316F0041F16FE04 7F707E4BB912E00307DAC3F814F8031FD9F803010713FE4B01C002007F9226FFFE00031F 13C04A01F804077F4A01E004017F020F01809338007FFC4A48C7EE1FFE4A48727EDA7FF0 06037F4A48727F4949727F4990C8EF3FF04948747E4A1A0F4948747E4948747E4948747E 4A86017F894A1B7F49C9727E488A491C1F4848767EA24848767EA24848767EA2491C0100 1F8AA2491C00003F8AA24989007F1F80A290CA193FA4481FC0A2481E1FA2C1FCA748CAD8 03F8CA121FA36C1E3FA26C1F80A46D1D7FA2003F1F006D65A2001F666D1C01A2000F666D 1C03A26C6C525AA26C6C525AA26C6C525A6D1C3F6C666D6C515A6E1BFF013F9AC7FC6E62 6D6C505A6D6C505A6D6C505A6E1A1F6D6C505A6D01C0F1FFE06D6D4E5B6E6C4E5BDA3FFC 060F90C8FC6E6C4E5A6E6C6CEF7FFC020301E0933801FFF06E01F804075B6E01FE041F5B 92263FFFC092B5C9FC6F01F802075B0307D9FFC390B512F8030191B712E06F6C1780041F 4CCAFC040316F0040016C0050F02FCCBFCDD007F138072747B7F7D>II<95387FFF80050FB512FC94B712C0040316F0041F16FE047F707E 4BB912E00307DAC00014F8031F01F8C7000713FE4B01C002007FDBFFFEC9001F13C04A01 F804077F4A01E004017F020F01809338007FFC4A48CBEA1FFE4A48727EDA7FF006037F4A 48727F4949727F4990CDEA3FF0496D4F7E6F19FF496D4E7F496D4E7F496D4E7FDACFFCF0 0FFC90267FC7FE4E487FDA83FF95383FF07FD9FF016D4D486C7E486D6DDDFFC07F496D6C 4CEB801F48486D6C4C496C7E6F6C4C5A48486D6C4C486D7E6F6C4C5A48486D6C4C486D7E 6F6D4B5A496D6D4B481301001F6F6C4A4980706C4A90C7FC496E6C4A481400003F6F6C4A 4881706C4A5A496E6C4A4881007F6F6D49481680706D495A90C96C6C4849153F716C4890 C9FC716C485A716C485A48706C484817C0716C485A4870D9FFE0161F715C725B7290CAFC 725A725AA24E7E4E7E4E7F95B57E4D806C4CD93FF0163F4D486C7E6C4C486C6C17804D48 6C7E4D486C7E4D486C7F6D4B486C6D157F4C496D7E003F4B90C76C6C16006D4A486E6C5D 4C486E7E001F4B486E6C5D6D4A486E6C14014C486E7F000F4B486E6D5C6D49496F6C1303 4B90C96C7E6C6C4948706C495A4B48707E6C6C4948706C495A4B48707E6C6C4948706D48 5A6D494870EBC03F6C4949DD7FE05BD97F8390CB6C6C485ADAC7FE95381FF8FF90263FCF FC726C90C7FCDAFFF872B5FC6D49725B6D49725B6D49725B4B197F6D90CD6C5A6D01C0F1 FFE06D6D4E5B6E6C4E5BDA3FFC060F90C8FC6E6C4E5A6E6C6CEF7FFC020301E0933801FF F06E01F804075B6E01FE041F5B92263FFFC092B5C9FC6F01F802075B0307D9FFC090B512 F8030191B712E06F6C1780041F4CCAFC040316F0040016C0050F02FCCBFCDD007F138072 747B7F7D>III<0078EF0780 00FCEF0FC0B3B3B3A46C171F007E1880A2007F173F6C1800A26D5E001F177E6D16FE6C6C 4B5A6D15036C6C4B5A6C6C4B5A6C6C4B5A6C6C6CEC7FC06D6C4A5AD93FF8010790C7FC6D B4EB3FFE6D90B55A010315F06D5D6D6C1480020F01FCC8FC020113E03A537B7F45>83 D88 DI<007C1A1FA200FEF23F80B3B3B3B3A76C1A7FA26C1B00A26D61A2 003F626D1801A2001F626D1803A26C6C4E5A6D180F0007626C6C4E5A6D183F6C6C4E5A6C 6D4D5A6E5E6D6C4C90C7FCD93FF8EE0FFE6D6C4C5A6DB4EE7FF86D01C04A485A6D01F002 075B6D01FC021F5B9028007FFFE003B5C8FC6E90B65A020F16F8020316E002001680033F 4AC9FC030714F09226003FFECAFC51747B7F5C>91 D<1402EC0F80EC3FE0ECFFF8497F90 3807F8FF90391FE03FC090393F800FE09039FE0003F8D803F8EB00FED80FE0EC3F8048C8 EA07C0007CED01F000F0ED007800C016182D0F80BD2E>98 D<17C0EE07F8EE3FFF4BB512 E0030F14FC923A7FFE1FFF80912703FFF00313F0021F90C7EA3FFEDAFFF0913803FFC001 0301809138007FF0D91FF8C9EA07FED9FF809338007FC0D807FCCBEA0FF8D83FC0F000FF 00FCCDEA0FC000E01A01521080BF53>I<197C953807FFC0067F13FC0507B612C0057F15 FC040FB50083EBFFE093B526F0001F13FE030F01FCC8387FFFE092B50080030313FE020F 01F0CA381FFFE0DAFFFCCCEA7FFE011F0180963803FFF02601FFF0CEEA1FFFD81FFED013 F0D8FF80F503FE00F0D2121E771080BF78>I104 DI< 1B301B781BF8A2F201F0A2F203E0A2F207C0A2F20F80A2F21F00A21A3EA262A262A24F5A A24F5AA24F5AA262190FA24FC7FCA2193EA261A261A24E5AA24E5AA24E5AA24E5AA24EC8 FCA2183EA260131001305E13F800014C5A1203D80FFC4B5A121DD838FE4B5A12F0D8407F 4B5A12004DC9FC6D7E173E6D7E5F6D7E5FA26D6C495AA26D6C495AA26D6C5C1607A26D6C 495AA2027F49CAFCA291383F803EA25EEC1FC05EEC0FE0EDE1F0EC07F1EDF3E0A26EB45A A26E5BA26E90CBFCA25D157E157C15384D64788353>112 D<1B301B78A21BF8A21BF01A 01A21BE01A03A21BC01A07A21B801A0FA21B0062A21A1E1A3EA21A3C1A7CA21A781AF8A2 62A21901A2621903A2621907A262190FA297C7FC61A2191E193EA2193C197CA2197819F8 A2611801A2611803A261A21807A261180FA296C8FC60A2181E183EA2183C187C13100130 1678017016F813F860000116011203486C5E000F1603121DD838FE5E00701607126000C0 5FEA407F0000160FA26D6C92C9FC5FA2171E6D6C143EA2173C6D6C147CA2177817F86D7E 5F16016D7E5F1603A26D6C5C1607A26D6C5C160FA294CAFC027F5BA2161EEC3F80163EA2 163C91381FC07CA2167891380FE0F8A25E15E1EC07F15E15F3EC03FB5E15FFA26E5BA36E 90CBFCA35D157EA2157C153C15384D96788353>I<1B301B78A21BF8A21BF0A21A01A21B E0A21A03A21BC0A31A07A21B80A21A0FA21B00A262A21A1EA21A3EA21A3CA21A7CA21A78 A21AF8A262A31901A262A21903A262A21907A262A2190FA297C7FCA261A2191EA2193EA2 193CA3197CA21978A219F8A261A21801A261A21803A261A21807A261A2180FA296C8FCA3 60A2181EA2183EA2183CA2187C131018781330017016F8A201F85E120117011203486C5E A2120D001D16031219D830FE5E12700060160712C000405FEA007F170FA295C9FC6D7E5F A2171EA26D6C143EA2173CA2177C6D7E1778A36D6C14F8A25FA216016D7E5FA21603A26D 6C5CA21607A26D6C5CA2160FA294CAFC147F5EA2161EEC3F80A2163EA2163CEC1FC0167C A21678A291380FE0F8A25EA2EC07F1A25EA215F3EC03FB5EA215FFA26E5BA48093CBFCA4 157EA4157C153C15384DC8788353>I<1B301B78A31BF8A21BF0A31A01A21BE0A31A03A2 1BC0A31A07A21B80A41A0FA21B00A362A21A1EA31A3EA21A3CA31A7CA21A78A31AF8A262 A41901A262A31903A262A31907A262A3190FA297C7FCA461A2191EA3193EA2193CA3197C A21978A319F8A261A41801A261A31803A261A31807A261A3180FA296C8FCA460A2181EA3 183EA2183CA3187C131018781330A2017016F8A201F85EA212011701120360487EA2120D 001D16031219D838FE5E123012700060160712E000C05FEA407F1200170FA295C9FCA26D 7E5FA2171EA36D7E173EA2173CA36D6C147CA21778A317F86D7E5FA316016D7E5FA41603 6D7E5FA31607A26D6C5CA3160FA294CAFC147FA25EA2161EA2EC3F80A2163EA2163CEC1F C0A2167CA21678A2EC0FE016F8A25EA3EC07F1A25EA315F3EC03FB5EA415FF805EA48093 CBFCA5157EA5157C153CA215384DFA788353>I<146014F0A2497E497E497E497E497F90 383EF7C09038FCF3F03901F8F1F83907F0F0FED81FC0EB3F80D87F80EB1FE0D8FE00EB07 F000F8140100E0EC007000801510C71400B3AD2431777E37>120 D<14F0B3AD6C151000E0157000F8EC01F000FE1407D87F80EB1FE0D81FC0EB3F80D807F0 EBFE003901F8F1F83900FCF3F090383EF7C06DB45A6D90C7FC6D5A6D5A6D5A6D5AA21460 2431777F37>II I<12F87E7E7EA26C7E6C7E7F6C7EEA0FFC6C7E6C6C7E14E06C13F86C13FF013F13E06D13 FF6DECFF807F13016D7E80140F14016E7E150FED007F291B839A25>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fz msbm7 7 7 /Fz 7 124 df67 D80 DII<003FB612 C0A23A33E0038180D83F001303003C903807070048EB06060070EB0E0EEC1C0C0060EB18 1CEC3838C7EA7030EC6070ECE0E049485A148190380383800203C7FC495AEB0E06EB0C0E EB1C1CEB3818EB3038EB7070EBE060EBC0E03801C1C0D981801360EA0383D80703C7FCD8 060714E0EA0E0ED81C0C1301D8181C1303D83838EB07C0D87030130ED86070131CD8E0E0 13F8B7FCA223287EA737>90 D<942601FFFE1C3894B600E0F203F8043F03FC1A1F0307B8 963801FFF0037F9026F8000101C0061F130091260FFFFCC8D81FF0943803FFF891B5C9D8 03FC053F1380010F01E0706C932607FFF8C7FCD9FFFECBD87FC04AB51280000701C0DE1F FC91B500F0C8FCD87FFCCC0007B8C9FCD8FFC0070116E048CE003F02F8CAFC00E0090301 FCCBFC950E7FB398>94 D<013FEC03E0D9FF80EB07F048ED1FE048ED7FC048913801FF80 0101903803FE000006EC0FF8D80003EB3FE04AB45A5CD907075B9026061FF3C7FC90380E 3FE790380CFF8690381FFE06ECFC0E90383FF00CEB7FC03A01FF001C07D807FEEB180ED8 0FF8EB1FFED83FE05CD87F805C48C75B007CEC0FC02C197D982D>123 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FA eufm10 10 6 /FA 6 116 df<497E903807C00E90380FF87C90383FFFFC90B5FC5A1207EA1F83383F80 3F397F0003F8A4127E12FEAF4A7E6C131F9039807FFE109039C0F3FF70D9E3E313C0267F FFC313806C01031300496C5AD81FF85B6C486C5A6C481370D8038013606CC9FC242A7BA6 2A>97 D<02101310027C1370903901FF80E04913F3010F13FF133F5BD801FC14C03803F8 0FEC003F150F5B1207A2151FAF6D133F6DEBFFE06D5A9038FF079FEC8F0F6C13FC6C01F8 13F014F06C13E0EB7F8090383F0007131E4914E0017014C0485A486C1480486C1400486C 130648B45B007FEBC01800E7EBF0300003EBFFE0C6FC6D5B011F5BD903FEC7FCEB003824 387FA62A>103 D<1304EAC01CEA403813F01261EA63E0EA6FC0127F5BA390C8FCA61418 143C147E903801FF804913F04913F8011F13FCEB3C3FEB700FEBE007EBC0031300A31401 AC5AA5138015F813C013E0127F1403EA3FC01380EA1E00000C14F01208C7FCEC07E015C0 1580A2EC0F00140E5C5C5C5C495AEB078091C7FC13021E4A7AB82B>I<1470380401E038 0603C0495A011FC7FCEA073E5B13FC5B14079038F01F80EC3FC0ECFFE013F39038F71FF0 EBFE0FEBFC0713F8140315E001F013C01580EC070014065C5C14703803F1E0003FB512C0 481480B6FCD807F0C7FCB07F6D13206D13E09038FF83C0ECCF806CEBFE006C5B6C5BEB7F E0EB1FC06DC7FC13061C3B7EB820>107 D<1302EA400EEAC01C1378EAE0F0EA63E0EA67 C0127F1380A21300A4127EB3A5127FAA5A138013C613EE13FC13F0EA7FE0EA3FC01380EA 1E00120C12080F3B79B817>I<1430147CD901FE1340903903FF80C0010FEBC38049EBFF 00017F5B01FC5B3903F81FF8EC01F091C8FCA5153015FC9038FC03FEEC0FFFEBFE3F90B6 FC14C16C1380495AD800F87F13E0134090C7FCA4EA01F8D807FE137E380FFF8048EBE0FE 4813F039707FFCF839C01FFFE0D880071380260003FCC7FC6D5AEB00E0222A81A725> 115 D E %EndDVIPSBitmapFont /FB 131[42 42 5[42 3[42 1[42 42 3[42 42 19[42 2[42 1[42 42 1[42 3[42 4[42 42 32[4 5[4 28[{}18 83.022 /XYDASH10 rf /FC 129[0 0 4[0 0 0 1[0 4[0 0 12[0 17[0 17[0 2[0 2[0 2[0 4[0 0 3[0 0 0 0 0 1[0 1[0 0 16[0 0 0 14[{}27 83.022 /XYBTIP10 rf /FD 129[0 0 4[0 0 0 1[0 4[0 8[0 4[0 17[0 17[0 2[0 2[0 2[0 4[0 4[0 0 0 0 0 1[0 1[0 0 16[0 0 0 14[{}26 83.022 /XYATIP10 rf %DVIPSBitmapFont: FE cmsy7 7 38 /FE 38 117 df0 D<1238127C12FEA3127C123807077A9114>I< 0060140600F0140E0078141E6C143C6C14786C14F039078001E03903C003C03901E00780 3900F00F00EB781E6D5A6D5A6D5A6D5A6D5A497E497EEB1E78497E497E497E3901E00780 3903C003C039078001E048C712F0001E147848143C48141E48140E006014061F1F769D34 >I<1338A50060130C00F8133E00FC137E00FE13FE383FBBF83807FFC000011300EA007C 48B4FC000713C0383FBBF838FE38FE00FC137E00F8133E0060130C00001300A517197B9A 22>I<1406140EB3B812E0A3C7000EC8FCB1B812E0A32B2B7CA834>6 D8 D10 D<913801FFC0021F13FC91B67E499038 007FC0D907F0EB07F0D91F80EB00FC49C8127E017C151F01F0ED078048486F7E48486F7E 48486F7E90CA1270481778001E83001C171C003C171E0038170E0078170F007083A200F0 1880481703A96C170700701800A200785F0038170E003C171E001C171C001E173C6C5F6C 17706D16F06C6C4B5A6C6C4B5A6C6C4B5A017C031FC7FC013F157E6D6C5CD907F0EB07F0 D901FFEB7FC06D90B55A021F01FCC8FC020113C039357CA842>13 D<137F3801FFC0000713F0380FC1F8381F007C003C131E0038130E0078130F00707F00F0 1480481303A56C13070070140000785B0038130E003C131E001F137C380FC1F86CB45A00 0113C06C6CC7FC19197C9A22>I<137F3801FFC0000713F0487F487F487FA2487FA2B612 80A76C1400A26C5BA26C5B6C5B6C5B000113C06C6CC7FC19197C9A22>I<160E163E16FE ED03F8ED0FE0ED3F80EDFE00EC03F8EC0FE0EC3F8002FEC7FCEB03F8EB0FE0EB3F8001FE C8FCEA03F8EA0FE0EA3F8000FEC9FC12F812FEEA3F80EA0FE0EA03F8EA00FEEB3F80EB0F E0EB03F8EB00FEEC3F80EC0FE0EC03F8EC00FEED3F80ED0FE0ED03F8ED00FE163E160E16 00AB007FB612FCB712FEA227357AA734>20 D<12E012F812FEEA3F80EA0FE0EA03F8EA00 FEEB3F80EB0FE0EB03F8EB00FEEC3F80EC0FE0EC03F8EC00FEED3F80ED0FE0ED03F8ED00 FE163E16FEED03F8ED0FE0ED3F80EDFE00EC03F8EC0FE0EC3F8002FEC7FCEB03F8EB0FE0 EB3F8001FEC8FCEA03F8EA0FE0EA3F80007EC9FC12F812E0CAFCAB007FB612FCB712FEA2 27357AA734>I24 D<49B512FE130F133F01FFC8FCEA01F8EA03E0EA078048C9FC12 1E121C123C123812781270A212F05AA77E1270A212781238123C121C121E7E6C7EEA03E0 EA01F86CB4FC013FB512FE130F130127277AA134>26 D<176017F01770A217781738173C 171C171E83717E717E717EEF00F8BAFC19801900CB12F8EF01E04D5A4D5A4DC7FC171E17 1C173C173817781770A217F01760391F7C9D42>33 D39 D<13E0EA01F0EA03F8A3EA07F0A313E0A2120F13C0A3EA1F80A21300A25A123EA35AA312 7812F8A25A12100D1E7D9F13>48 D<017F157F2601FFE0903803FFC0000701F890380FF1 F0260F83FC90381F0038261E00FF013C7F001890263F8078130C4890261FC0E07F007090 260FE1C07F0060EB07E3913803F780486DB4C7EA01806E5A157E157F81824B7E0060DAF7 E0EB0300913801E3F0DBC3F85B6C90260381FC13066C90260F00FE5B001C011E90387F80 3C6C017C90381FE0F82607C7F86DB45A2601FFE0010313C06C6CC86CC7FC391B7C9942> I<49B5FC130F133F01FFC7FCEA01F8EA03E0EA078048C8FC121E121C123C123812781270 A212F05AA2B7FCA300E0C8FCA27E1270A212781238123C121C121E7E6C7EEA03E0EA01F8 6CB4FC013FB5FC130F130120277AA12D>I<150EA2151E151C153C1578157015F015E014 0115C0140315801407EC0F00140E141E141C143C14381478147014F0495A5C13035C1307 91C7FC5B131E131C133C13381378137013F05B1201485A5B120790C8FC5A120E121E121C 123C5A127012F05A12601F3576A800>54 D<140C141CA2143CEB3FB8EBFFF8EA03E03807 807C380F007E001E13FF001C13E7003C1480A2D87C0113C0007813C3A2130300F8EB83E0 A213071403A2130F130EA3131E131CA2133C1338A21378D8787013C0A2387CF00713E000 3C1480A2001FEB0F0013C0000F131E00075B3803E0F8EBFFF03807BF8090C8FCA31B317D AC22>59 D<1406140EB3B2007FB712E0B8FC7E2B287CA734>63 D<161E163EA2167E16FE A2150116BE1503163E15071506150E151CA215381530ED703F156015E04A487EA2EC0380 EC0700A2140E5C835C027FB5FCA291B6FC903901C0000F13034A80D84007C7FCEA600ED8 F01E1407D8FC7C81B45A49EDF78049913803FE006C485D6C48EC01F0000ECBFC312D7DA9 35>65 D67 D<0103B512C0013F14FC90B712802703F0780713E03B0F 80F8007FF0D81E00EC0FF848ED03FC007C15010078ED00FE00F8167E00E0167FC748143F 1301171FA35C1303A2171E173E5C0107153C177C4A1478010F15F0160191C713E049EC03 C0EE0780011EEC0F00013E141C1678013C495A017CEB07C00178013FC7FC9038F803FC48 B512E04891C8FC4813F030287EA734>I76 D<91383807F89138F03FFFD903E0B5 128090260781E013C0903A0E07801FE090393C0F000FD9781EEB07F0494813033801E07C 2603C078EB01F800075B1381D80F011400001F5B381E03C0003EC9FC123C127CA217F000 78150112F8A217E0160317C0160717806CED0F005E161E007E5D5E007F5D6C6C495A6DEB 03806C6C010FC7FCD80FF8133E3907FF01F86CEBFFE0C691C8FCEB1FF82D2A7BA835>79 D<0103B512E0013F14FC90B7FC2703F0780313C03B0F80F8007FE0D81E00EC1FF0481507 007CED03F80078150112F800E01500C75A130117F0160117E04A1303010315C0EE0780EE 0F00161E4A5B010714F0ED03E09138801F8090260F8FFEC7FCEC9FF0ECBF8091C9FC5BA2 131E133EA2133C137C137813F8A25B120113C090CAFC2D2B7EA72F>I83 D<18C01703010FB71280017FEDFE0048B75A4816E0270F0001F0C8FC001E495A5A127C14 07485C5A12C0C7120F5DA3141F92C9FCA35C143EA3147E147CA314FC5CA313015CA3495A A25C1307A2495A91CAFC130C322E7CA926>I<00E0153016706C15F0007015E000781401 003815C0003C1403001C1580001E1407000E1500000F5C6C140E6D131E0003141C6D133C 000114386D1378000014706D13F001705BEB780101385BEB3C03011C5BEB1E07010E90C7 FCEB0F0FEB070E149EEB039C14FC6D5AA26D5AA2146024247CA22D>95 D<147EEB03FEEB0FE0EB1F00133E5BB35BA2485AEA07E0EAFF8000FCC7FCB47EEA07E0EA 01F06C7EA2137CB37F7FEB0FE0EB03FEEB007E173B7BAB22>102 D<12FCB47EEA0FE0EA01F06C7E137CB37FA27FEB0FC0EB03FEEB007EEB03FEEB0FC0EB1F 00133EA25BB35B485AEA0FE0EAFF8000FCC7FC173B7BAB22>I<1306130E131E131CA213 3C13381378137013F013E0120113C0A212031380120713005A120EA2121E121C123C1238 12781270A212F05A7E1270A212781238123C121C121E120EA2120F7E1380120313C01201 A213E0120013F0137013781338133C131CA2131E130E13060F3B79AB1B>I<12E0A27E12 70A212781238123C121C121E120EA27EA21380120313C0120113E01200A213F013701378 1338133C131CA2131E130E131E131CA2133C13381378137013F013E0A2120113C0120313 80120713005AA2120E121E121C123C123812781270A212F05AA20F3B7CAB1B>I<12E0B3 B3B3A5033B78AB14>I<12E0A27E1270A212781238123C121CA2121E120E120F7EA27F12 03A27F12017F1200A27F137013781338A2133C131C131E130EA2130F7F801303A2801301 801300A2801470A214781438143C141CA2141E140E140F80A2158014031401193B7CAB22 >110 D<00E0EC01C0B3AEB7FCA27E22237BA22D>116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FF cmr5 5 17 /FF 17 117 df6 D<13301360EA01C0EA038013001206120E5AA25AA3 5AA312F0AB1270A37EA37EA27E12067E1380EA01C0EA006013300C297B9E16>40 D<12C0126012387E120C7E1207EA0380A2EA01C0A3EA00E0A313F0AB13E0A3EA01C0A3EA 0380A2EA070012065A121C5A12605A0C297C9E16>I<14E0B0B712C0A3C700E0C7FCB022 237C9B2B>43 D48 D<1360EA01E0120F12FF12F11201B3A3387FFF80A2111C7B9B1C>IIII<001C13E0EA1FFF14C0140013FC0018C7FCA513FCEA1BFF381F07 C0381C01E01218EB00F0C7FC14F8A2127012F8A214F01301006013E0387003C0383C0F80 380FFF00EA03F8151D7D9B1C>II<12FEA2121EA9EB1F C0EBFFF0381FC0F8EB003C001E131EA2140FA6141EA2001F133C381DC0F8381CFFE03818 1F80181D7D9C1F>98 D<121C123EA3121CC7FCA612FEA2121EAEEAFFC0A20A1D7D9C11> 105 D<38FE1FC0EB7FE0381EC0F0381F0078A2121EAB38FFC3FFA218127D911F>110 D<13FE3807FFC0380F01E0383C0078003813380078133C48131EA60078133C0038133800 3C1378380F01E03807FFC03800FE0017127E911C>I<38FE1FC0EBFFF0381FC0F8EB003C 001E131EA2140FA6141E143E001F137CEBC0F8381EFFE0EB1F8090C7FCA6EAFFC0A2181A 7D911F>I<1203A35AA25AA2123FEAFFFCA2EA0F00A81306A5EA078CEA03F8EA01F00F1A 7E9916>116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FG cmmi5 5 31 /FG 31 118 df<137F3801FFC0390781E060380E00F048EB78C0123C48EB7D80143D48EB 3F00143EA2143CA20070137C387801FC393C0F9E30391FFE0FE03907F007C01C127C9126 >11 D<14FCEB03FF90380F038090381C01C01338016013E0A201C013C038018003A21580 390307F700EB0FFEA2EB07E7380600071580A35AA31500001C5B141E001E131C001F1378 3833F7F03830FFC090C8FCA25AA45AA21B257E9C21>I<3903F00180EA0FFC391FFE0300 123F387E3F0638E0078638C0018C008013CCC7FC14D814F81470A31460A314E0A3495AA4 495AA26DC7FC191B7E911F>I21 D<0003B512C0000F14E05A4814C0397030600038C070E0 EA0060A213E0A2EA01C0A21203497E120780EB0078000613701B127D9123>25 D<127012F812FCA2127C120CA31218A2123012601240060D7A8413>59 D<146014E0130114C0A213031480130714005B130EA2131E131C133C133813781370A213 F05B12015BA212035B120790C7FC5A120EA2121E121C123C123812781270A212F05AA213 297B9E1F>61 D65 D<0003B512F815FE3A003E001F80ED0FC0150715035B1507A2ED0F8049EB 1F00157E90B512F85D3901F001F8EC007E153E81485AA3151E4848133E5D5DEC07F0B612 C04AC7FC221C7C9B2B>I<91387F8040903907FFE0C090381FC07190393E001B8001F813 0FEA01E0484813074848140048C7FC5A123E15064891C7FCA35AA41518A212785D6C5C15 E06C495A260F8007C7FC3807E01E3801FFF838003FC0221E7C9C29>I<0003B512F815FE 3A003E001F80ED07C0ED03E0150149EB00F0A216F8A25BA4484814F01501A216E0484813 0316C0ED0780ED0F004848131E5D15F8EC07E0B6128002FCC7FC251C7C9B2E>I<903807 F02090381FFC609038780EE09038E003C03801C001EA0380A2D807001380A26DC7FCA27F EA03FC3801FFC06C13F0EB3FF8EB01FCEB003E141E140EA21230A200705BA25C00785B38 FE01E038C7FF80D881FEC7FC1B1E7B9C24>83 D<3AFFFC01FFC0A23A0F80001C001518A3 48C75AA4003E5CA4485CA448495AA34AC7FC14061278141C6C5B381F01E03807FF80D801 FEC8FC221D7B9B27>85 DI<3CFFF81FFF01FF8001F0495A3C1F0003F000780001801530 5F000F13075F020D495AA2021949C7FC913831F80701C0140602605B000701E0131C02C0 1318D9C1805B13C302005B01C66D5A13E6D803ECEB7D8001F8137F93C8FC49137EA24913 7C49137815386C481330311D7B9B35>I<1330A31260A5133813F81267127FEAFFF01330 12F812E01260AA133813F81267127FEAFFF0133012F812E01260A21300A30D277B9D19> 93 D97 DI<137F3801FFC0EA07C3380F03E0381C07C0EA3C0348C7FC A25AA500701340007813E0383C03C0381FFF00EA07F813127C911B>I103 D<137013F8A213F013E01300A6EA0F80EA1FC0EA31E01261A2EAC3C01203EA0780A3EA0F 001308EA1E18A213301370EA0FE0EA07800D1D7D9C16>105 DIII<3A0F01F807E03A3F87FE1FF83A33 CE1F387C3A63D80F603CD8C3F013C001E01380D803C01300A22607801E5BA3EEF0404848 4814C0ED01E0EEE18016E3001E90397800FF00000C0130137C2A127D9133>I<380F03F0 383F87FC3833DC1EEA63F8EAC3F013E0EA03C0A248485AA3EC7820D80F00136014F015C0 14F1001EEB7F80000CEB3E001B127D9125>I<3803C0F8380FE3FE380CFF0F3918FC0780 3830F80313F01200A23801E007A3EC0F00EA03C0141E6D5A6D5A3807BFE0EB8F800180C7 FCA248C8FCA4EA7FE012FF191A7F911F>112 DI<137E3801FF80EA0381380703C0380E0780EB0300EA0F80EA 07F86CB4FC6C1380EA000FEA3003127812F8EB0700EAF00EEA7FFCEA1FF012127C911C> 115 D<13C0EA01E0A3EA03C0A4EAFFFCA2EA0780A2EA0F00A4121EA31304EA3C0CA21318 1370EA1FE0EA0F800E1A7D9917>I<380F800C381FC01EEA39E012615C12C1EA03C0A25C EA0780A21540ECF0C0A21381903883F1803903FE7F003800F81E1A127D9123>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FH msbm10 10 11 /FH 11 124 df67 D78 D<007FB612C0B712FC6C15 FF2703C01E071380000190393C01C7E00238EBE1F0923800E0F81738EEF03CEE701C171E 170EA7171E171CEEF03CEEE03817F8923801E1F0EEC7E0923803FF80023FB5120016FC16 E00238C8FCB3A60003133C007FB512F0B6FC7E2F397EB834>80 D<913801FFF0021F13FF 027F14C0903A01FFC07FF001079038001FFCD91FFCEB07FFD93F78903803DF80D97C7090 3801C7C0D9F0F0ECE1E0484848903800E0F0D803C1EDF078260781C0EC703C0103ED781C 000F49EC381E000E170ED81E07ED3C0F001C90C8EA1C07003C188000381703007818C000 70170149151E010E150EA200F018E000E01700AB00F01701007018C0A2010F151E6D151C 0078170300381880003C1707001C1800001E6DEC3C0FD80E03ED380E000F171E00076DEC 781C0181ED703C2603C1E0ECF078D801E04B5A6C6C6C903801E1E0D97C70ECC7C0D93F78 903803DF80D91FFC49B4C7FCD907FFEB1FFC01019038C07FF06D6CB512C0021F91C8FC6E 13FC913807001E6F7E6E6C6C7E0201EB03E09238E001F8913B00F000FF01C0037CEB3FFF 6F130F92261F80011380923A07E0007E00923903FC03FC0300B512F0043F13C0DC07FEC7 FC3B4B7DBA35>I<007FB612E0B712FE6C6F7E2703C01E0313E0000190393C00F3F00238 EB70F8EE783CEE381E83EE3C07161C18801703A617071800EE3C0FEE380E173EEE78FCEE F7F892380FFFE0023FB5128004FCC7FC16B8913838F03CED701CED781EED380EED3C0FED 1C07031E7FED0E03030F7FED0701EE81E0ED0380707E030113701778EEE0380300133C70 7EEE700EEE780F9338380780EE3C03041C13C093381E01E00003013C90380E00F0007FB5 39F00FFFFEB67F6C8137397DB836>I<0007B712FC5AA23B0E1FF003C038903A3F000780 7801FC4A5AD80FF0495B49EB0E01D81F80011E5BED3C0390C738380780001E027890C7FC ED700FEDF00E001C903801E01E4B5A02031338C7EB80780207137091380F00F091380E01 E0021E5BEC1C03023C5BEC3807027890C8FC4A5AECE01E0101131CECC03C010313389038 0780784A5A495BEB0E01011E49EB0180D93C0314039038380780017890C7FCD9700F1407 EBF00E3801E01E4948EC0F0000031338D980785C00071370D900F05C48495CD81E0115F7 261C03C0EB01E7003C49495AD83807EC0F8E007890C7EA3F0E4848EB01FEB812FEA33139 7DB83E>90 DI<97B56CF60380077F02FC1E1F061FB76C1DFF0503B800E00A 0F1300057F49C701F8F47FF8932607FFFEC8D807FC983807FF80047F0180DB01FFE17FFC C7FC922607FFF0CAD83F80963803FFE0037F90CBD81FE0DF3FFEC8FC912607FFE0DE07F0 953803FFF0DA3FFECCD803FC067F90C9FC902603FFE0DF00FE943807FFF0011F90CED87F C093B5CAFCD9FFF0E11FF0033F13F0000F90CF6CB46C013FB5CBFCD87FF80A0390B712E0 D8FF800A0004FCCCFC00FCD1001F92CDFC00E00C001480C11380CAC2>94 D<0060150600F8150F6C151F6C153F6C157E6D14FC6DEB01F8D8F7E0EB03F0D8F3F0EB07 E0D8F1F8EB0FC0D8F0FCEB1F80017EEB3F006D137E6D6C5A90380FC1F8903807E3F09038 03F7E06DB45A6D5B6EC7FCA24A7E497F903803F7E0903807E3F090380FC1F890381F80FC 90383F007E017E7F49EB1F80D8F1F8EB0FC0D8F3F0EB07E0D8F7E0EB03F0B448EB01F849 EB00FC90C8127E48153F48151F48150F00601506282874A841>110 D<0060150600F8150F6C151F007E153F6C157F6C6C14FF6C6C5B6C6C5B6C6CEB07EF6C6C EB0FCF6C6CEB1F8F017EEB3F0F6D137E90381F80FC90380FC1F8903807E3F0903803F7E0 903801FFC06D1380EC7F00A2ECFF804913C0903803F7E0903807E3F090380FC1F890381F 80FC90383F007E017E133F49EB1F8F4848EB0FCF4848EB07EF4848EB03FF48487F48487F 48C8127F007E153F48151F48150F00601506282874A841>I<02F815FCD907FCEC01FE01 1F1507013F150F017FED3FF801FFED7FF0D9F81C903801FFC0D801C04A1380D980189038 0FFE004C5AC7EC7FF00238495ADA30035B5DDA701F5B9126603FFBC7FCEDFFE702E113C6 02C7130E903901CFFE0CECBFF8903903FFF01C49EBC018158090390FFE003849481330D9 7FF01403495A00030180EB70074890C7133ED81FFCEC7FFE48485DD8FFE05D495D90C813 C0007E033EC7FC37247CA337>123 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FI cmmi7 7 73 /FI 73 127 df11 DI<137E48B4EB0180000713C0489038E0030048 1406383E01F0393800700C4813380060EB181848131CEC0C305AC75B14065DA3EC0780A2 92C7FCA31406A3140EA2140C141CA45CA31430A2142021267E9923>II18 D21 D<137001F81338157CA248485BA44848485AA44848485A A44848485AEDC180A3001F90380F8300A2141F9038C03786393FE0E7CC9038FFC3FC393E 7F00F090C9FC5AA45AA45A5A21267D9928>II<48B61280000715C04815 80481500263C0C06C7FC127012C0EB1C0EEA0018A21338A2EB701EA313F013E01201141F 120313C0000780A2380F800FA26C486CC7FC221A7D9827>25 D<14FCEB03FF9038078780 90381E03C0EB3C01017813E0A213F0000114F013E01203A23907C003E0A4390F8007C0A2 1580EC0F00EA1F00141E6D5A6D5A383EE1F0EB7FC0011FC7FC90C8FC5AA45AA45A5A1C26 7D9922>I<010FB5FC013F148049140048B6FC2603F07EC7FC3807C01FEA0F80497E5A12 3EA2003C5B127CA30078133E12F8143C0078137C14785C6C485A495A381E0F80D80FFEC8 FCEA03F8211A7D9826>I<48B512F8000714FC4814F84814F0D83C07C7FC1270EAC00613 0E1200A3131E131CA2133CA35BA313F8A3485AA26C5A1E1A7D981F>I<1403A21406A45C A45CA4903807FF80011F13E090387C30F0D801F0133C3803C060D80780131ED80F00131F 48140F003E13C0A25AA239F801801FA3151E903803003E153C157C1578D8780613F0EC01 E0003CEB03C0001EEB0F80390F0C3E003807FFF8000113E0D8000CC7FC5BA45BA45BA220 347CA728>30 D<15185DA45DA45DA44A5AD803E01438D807F01478D80C7814FC39187C03 000030157C163C1260D9F806131C00C01518A2EA01F05C1630EA03E0A24A1360EA07C016 C0ED0180EC30030003EC070001E0130E00015C9038F8607039007E61E090383FFF80D907 FEC7FCEB00C0A4495AA449C8FCA326347DA72C>32 D34 D<157E000349B4FC0006491380484913C048EB0F0391381C01E048EB18005C4A13605A5C A248484813C0A291C7FC49EB018000E01403ED0700D87006130E5D003C143CD83F0E13F8 391FEE07E06CB55A00035CC649C7FCEB1FF0013CC8FCA35BA313F8A35B5B23267C992C> 39 D<1238127C12FEA3127C123807077A8614>58 D<1238127C12FE12FFA2127F123B12 03A31206A3120C121812381270122008127A8614>I<160E163E16FEED03F8ED0FE0ED3F 80EDFE00EC03F8EC0FE0EC3F8002FEC7FCEB03F8EB0FE0EB3F8001FEC8FCEA03F8EA0FE0 EA3F8000FEC9FC12F812FEEA3F80EA0FE0EA03F8EA00FEEB3F80EB0FE0EB03F8EB00FEEC 3F80EC0FE0EC03F8EC00FEED3F80ED0FE0ED03F8ED00FE163E160E27277AA134>II<12E012F812 FEEA3F80EA0FE0EA03F8EA00FEEB3F80EB0FE0EB03F8EB00FEEC3F80EC0FE0EC03F8EC00 FEED3F80ED0FE0ED03F8ED00FE163E16FEED03F8ED0FE0ED3F80EDFE00EC03F8EC0FE0EC 3F8002FEC7FCEB03F8EB0FE0EB3F8001FEC8FCEA03F8EA0FE0EA3F8000FEC9FC12F812E0 27277AA134>I64 D<4B7E1503150782150F151FA2153FA2156F15CF82EC0187140315071406140E140C0218 7FA2EC30031460A214C013011480D903007F91B5FC5B90380C0001A25B13380130805B01 E013005B12011203000F4A7ED8FFF890381FFFE0A22B2A7DA932>I<013FB512F816FF90 3A01FC001FC04AEB07E0EE03F001031401A24A14F8A2130717F04A130317E0010F1407EE 0FC04AEB1F80EE7E00011F495A91B512F0A291388001FC013FEB007E8291C7EA1F80160F 4915C0A2137EA213FEEE1F805BEE3F000001153E16FE49EB01F84B5A0003EC1FC0B7C7FC 15F82D287DA732>I<4AB41308020FEBE01891397F80F038903A01F8001870D903E0EB0C F0D90F80130749C71203013E15E05B491401485A484815C0485A120F5B001F168090C8FC 4892C7FCA2127EA4127C12FCA21606007C5DA35E007E5D123E5E6C5D6C6C495A00074AC7 FCD803E0130E6C6C13383900FE01F090383FFFC0D907FCC8FC2D2A7DA830>I<013FB512 FC16FF903A01FC001FC04AEB03E0EE01F801031400177C4A80A2010781A25CA2130F1880 5CA2011F1600A24A5CA2133F173E91C8127E177C4915FC5F017E14015F01FE4A5AA2494A 5A4C5A00014BC7FC167C495CED03E00003EC1FC0B600FEC8FC15F031287DA736>I<013F B612FCA2903901FC00014AEB007C173C0103153817185CA21307A24A13C0A2010F010113 005E14C01503011F130F91B5C7FCA2EC800F013F7F15061400A249010E13E0030C13C001 7E90C7FC160101FEEC0380A249EC0700A20001150E161E495C16FC0003EC07F8B7FC5E2E 287DA731>I<013FB612F0A2903901FC00074A1301160001031560A25CA21307A25CED01 80010F0103130093C7FC14C05D131F151EECFFFEA290383F801E150C1400A249131C1518 137E92C8FC13FEA25BA21201A25BA21203B512F0A22C287DA72A>I<4AB41308020FEBE0 1891397F80F038903A01F8001870D903E0EB0CF0D90F80130749C71203013E15E05B4914 01485A484815C0485A120F5B001F168090C8FC4892C7FCA2127EA4127C00FC91387FFFE0 A2923800FE00127C5EA21501007E5D123EA27E6C6C495A6C6C13076C6C130FD801F8131C D800FEEBF06090393FFFC020D907FEC8FC2D2A7DA834>I<903B3FFFF01FFFF8A2D901FC C7EAFE004A5CA2010314015F5CA2010714035F5CA2010F14075F5CA2011F140F91B65AA2 913880000F013F141F5F91C7FCA249143F94C7FC137EA201FE5C167E5BA2000115FE5E5B A200031401B539C07FFFE0A235287DA736>I<90383FFFF0A2903801FC005CA21303A25C A21307A25CA2130FA25CA2131FA25CA2133FA291C7FCA25BA2137EA213FEA25BA21201A2 5BA21203B512C0A21C287DA71D>I<90263FFFF0EB7FF8A2D901FCC7EA1FC04AEC1E005F 010315704C5A4AEB03804CC7FC0107141C5E4A13E04B5A010FEB0780030EC8FC4A5A157C 011F13FE14C3EC877F149E90393FB83F8014F09138C01FC0148049486C7EA2017E6D7EA2 01FE6D7EA2496D7EA200016E7EA249147FA2000382B539C007FFF8A235287DA738>75 D<90383FFFF8A2D901FCC7FC5CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133F A291C8FCA249141C1618137E163801FE1430167049146016E000011401ED03C0491307ED 0F800003147FB7FC160026287DA72E>III<013FB512F816FF903A01FC001FC04AEB07 E0EE01F0010315F816005CA2130716015CA2010FEC03F0A24AEB07E0EE0FC0011FEC1F80 EE3E0091388001FC91B512E093C7FCD93F80C8FC91C9FCA35B137EA313FE5BA312015BA2 1203B512C0A22D287DA72A>80 D<4AB4FC021F13E091387E01F8903901F8007ED907E013 1FD90F80EB0F8049C7EA07C0137E49EC03E0485A4915F0484814011207485A4915F8121F 90C8FC5A17F0007E1503A4007CED07E012FC17C0160F1780161F007C1600163E007E157E 003E017C5BD901FE5B3A1F038701F09039070387C03A0F86018F80D807C6019FC7FCD803 F613FC3900FF03F090393FFFC006EB07FDD90001130E6F5A163C6F5AEDFFF85E6E5B5E6F 5A033EC7FC2D347DA834>I<91381FE0089138FFFC18903903E01E389039078007709039 0E0003F0491301491300017814E0137013F0A2000115C0A216007F7F6CB47E14F86DB47E 6D13F06D7F01077F01007F1407EC00FF153F81A3001880A20038141E12300038141C153C 00781438007C5C007E5C0077EB03C026E3E00FC7FC38C0FFFE38801FF0252A7CA829>83 D<000FB712E05A9039800FE007D81E009038C001C05A0038011F1300123000705C006015 01023F148012E0481400A2C74890C7FCA2147EA214FEA25CA21301A25CA21303A25CA213 07A25CA2130FA25CA2131F001FB57EA22B287DA727>I<3B7FFFE003FFF0A2D803F8C7EA 3E0049143C16180007153816305BA2000F157016605BA2001F15E05E5BA2003F14015E90 C7FCA248140393C7FC127EA200FE5C15065AA2150E150C151C5D007C5C5D6C495A003F49 5A261F800FC8FC3807C07C3801FFF038007F802C297BA72D>III<903B3FFF E00FFFC0A2010190390001FC006D4814F017C0027F495A4CC7FC6E130E6F5A021F5B6F5A 5E91380FE1C0EDE380DA07F7C8FC15FE6E5A5D6E7EA2811403EC077F140E4A7E02187FEC 301F02607F14C049486C7EEB030001066D7E5B01386D7E5B01F06D7E485AD80FF0497ED8 FFFC90381FFFE0A232287DA736>II<010FB612C05B9139E0003F800280EB7F00013EC712FE013C495A0138495A 49495A4B5A0160495A01E0495A4949C7FC5D90C75A4A5A4A5A4A5A4A5A4A5A4A5A4AC8FC 14FE495A495A494813304948137049481360133F4A13E049C75A01FE1301485A4848495A 485A484813074848130F4848013FC7FC484848B4FCB7FC5D2A287CA72D>I<12C0AC1303 131F13FF12C7B5FCA213E3130312F812C0B1131F13FF12C7B5FCA213E3130312F812C012 00A710367BA91B>92 D<1306A31218A8EB07C0130F137FEA1BFF121F38FFFE0013F61386 EAFC0612F81218AFEB07C0130F137FEA1BFF121F38FFFE0013F61386EAFC0612F81218A4 90C7FCA312357CA81B>I97 DII<15F8141FA2 EC01F0A21403A215E0A21407A215C0A2140FEB1F8F90387FCF80EBF0EF3803C03FEA0780 390F001F00A2001E5B123E003C133E127C147E5A147CA214FC5AECF830A3903801F060A2 EA7803010E13C0393C1CF980381FF07F3907C01E001D297CA723>I III<133EEA07FEA2EA007CA213FCA25BA21201A25BA2120314FCEB E3FF9038EF0780D807FC13C0EBF00313E0A2EA0FC014071380A2121FEC0F801300A248EB 1F00A2003E1406143E127EEC7C0C127C151800FCEB3C30157048EB1FE00070EB0F801F29 7CA727>I<130E131F5BA2133E131C90C7FCA7EA03E0487EEA0C78EA187C1230A212605B 12C0A2EA01F0A3485AA2485AA2EBC180EA0F81A2381F0300A213066C5A131CEA07F06C5A 11287DA617>I<1407EC0F80141FA21500140E91C7FCA7EB03E0EB07F8EB0C3C1318EB30 3E136013C0A248485AA2C7FCA25CA4495AA4495AA4495AA4495AA21238D87C1FC7FC12FC 133E485AEA70F8EA7FE0EA1F80193380A61B>I<133EEA07FEA2EA007CA213FCA25BA212 01A25BA21203EC07809038E01FC0EC38600007EB61E014C3EBC187EBC307D80FC613C090 38CC038001B8C7FC13E0487E13FEEB3F80EB0FC0486C7E1303003E1460A2127EECC0C012 7CECC18012FC903801E30038F800FE0070137C1B297CA723>I<137CEA0FFCA2EA00F8A2 1201A213F0A21203A213E0A21207A213C0A2120FA21380A2121FA21300A25AA2123EA212 7EA2EA7C18A3EAF830A21320EA786013C0EA3F80EA0F000E297EA715>I<3B07801FC007 E03B0FE07FF01FF83B18F0E0F8783C3B30F1807CE03E903AFB007D801ED860FEEB3F005B 49133E00C14A133E5B1201A24848495BA35F4848485A1830EE01F0A23C0F8003E003E060 A218C0933801E180271F0007C013E3933800FF00000E6D48137C341B7D993B>I<390780 1FC0390FE07FF03918F0E0F83930F1807CEBFB00D860FE133C5B5B00C1147C5B1201A248 485BA34A5AEA07C01660EC03E0A23A0F8007C0C0A2EDC180913803C300D81F0013C7EC01 FE000EEB00F8231B7D9929>I<9038F007C03901FC1FF039031E78780006EBE03C90381F C01C000CEB801E14005B0018141F133E1200137E153E137CA213FC157C5B1578000114F0 A2EC01E0EC03C03903FC07809038FE1F00EBE7FCEBE1F0D807E0C7FCA25BA2120FA25B12 1FEAFFF8A22025809922>112 DI<3807 803E390FE0FF803818F3C13930F703C0EBFE073860FC0F13F8158039C1F0070091C7FC12 01A2485AA4485AA4485AA448C8FCA2120E1A1B7D991F>II<131C133EA25BA45BA4485AB512E0A23801F000485AA4485AA4485AA448C7FC1460A2 14C0123EEB0180EB0300EA1E06EA1F1CEA0FF8EA03E013267EA419>II<3903E001C03907F003E0380C7807EA187C0030130314011260EBF80000C014C0A2 EA01F0A2EC0180EA03E0A2EC0300EA07C0A21406A25CA200035B6D5A3801F0E06CB45A01 3FC7FC1B1B7D9921>II<90387C03C03901FF0FF03907079C30390E03B078000CEBF0F800 1813E1123015F0396007C0E015001200A2495AA449C7FC15301238007C1460EAFC3E15C0 EAF87E39F06F03803970C70700383F83FE381F01F81D1B7D9926>II<013E13C0137F9038FF81 8048EBC3004813FF380701FE3806000C00045BC75A5C5CEB03800106C7FC5B5B5B5B9038 C00180EA038039060003005C380FF81E381FFFFE38383FFC38601FF86D5A38C007C01A1B 7D9920>I<1404140EA2140FEC0780B612C015E015C0C7EA0F80EC1E005C143814101B0D 74A922>126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FJ cmmi10 10 82 /FJ 82 127 df11 DII<1403EC3F F891387FFF80D901E313C014800103133F9138001F80ED070092C7FC80A280A280801301 8080130080147F81143F8149B47E130790380F8FF0EB3E0F496C7E13F83801F003D803E0 7F1207380FC0011380121FEA3F0014005A127EA212FE5D481301A35DA24813035D6C1307 5D127C4A5A6C91C7FC5C6C133E6C6C5A3807C0F03801FFE0D8003FC8FC223D7DBB25>I< EC3FF0EB01FF010F13E090383FC00049C7FC13FCEA03F8485A5B120F485AA2485AA2387F FFFE80A290C8FC5A5AA5127EA4123E123F7E6C6C13606D13E03903E003C03901F01F0038 007FFCEB0FE01C257DA322>I<1406A6ED7FC0913807FFE0ED806091381FFFE091383C7F 8002F0C7FC495A495A495A49C8FC130E131E5B5B5BA2485AA2485A485AA248C9FCA3121E A2123E123CA3127C1278A412F8A57EA2127C127E127F7F6C7E13F0EA1FFE380FFFC06C13 F86C13FEC66D7E013F7F01077F1300EC1FF0140714031401A35DA290381803C0131C9038 0F0780D903FEC7FCEB00F8234B7CB924>III<133F14C0EB07F06D7E801301A26D7EA3147FA36E7EA36E7EA3 6E7EA36E7EA36E7EA36E7EA26E7EA214014A7E5C4A7E91381E3F80143C14784A6C7E1301 EB03E049486C7EEB0F80EB1F00496D7E137E5B48486D7E485A485A000F6E7E485A485A48 C87E12FE167F4816800070151F293B7CB930>21 DI<017E1438D83FFE147E16FEA2 D801FC14FC12000001140116F85BED03F0120315074914E0150F000715C0ED1F805BED3F 00000F147EA2495B4A5A001F495A5D49485A4A5A003F49C7FC143EEB00F8495A48485AEB 0F80D87E3EC8FC13F8EAFFE0138000F8C9FC27257CA429>I<1406A6913807FFC04A13E0 91383F80609138FDFFE0903903F87F804948C7FC495A495A495A137F91C8FC5B5B1201A2 5BA512007F137E90383F3FF090381FFFFC90380FC01C90381FFFF890383C7FE001F0C8FC 485A485A485AA248C9FC121EA25AA2127C1278A312F87EA2127E127F7FEA3FE013FC6CB4 FC6C13E06C13F8000113FF6C6C13C0010F13F001037FEB007F140F14031400A4010C5BEB 0E0190380783E0903801FF80D9007EC7FC234B7EB924>I<013FB612E090B712F05A1207 17E0270F807006C7FC391E00600E48140C003813E04813C048141CEAC001120014800103 5BA213071400A25B1578011E137CA3133E133C137C157E13FC5B1201157F1203497FA3D8 01C0131C2C257EA32F>I<15FE913803FF8091380F83E091383E01F091387C00F85C4948 13FC0103147C4948137E5C130F495AA249C7FC16FE5B137EA2150113FE4914FCA2000114 0316F85BED07F01203ED0FE04914C0151F000715806DEB3F00157E6D5B390FEE01F09038 E707E09038C3FF80D9C0FCC7FC001F90C8FCA25BA2123FA290C9FCA25AA2127EA212FEA2 5AA2127027377EA42B>I<027FB512C00103B612E0130F5B017F15C09026FF81FEC7FC39 01FC007E48487F485A497F484880485AA248C7FCA2127EA2153F00FE92C7FC5AA25D157E 5A5DA24A5AA24A5A007C495A5D003C495A003E013FC8FC6C137C380F81F83803FFE0C66C C9FC2B257DA32F>I<013FB512FE90B7FC5A5A4815FE260F801CC7FCEA1E005A00385B5A 5A481378C7FC147014F0A4495AA31303A3495AA3130FA25C131FA3133FA291C8FC131E28 257EA324>I<1503A35DA21506A2150EA2150CA2151CA21518A21538A21530A21570A2EC 07FE91383FFFC0903901FCE3F0903907E0E0F890391F80C03ED93E007FEB7C01D801F8EC 0F80D803F0018013C0D807E014071403D80FC015E0D81F801300A248485AA2007E1306A2 020E130F12FE48010C14C0A2021CEB1F80A20218EB3F00A20238137E007C5D1430007E4A 5A003E90387003F06CEC07C09138600F80D80F80013FC7FC3903E0E0FC3901F8E7F03900 7FFF80D90FFCC8FCEB01C0A25CA21303A291C9FCA25BA21306A2130EA2130CA22B4B7CB9 31>30 DI<160C161C1618A316 381630A316701660A316E05EA315015EA301F80103130FD803FE9138001F80D8070F153F 000E018015C0001C5C001814060038161F0030160FD8701F010E13070060140C1703D8E0 3F168000C0EB001C491318EA007E180001FE13384913305F000116064913700360130E5F 000316184901E013384B133017705F0201495AD801F849485A4CC7FC160E2600FC035B01 7EEB0078013FEB01E090390FE30F80902603FFFEC8FC9038003FF00206C9FCA2140E140C A3141C1418A314381430A314701460324B7EB936>I 34 D39 D<13F8EA03FC120FEA1FF8EA3F80EA7E00127C5AA25AA47EA2127C 127EEA3F80EA1FF8EA0FFC1203EA00F80E167CA817>44 D<121C127FEAFF80A5EA7F0012 1C0909798817>58 D<121C127FEAFF80A213C0A3127F121C1200A412011380A212031300 5A1206120E5A5A5A12600A19798817>II<150C151E153EA2153C157CA2157815F8A215F01401A215E01403A2 15C01407A21580140FA215005CA2141E143EA2143C147CA2147814F8A25C1301A25C1303 A2495AA25C130FA291C7FC5BA2131E133EA2133C137CA2137813F8A25B1201A25B1203A2 5B1207A25B120FA290C8FC5AA2121E123EA2123C127CA2127812F8A25A12601F537BBD2A >I<126012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF903800 7FC0EC1FF0EC07FCEC01FF9138007FC0ED1FF0ED07FCED01FF9238007FC0EE1FF0EE07FC EE01FF9338007F80EF1FC0A2EF7F80933801FF00EE07FCEE1FF0EE7FC04B48C7FCED07FC ED1FF0ED7FC04A48C8FCEC07FCEC1FF0EC7FC04948C9FCEB07FCEB1FF0EB7FC04848CAFC EA07FCEA3FF0EA7FC048CBFC12FC1270323279AD41>I64 D<1760177017F01601A21603A21607160FA24C7EA216331673166316C3A2ED0183A2ED03 03150683150C160115181530A21560A215C014011580DA03007FA202061300140E140C5C 021FB5FC5CA20260C7FC5C83495A8349C8FC1306A25BA25B13385B01F01680487E000716 FFB56C013F13FF5EA2383C7DBB3E>I<0103B77E4916F018FC903B0007F80003FE4BEB00 FFF07F80020FED3FC0181F4B15E0A2141FA25DA2143F19C04B143F1980027F157F190092 C812FE4D5A4A4A5AEF0FF04AEC1FC005FFC7FC49B612FC5F02FCC7B4FCEF3FC00103ED0F E0717E5C717E1307844A1401A2130F17035CA2131F4D5A5C4D5A133F4D5A4A4A5A4D5A01 7F4BC7FC4C5A91C7EA07FC49EC3FF0B812C094C8FC16F83B397DB83F>I<9339FF8001C0 030F13E0037F9038F80380913A01FF807E07913A07F8000F0FDA1FE0EB079FDA3F809038 03BF0002FFC76CB4FCD901FC80495A4948157E495A495A4948153E017F163C49C9FC5B12 01484816385B1207485A1830121F4993C7FCA2485AA3127F5BA312FF90CCFCA41703A25F 1706A26C160E170C171C5F6C7E5F001F5E6D4A5A6C6C4A5A16076C6C020EC8FC6C6C143C 6C6C5C6CB4495A90393FE00FC0010FB5C9FC010313FC9038007FC03A3D7CBA3B>I<0103 B7FC4916E018F8903B0007F80007FE4BEB00FFF03F80020FED1FC0180F4B15E0F007F002 1F1503A24B15F81801143F19FC5DA2147FA292C8FCA25C18035CA2130119F84A1507A213 0319F04A150FA2010717E0181F4A16C0A2010FEE3F80A24AED7F00187E011F16FE4D5A4A 5D4D5A013F4B5A4D5A4A4A5A057FC7FC017F15FEEE03FC91C7EA0FF049EC7FC0B8C8FC16 FC16C03E397DB845>I<0103B812F05BA290260007F8C7123F4B1407F003E0020F150118 005DA2141FA25D19C0143FA24B1330A2027F1470190092C7126017E05C16014A495A160F 49B6FCA25F9138FC000F01031407A24A6DC8FCA201075C18034A130660010F160693C7FC 4A150E180C011F161C18184A1538A2013F5E18F04A4A5AA2017F15074D5A91C8123F4991 3803FF80B9FCA295C7FC3C397DB83D>I<0103B812E05BA290260007F8C7123F4B140FF0 03C0140F18015DA2141FA25D1980143FA25D1760027F14E095C7FC92C75AA24A1301A24A 495A16070101141F91B6FC94C8FCA2903903FC001F824A130EA21307A24A130CA2010F14 1CA24A90C9FCA2131FA25CA2133FA25CA2137FA291CBFC497EB612C0A33B397DB835>I< DCFF8013E0030F13F0037F9038FC01C0913A01FF803E03913A07FC000F07DA0FE0EB038F DA3FC0903801DF804AC812FFEB01FED903F8157F4948ED3F00495A495A494881017F161E 49C9FC5B12014848161C5B1207485A1818121F4993C7FCA2485AA3127F5BA312FF90CCFC 93387FFFFE93B5FCA29338007FC0715A177F95C7FCA27E5F5F7F123F16016C7E5F6C6C14 036D14071207D803FCEC1EF86C6C143C26007F80EBF07890393FF007E0010FB5EA803001 0349C9FC9038003FE03B3D7DBA41>I<0103B5D8F803B512F8495DA290260007F8C73807 F8004B5DA2020F150F615DA2021F151F615DA2023F153F615DA2027F157F96C7FC92C8FC A24A5D605CA249B7FC60A202FCC7120101031503605CA201071507605CA2010F150F605C A2011F151F605CA2013F153F605CA2017F157F95C8FC91C8FC496C4A7EB690B6FCA34539 7DB845>I<0107B512FCA216F890390007F8005DA2140FA25DA2141FA25DA2143FA25DA2 147FA292C7FCA25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2 133FA25CA2137FA291C8FC497EB6FCA326397DB824>I<0203B512FCA3DA000113006F5A A215015EA315035EA315075EA3150F5EA3151F5EA3153F5EA3157F93C7FCA35D5DA31401 A25DA21403120FD83F805B127FEBC007D8FF805BA24A5AEB001F00FC5C00E0495A006049 C8FC007013FE383801F8381E07F03807FFC0D801FEC9FC2E3B7AB82E>I<0103B500F890 3807FFFC5BA290260007F8C813804BEDFC0019F0020F4B5AF003804B4AC7FC180E021F15 38604B5CEF0380023F4AC8FC170E4B133C1770027F5C4C5ADB0007C9FC160E4A5B167E4A 13FE4B7E01015B92380E7F80ECFC1CED383F010301E07FECFDC04A486C7EECFF00D907FC 6D7E5C4A130783130F707E5C1601011F81A24A6D7EA2013F6F7EA24A143F84137F717E91 C8123F496C81B60107B512C0A26146397DB847>I<0103B6FC5B5E90260007FCC8FC5D5D 140FA25DA2141FA25DA2143FA25DA2147FA292C9FCA25CA25CA21301A25CA21303A25CA2 130718404A15C0A2010F150118804A1403A2011F16005F4A1406170E013F151E171C4A14 3C177C017F5D160391C7120F49EC7FF0B8FCA25F32397DB839>I<902603FFF893383FFF 80496081D900079438FF80000206DC01BFC7FCA2020E4C5A1A7E020C1606190CDA1C7E16 FE4F5A02181630A20238166162023016C1F00181DA703F158395380303F002601506A202 E0ED0C076202C01518183001016D6C140F06605B028015C0A20103923801801FDD03005B 140092380FC00649173F4D91C8FC01065DA2010E4B5B4D137E130C6F6C5A011C17FEDCE1 805B011802E3C7FCA2013802E6130104EC5C1330ED03F8017016034C5C01F05CD807FC4C 7EB500E0D9C007B512F01680150151397CB851>I<902603FFF891381FFFF8496D5CA2D9 0007030113006FEC007C02061678DA0EFF157081020C6D1460A2DA1C3F15E0705CEC181F 82023815016F6C5C1430150702706D1303030392C7FC02607FA2DAE0015C701306ECC000 8201016E130EEF800C5C163F0103EDC01C041F131891C713E0160F49EDF0381830010614 0717F8010E02031370EFFC60130CEE01FE011C16E004005B011815FF177F133860013015 3FA20170151F95C8FC01F081EA07FCB512E01706A245397DB843>I<4BB4FC031F13F092 38FE01FC913903F0007EDA07C0EB1F80DA1F80EB0FC0023EC7EA07E002FCEC03F0495A49 48EC01F8495A4948EC00FC495A49C912FE49167E13FE49167F1201485AA2485AA2120F5B 001F17FFA2485AA34848ED01FEA400FFEE03FC90C9FCA2EF07F8A2EF0FF0A218E0171F18 C0EF3F806C167F180017FE4C5A6C6C5D1603001F4B5A6D4A5A000FED1F806C6C4AC7FC6D 147E0003EC01F8D801FC495AD8007EEB0FC090263F807FC8FC903807FFF801001380383D 7CBA3F>I<0103B7FC4916E018F8903B0007F80007FC4BEB00FE187F020FED3F80F01FC0 5DA2021F16E0A25DA2143FF03FC05DA2027FED7F80A292C8130018FE4A4A5A604AEC07F0 4D5A0101ED3FC04CB4C7FC91B612FC17E0D903FCCAFCA25CA21307A25CA2130FA25CA213 1FA25CA2133FA25CA2137FA291CBFC497EB6FCA33B397DB835>I<4BB4FC031F13F09238 FE01FC913903F0007EDA07C0EB1F80DA1F80EB0FC0023EC7EA07E002FCEC03F0495A4948 EC01F8495A4948EC00FC495A013F16FE49C9FC13FE187F485A12035B12075B120F4916FF 121FA2485AA34848ED01FEA448C9EA03FCA3EF07F8A218F0170F18E0171F18C0EF3F807E EF7F0017FEDA07C05B6C90391FF001F8903980383803001F496C485A9139E00C0FE0260F C0C0EB1F80D807E1D90E3FC7FC0280137ED803F1EB07F8D801F95C3A007FC00FC0903A3F E07F0003903807FFFE0100018F5BDA000F1306170E171E705A177CEEC1F816FF5FA25F5F 6F5B6F48C7FCED00F8384B7CBA42>I<0103B612F849EDFF8018E0903B0007F8001FF84B EB03FCEF00FE020F157FA24BEC3F80A2021F16C0A25DA2143FF07F805DA2027FEDFF0060 92C7485A4D5A4A4A5A4D5A4AEC1F80057FC7FC0101EC07F891B612E094C8FC9139FC000F C00103EC03F0707E4A6D7E831307177E5C177F010F5D5F5CA2011F1401A25CA2133F1603 4A4A1360A2017F17E019C091C71401496C01011480B61503933900FE0700EF7E0ECAEA1F FCEF07F03B3B7DB83F>I<92391FE00380DBFFFC130002036D5A91390FE01F8F91393F00 07DF027EEB01FE02F81300495A4948147E177C4948143C495AA2011F153891C8FCA34915 30A28094C7FC80806D7E14FEECFFE06D13FE6DEBFFC06D14F06D806D80021F7F02037FEC 003F03037F1500167F163F161FA3120C160FA2001C151F94C7FCA3003C153EA25E003E5D 127E007F4A5A6D495A6DEB0FC0D8F9F0495AD8F0FE01FEC8FC39E03FFFF8010F13E0D8C0 0190C9FC313D7CBA33>I<0003B812FEA25A903AF8003FC00101C0913880007E4848163C 90C7007F141C121E001C92C7FCA2485CA200305C007017180060130112E0485CA21403C7 16005DA21407A25DA2140FA25DA2141FA25DA2143FA25DA2147FA292C9FCA25CA25CA213 01A25CA21303A25CEB0FFC003FB6FC5AA237397EB831>I<003FB56C48B51280485DA226 007F80C7381FF00091C8EA07C0604993C7FCA2491506A20001160E170C5BA20003161C17 185BA20007163817305BA2000F167017605BA2001F16E05F5BA2003F15015F5BA2007F15 0394C8FC90C8FCA25E4815065A160E160C161C161816385E127E5E4B5A6C4A5A4BC9FC6C 6C131E6C6C5B6C6C13F83903F807E06CB55A6C6C48CAFCEB0FF0393B7BB839>I<267FFF FC91383FFFC0B55DA2000390C83807FC006C48ED03E06060000094C7FC5F17065FA25F6D 5DA26D5D17E05F4C5AA24CC8FC6E1306A2013F5C161C16185EA25E6E5BA2011F495A1503 93C9FC1506A25D6E5AA2010F5B157015605DA2ECE18002E3CAFC14F3EB07F614FE5C5CA2 5C5CA26D5AA25C91CBFC3A3B7CB830>I<277FFFFC01B500F890B51280B5FC60000390C7 D807FCC7380FF80001FC4BEC03E000016204035E98C7FC621A0604075DA2040F5DA2041B 5D6216336D02735D1663000003C34A5A83DB01834AC8FC04815CDB0301140603075D1506 030C5DA203185D1970033015606115606D01E04A5A15C090267F01804AC9FC17FEDA0300 14060400130E0206150C020E5D140C4A5DA24A5D18E04A5D715A5C4A92CAFCA26DC85AA2 013E157C1778133C1770133801301560513B7CB84E>I<49B500F890387FFFF095B5FC1A E0D90003018090380FFC004BC713E00201ED07804EC7FC6E6C140E606F5C705B606F6C48 5A4D5A031F91C8FCEEE0065F6F6C5A5F03075B705A16F96FB45A94C9FC6F5AA36F7EA34B 7FED037F9238063FC0150E4B6C7E1538ED700F03E07F15C04A486C7EEC0300020613034A 805C4A6D7E14704A1300494880495A49C86C7E130E011E153F017E4B7ED803FF4B7E007F 01E0011FEBFFC0B5FC6144397EB845>II<91B7 12FCA25B9239E00007F84AC7EA0FF0D903F8EC1FE04AEC3FC04AEC7F804A150049485C91 C7485A4C5A010E4A5A4C5A010C4A5A011C4A5A01185D167F4CC7FC90C7485A4B5A4B5A4B 5A5E151F4B5A4B5A4BC8FC4A5A4A5A4A5A5D140F4A5A4A5A4A48130C4AC7FC495A4A141C 01031518495A494814384948143049481470495A49C812F0495D00011501484814034848 4A5A4848140F4848141F4848EC7F804848EB07FF90B7FCB8FC94C7FC36397BB839>I<12 C0B21460EB03E0130F137FEAC1FF12C7B5FCA2EBFC6013F013C0EAFE0012F812C0B3A6EB 03E0130F137FEAC1FF12C7B5FCA2EBFC6013F013C0EAFE0012F812C0C7FCAB134F7ABC20 >92 D<147E903803FF8090390FC1C38090391F00EFC0017E137F49133F485A4848EB1F80 12075B000F143F48481400A2485A5D007F147E90C7FCA215FE485C5AA214015D48150CA2 1403EDF01C16181407007C1538007E010F1330003E131F027B13706C01E113E03A0F83C0 F9C03A03FF007F80D800FCEB1F0026267DA42C>97 D<133FEA1FFFA3C67E137EA313FE5B A312015BA312035BA31207EBE0FCEBE3FF9038E707C0390FFE03E09038F801F001F013F8 EBE000485A15FC5BA2123F90C7FCA214015A127EA2140312FE4814F8A2140715F05AEC0F E0A215C0EC1F80143F00781400007C137E5C383C01F86C485A380F07C06CB4C7FCEA01FC 1E3B7CB924>II<163FED1FFFA3ED007F167EA216FEA216FCA21501A216F8A21503A216 F0A21507A2027E13E0903803FF8790380FC1CF90381F00EF017EEB7FC049133F485A4848 131F000715805B000F143F485A1600485A5D127F90C7127EA215FE5A485CA21401A248EC F80CA21403161CEDF0181407007C1538007E010F1330003E131F027B13706C01E113E03A 0F83C0F9C03A03FF007F80D800FCEB1F00283B7DB92B>II<16F8ED03FEED0F87 92381F0F80ED3E3F167F157CA215FC1700161C4A48C7FCA414035DA414075DA20107B512 F0A39026000FE0C7FC5DA4141F5DA4143F92C8FCA45C147EA514FE5CA413015CA4495AA4 5C1307A25C121E123F387F8F80A200FF90C9FC131E12FEEA7C3CEA7878EA1FF0EA07C029 4C7CBA29>III<14E0EB03F8A21307A314F0EB01C0 90C7FCAB13F8EA03FEEA070F000E1380121C121812381230EA701F1260133F00E0130012 C05BEA007EA213FE5B1201A25B12035BA20007131813E01438000F133013C01470EB8060 14E014C01381EB838038078700EA03FEEA00F815397EB71D>I<150FED3F80A2157FA316 00151C92C7FCABEC0F80EC3FE0ECF0F0903801C0F849487E14005B130E130C131CEB1801 133801305BA2EB0003A25DA21407A25DA2140FA25DA2141FA25DA2143FA292C7FCA25CA2 147EA214FEA25CA21301001E5B123F387F83F0A238FF87E0495A00FE5BD87C1FC8FCEA70 7EEA3FF8EA0FC0214981B722>IIIIII<90390F8003F090391FE00FFC 903939F03C1F903A70F8700F80903AE0FDE007C09038C0FF80030013E000014913030180 15F05CEA038113015CA2D800031407A25CA20107140FA24A14E0A2010F141F17C05CEE3F 80131FEE7F004A137E16FE013F5C6E485A4B5A6E485A90397F700F80DA383FC7FC90387E 1FFCEC07E001FEC9FCA25BA21201A25BA21203A25B1207B512C0A32C3583A42A>I<02FC 13C0903803FF0190380F838390383F01C790397E00EF8049137F485A4848133F00071500 5B485A001F5C157E485AA2007F14FE90C75AA3481301485CA31403485CA314075D140F12 7C141F007E495A003E137F381F01EF380F839F3903FF1F80EA00FC1300143F92C7FCA35C 147EA314FE5C130190387FFFF0A322357DA425>I<3903E001F83907F807FE390E3C1E07 391C3E381F3A183F703F800038EBE07F0030EBC0FF00705B00601500EC007E153CD8E07F 90C7FCEAC07EA2120013FE5BA312015BA312035BA312075BA3120F5BA3121F5B0007C9FC 21267EA425>I<14FF010313C090380F80F090383E00380178131C153C4913FC00011301 13E0A33903F000F06D13007F3801FFE014FC14FF6C14806D13C0011F13E013039038003F F014071403001E1301127FA24814E0A348EB03C012F800E0EB07800070EB0F006C133E00 1E13F83807FFE0000190C7FC1E267CA427>II<13F8D803FE1438D8070F147C000E6D13FC121C1218003814011230 D8701F5C12601503EAE03F00C001005B5BD8007E1307A201FE5C5B150F1201495CA2151F 120349EC80C0A2153F1681EE0180A2ED7F0303FF130012014A5B3A00F8079F0E90397C0E 0F1C90393FFC07F8903907F001F02A267EA430>I<01F8EB03C0D803FEEB07E0D8070F13 0F000E018013F0121C12180038140700301403D8701F130112601500D8E03F14E000C090 C7FC5BEA007E16C013FE5B1501000115805B150316001203495B1506150E150C151C1518 15385D00015C6D485A6C6C485AD97E0FC7FCEB1FFEEB07F024267EA428>I<01F816F0D8 03FE9138E001F8D8070F903801F003000ED9800314FC121C12180038020713010030EDE0 00D8701F167C1260030F143CD8E03F163800C001005B5BD8007E131F183001FE5C5B033F 1470000117604991C7FCA218E000034A14C049137E17011880170318005F03FE1306170E 000101015C01F801BF5B3B00FC039F8070903A7E0F0FC0E0903A1FFC03FFC0902703F000 7FC7FC36267EA43B>I<903907E001F090391FF807FC9039783E0E0F9039E01F1C1FD801 C09038383F803A03800FF07F0100EBE0FF5A000E4A1300000C157E021F133C001C4AC7FC 1218A2C7123FA292C8FCA25CA2147EA214FEA24A130CA20101141C001E1518003F5BD87F 81143801835C00FF1560010714E03AFE0E7C01C0D87C1C495A2778383E0FC7FC391FF00F FC3907C003F029267EA42F>I<13F8D803FE1470D8070F14F8000EEB8001121C12180038 1403003015F0EA701F1260013F130700E0010013E012C05BD8007E130F16C013FE5B151F 000115805BA2153F000315005BA25D157EA315FE5D1401000113033800F80790387C1FF8 EB3FF9EB0FE1EB00035DA2000E1307D83F805B007F495AA24A5A92C7FCEB003E007C5B00 705B6C485A381E07C06CB4C8FCEA01FC25367EA429>II<1504151E151FA2ED0F8016C0ED07E0007FB612F0B712F8A26C 15F0C8EA1FC0ED3F00157E5D5D5D1560251271BB2A>126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FK cmbx10 10 72 /FK 72 128 df<913803FFC0027F13F00103B512FC010FEB00FED93FF8133FD97FE0EBFF 8049485A5A1480484A13C04A6C1380A36F1300167E93C7FCA592383FFFC0B8FCA4000390 C7FCB3ABB5D8FC3F13FFA4303A7EB935>12 D<912603FFC0EB7FF8027F9039F00FFFFE49 B5D8FC7F6D7E010F903B007FFFE01FC0D91FF8011F90380007E0D97FE0D97FFCEB1FF049 484948133F485C02805C484E7E02004A6D5AA281735A047F6E5A96C8FCA5953807FFF8BB FCA4000390C7397FE0001FB3ABB5D8FC1FB50087B512E0A44B3A7EB950>14 D33 D39 D<141C143C14F8EB01F0EB03E01307EB0FC0EB1F8014005B137E13FE5B12015B1203A248 5AA2120F5B121FA25B123FA4485AA512FFB1127FA56C7EA4121F7FA2120F7F1207A26C7E A212017F12007F137E7F7F1480EB0FC0EB07E01303EB01F0EB00F8143C141C165377BD25 >I<12E07E127C7E7E7F6C7E6C7E12037F6C7E7F12007F137E137FA2EB3F80A214C0131F 14E0A2130F14F0A4EB07F8A514FCB114F8A5EB0FF0A414E0131FA214C0133F1480A2EB7F 00A2137E13FE5B12015B485A5B1207485A485A90C7FC123E5A12F05A16537BBD25>I43 DIII<141E 143E14FE1307133FB5FCA313CFEA000FB3B3A6007FB61280A4213779B630>49 DIII<001C15C0D81F80 130701F8137F90B61280A216005D5D15F05D15804AC7FC14F090C9FCA8EB07FE90383FFF E090B512F89038FC07FC9038E003FFD98001138090C713C0120EC813E0157F16F0A216F8 A21206EA3F80EA7FE012FF7FA44914F0A26C4813FF90C713E0007C15C06C5B6C491380D9 C0071300390FF01FFE6CB512F8000114E06C6C1380D90FF8C7FC25387BB630>II<123C123EEA3FE090B71280A41700485D5E5E 5EA25E007CC7EA0FC000784A5A4BC7FC00F8147E48147C15FC4A5A4A5AC7485A5D140F4A 5A143F92C8FC5C147E14FE1301A2495AA31307A2130F5CA2131FA5133FA96D5A6D5A6D5A 293A7BB830>I<49B47E010F13F0013F13FC9038FE01FF3A01F8007F804848EB3FC04848 EB1FE0150F485AED07F0121FA27FA27F7F01FEEB0FE0EBFF809138E01FC06CEBF03F02FC 13809138FF7F006C14FC6C5C7E6C14FE6D7F6D14C04914E048B612F0EA07F848486C13F8 261FE01F13FC383FC007EB8001007F6D13FE90C7123F48140F48140715031501A21500A2 16FC7E6C14016D14F86C6CEB03F06D13076C6CEB0FE0D80FFEEB7FC00003B61200C614FC 013F13F00103138027387CB630>III65 DII< B87E17F817FF18C028007FF8000713F09338007FF8EF1FFE717E050313807113C0A27113 E0F07FF0A2F03FF8A219FC181FA219FEA419FFAC19FEA419FC183FA219F8187F19F0F0FF E0A24D13C04D13804D1300EF1FFEEF7FFC933807FFF0B912C095C7FC17FC178040397DB8 49>IIIIII<010FB612C0A4D90001EBE000B3B3EA0F80 EA3FE0EA7FF0A2EAFFF8A35E5C13F0007F495BD83FE091C7FC391F800FFE390FF03FFC6C B512F0000114C026003FFCC8FC2A3A7FB831>IIIIIIIIII<003FB91280A4D9F800EBF003D87FC09238007F C049161F007EC7150FA2007C1707A200781703A400F818E0481701A4C892C7FCB3AE010F B7FCA43B387DB742>IIII89 D<003FB712FEA4913980007FFC01FCC7EA FFF801F05B01C015F0494913E090C75A4816C0007E4A13805D007C16004B5A157F00785D 4B5A5C5EC7485B5C5E5C4A5B93C7FC5C4A5A5D14FF495B5D5B495B4B131E5B5D4990C7FC 5B5C4948143E13FF5C485B48167E4A147C484914FC5A4A13014890C7120348150F49143F 4848EB01FFB8FCA42F397BB83A>I97 D<13FFB5FCA412077EAF4AB47E020F 13F0023F13FC9138FE03FFDAF00013804AEB7FC00280EB3FE091C713F0EE1FF8A217FC16 0FA217FEAA17FCA3EE1FF8A217F06E133F6EEB7FE06E14C0903AFDF001FF80903AF8FC07 FE009039F03FFFF8D9E00F13E0D9C00390C7FC2F3A7EB935>I<903801FFC0010F13FC01 7F13FFD9FF8013802603FE0013C048485AEA0FF8121F13F0123F6E13804848EB7F00151C 92C7FC12FFA9127FA27F123FED01E06C7E15036C6CEB07C06C6C14806C6C131FC69038C0 7E006DB45A010F13F00101138023257DA42A>II<903803FF80011F13F0017F13FC3901FF83FE3A03FE 007F804848133F484814C0001FEC1FE05B003FEC0FF0A2485A16F8150712FFA290B6FCA3 01E0C8FCA4127FA36C7E1678121F6C6C14F86D14F000071403D801FFEB0FE06C9038C07F C06DB51200010F13FC010113E025257DA42C>II<161FD907FEEBFFC090387FFFE348B6EAEFE02607 FE07138F260FF801131F48486C138F003F15CF4990387FC7C0EEC000007F81A6003F5DA2 6D13FF001F5D6C6C4890C7FC3907FE07FE48B512F86D13E0261E07FEC8FC90CAFCA2123E 123F7F6C7E90B512F8EDFF8016E06C15F86C816C815A001F81393FC0000F48C813804815 7F5A163FA36C157F6C16006D5C6C6C495AD81FF0EB07FCD807FEEB3FF00001B612C06C6C 91C7FC010713F02B377DA530>I<13FFB5FCA412077EAFED7FC0913803FFF8020F13FE91 381F03FFDA3C01138014784A7E4A14C05CA25CA291C7FCB3A3B5D8FC3F13FFA4303A7DB9 35>II<141FEC7FC0ECFFE0A24913F0A56D13E0A2EC7FC0EC1F0091C7 FCA9EC0FF0EB0FFFA4EB007F143FB3B0121FEA3F80EA7FC0EAFFE0EC7FE0A215C014FF6C 481380903883FE006CB45A000F13F0000113801C4B86BA1D>I<13FFB5FCA412077EAF92 380FFFE0A4923803FC0016F0ED0FE0ED1F804BC7FC157E5DEC03F8EC07E04A5A141FEC7F E04A7E8181A2ECCFFEEC0FFF496C7F806E7F6E7F82157F6F7E6F7E82150F82B5D8F83F13 F8A42D3A7EB932>I<13FFB5FCA412077EB3B3ACB512FCA4163A7DB91B>I<01FED97FE0EB 0FFC00FF902601FFFC90383FFF80020701FF90B512E0DA1F81903983F03FF0DA3C009038 87801F000749DACF007F00034914DE6D48D97FFC6D7E4A5CA24A5CA291C75BB3A3B5D8FC 1FB50083B512F0A44C257DA451>I<01FEEB7FC000FF903803FFF8020F13FE91381F03FF DA3C011380000713780003497E6D4814C05CA25CA291C7FCB3A3B5D8FC3F13FFA430257D A435>I<903801FFC0010F13F8017F13FFD9FF807F3A03FE003FE048486D7E48486D7E48 486D7EA2003F81491303007F81A300FF1680A9007F1600A3003F5D6D1307001F5DA26C6C 495A6C6C495A6C6C495A6C6C6CB45A6C6CB5C7FC011F13FC010113C029257DA430>I<90 39FF01FF80B5000F13F0023F13FC9138FE07FFDAF00113800007496C13C06C0180EB7FE0 91C713F0EE3FF8A2EE1FFCA3EE0FFEAA17FC161FA217F8163F17F06E137F6E14E06EEBFF C0DAF00313809139FC07FE0091383FFFF8020F13E0020390C7FC91C9FCACB512FCA42F35 7EA435>I<49B4EB0780010FEBE00F013FEBF81F9039FFC07C3F0003EB803E3A07FE000F 7F4848EB07FF121F497F123F497F127FA25B12FFAA6C7EA36C7E5D6C7E000F5C6C6C5B6C 6C133F6CEBC0FD39007FFFF1011F13C10101130190C7FCAC037F13FEA42F357DA432>I< 9038FE03F000FFEB0FFEEC3FFF91387C7F809138F8FFC000075B6C6C5A5CA29138807F80 ED3F00150C92C7FC91C8FCB3A2B512FEA422257EA427>I<90383FF0383903FFFEF8000F 13FF381FC00F383F0003007E1301007C130012FC15787E7E6D130013FCEBFFE06C13FCEC FF806C14C06C14F06C14F81203C614FC131F9038007FFE140700F0130114007E157E7E15 7C6C14FC6C14F8EB80019038F007F090B512C000F8140038E01FF81F257DA426>I<130F A55BA45BA25B5BA25A1207001FEBFFE0B6FCA3000390C7FCB21578A815F86CEB80F01481 6CEBC3E090383FFFC06D1380903803FE001D357EB425>I<01FFEC3FC0B5EB3FFFA40007 14016C80B3A35DA25DA26C5C6E4813E06CD9C03E13FF90387FFFFC011F13F00103138030 257DA435>IIIII<003FB612 C0A3D9F0031380EB800749481300003E5C003C495A007C133F5D0078495A14FF5D495B5B C6485B92C7FC495A131F5C495A017FEB03C0EBFFF014E04813C05AEC80074813005A49EB 0F80485A003F141F4848133F9038F001FFB7FCA322257DA42A>I<390F8003E0393FC007 F8EBE00F397FF01FFC00FF14FEA4007F14FC393FE00FF8EBC007390F8003E01F0C78BA30 >127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FL cmsy10 10 59 /FL 59 117 df<007FB81280B912C0A26C17803204799641>0 D<121C127FEAFF80A5EA 7F00121C0909799917>I<0060150600F8150F6C151F007E153F6C157E6C6C14FC6C6CEB 01F86C6CEB03F06C6CEB07E06C6CEB0FC06C6CEB1F80017EEB3F006D137E6D6C5A90380F C1F8903807E3F0903803F7E06DB45A6D5B6EC7FCA24A7E497F903803F7E0903807E3F090 380FC1F890381F80FC90383F007E017E7F49EB1F804848EB0FC04848EB07E04848EB03F0 4848EB01F84848EB00FC48C8127E007E153F48151F48150F00601506282874A841>II<15301578 B3A6007FB812F8B912FCA26C17F8C80078C8FCB3A3007FB812F8B912FCA26C17F836367B B641>6 D8 D10 D<923803FFC0033F13FC4AB67E020715E0913A1FFE007FF8DA7FE0EB07 FE4AC87ED903FCED3FC0D907F0ED0FE0D90FC0ED03F049486F7E49CA7E017E177E498349 834848EF0F80000319C04917074848EF03E0000F19F049170148CC12F8A2001E1978003E 197CA2003C193C007C193EA20078191EA300F8191FA248190FAA6C191FA20078191EA300 7C193EA2003C193C003E197CA2001E1978001F19F8A26C6CEF01F06D1703000719E06C6C EF07C06D170F000119806C6CEF1F006D5F017E177E6D5F6D6C4B5A6D6C4B5AD907F0ED0F E0D903FCED3FC0D900FF03FFC7FCDA7FE0EB07FEDA1FFEEB7FF80207B612E002011580DA 003F01FCC8FC030313C0484E7BBB53>13 DII<00 7FB812F8B912FCA26C17F8CCFCAE007FB812F8B912FCA26C17F8CCFCAE007FB812F8B912 FCA26C17F836287BA841>17 D20 D<126012F812FEEA7F80EA3FE0EA0FF8EA03FEC6 6C7EEB3FE0EB0FF8EB03FE903800FF80EC3FE0EC0FF8EC03FE913800FF80ED3FE0ED0FF8 ED03FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FC0171FEF7F80933801FF00EE 07FCEE1FF0EE7FC04B48C7FCED07FCED1FF0ED7FC04A48C8FCEC07FCEC1FF0EC7FC04948 C9FCEB07FCEB1FF0EB7FC04848CAFCEA07FCEA1FF0EA7FC048CBFC12FC1270CCFCAE007F B81280B912C0A26C1780324479B441>I24 D<020FB6128091B712C01303010F1680D91FF8C9FCEB7F8001FECAFCEA01F8 485A485A485A5B48CBFCA2123EA25AA2127812F8A25AA87EA21278127CA27EA27EA26C7E 7F6C7E6C7E6C7EEA00FEEB7F80EB1FF86DB71280010316C01300020F1580323279AD41> 26 D<007FB512FCB712C016F06C15FCC8EA07FE9238007F80EE1FC0EE07E0707E707E70 7E177C83A283A2EF0F80A2170718C0A21703A81707A21880170FA2EF1F00A2173EA25F17 FC4C5A4C5A4C5AEE1FC0EE7F80DB07FEC7FC007FB65AB712F016C06C02FCC8FC323279AD 41>I<05041402051E140F057E143FDC01FE14FF4C48EB01FEDC0FF0EB07F8DC3FC0EB1F E04CC7EA3F80DB01FEECFF00DB07F8EB03FCDB0FE0EB07F0DB3FC0EB1FE003FFC7EA7F80 DA01FC02FEC7FCDA07F8EB03FCDA1FE0EB0FF0DA3F80EB1FC002FFC7EA7F80D903FCD901 FEC8FCD90FF0EB07F84948495AD97F80EB3FC0D801FEC7B4C9FCD803F8EB01FCD80FF0EB 07F8D83FC0EB1FE048C7EA3F8000FE4ACAFCA2007F6E7ED83FC0EB1FE0D80FF0EB07F8D8 03F8EB01FCD801FE6DB4FC26007F80EB3FC0D91FE0EB0FF06D6C6D7ED903FCEB01FED900 FF9038007F80DA3F80EB1FC0DA1FE0EB0FF0DA07F8EB03FCDA01FCEB00FE6EB4EC7F80DB 3FC0EB1FE0DB0FE0EB07F0DB07F8EB03FCDB01FEEB00FFDB007FEC3F80DC3FC0EB1FE0DC 0FF0EB07F8DC03FCEB01FE706CEB00FFDC007E143F051E140F48377BB053>I<00401420 00F0147800FC147EB4EC7F806C6C6D7ED81FE0EB0FF0D807F8EB03FCD801FCEB00FE6CB4 EC7F80D93FC0EB1FE0D90FE0EB07F0D907F8EB03FCD901FEEB00FFD9007FEC3F80DA3FC0 EB1FE0DA0FF0EB07F8DA03F8EB01FCDA01FE6DB4FC9126007F80EB3FC0DB1FE0EB0FF06F 6C6D7EDB03FCEB01FEDB00FF9038007F80DC3F80EB1FC0DC1FE0EB0FF0DC07F8EB03FCDC 01FCEB00FE706C147FA24C4814FEDC07F8EB03FCDC1FE0EB0FF0DC3F80EB1FC004FFC7EA 7F80DB03FC903801FE00DB0FF0EB07F84B48495ADB7F80EB3FC0DA01FEC7B4C7FCDA03F8 EB01FCDA0FF0EB07F8DA3FC0EB1FE04AC7EA3F80D901FE02FFC8FCD907F8EB03FCD90FE0 EB07F0D93FC0EB1FE001FFC7EA7F80D801FC02FEC9FCD807F8EB03FCD81FE0EB0FF0D87F 80EB3FC048C7485A00FC027ECAFC00F0147848377BB053>I<181EA4181F84A285180785 727EA2727E727E85197E85F11F80F10FC0F107F0007FBA12FCBCFCA26C19FCCCEA07F0F1 0FC0F11F80F13F00197E61614E5A4E5AA24E5A61180F96C7FCA260181EA4482C7BAA53> 33 D<1430A31478A314FCA2497EA2497E497FA2497F90381F7BE090383E79F09038FC78 FCD801F8137ED807F0EB3F80D83FE0EB1FF0D8FF80EB07FCD8FE00130100F8EC007C00C0 150CC71400B3B3AD1430264A7EB92A>I<14301478B3B3AD00C0150C00F8157C00FEEC01 FCD8FF801307D83FE0EB1FF0D807F0EB3F80D801F8EB7E00D800FC5B90383E79F090381F 7BE06DB45A6D5BA26D90C7FC6D5AA26D5AA21478A31430A3264A7EB92A>I<0278151EA4 02F8151F4A81A20101834A150701038349486F7EA249486F7E49CA7E4983017E177E4983 4848EF1F804848EF0FC0D80FE0EF07F0003FBA12FCBCFCA2003F19FCD80FE0CAEA07F0D8 03F0EF0FC06C6CEF1F806C6CEF3F00017E177E6D5F6D5F6D6C4B5A6D6C4B5AA26D6C4B5A 01015F6E150F010094C7FCA26E5D0278151EA4482C7BAA53>I39 D49 D<91381FFFFE91B6FC1303010F14 FED91FF0C7FCEB7F8001FEC8FCEA01F8485A485A485A5B48C9FCA2123EA25AA2127812F8 A25AA2B712FE16FFA216FE00F0C9FCA27EA21278127CA27EA27EA26C7E7F6C7E6C7E6C7E EA00FEEB7F80EB1FF06DB512FE010314FF1300021F13FE283279AD37>I54 D<126012F0AD12FCA412F0AD126006207BA400>I<00601618 00F0163C6C167CA200781678007C16F8A2003C16F0003E1501A26CED03E0A26C16C06D14 07A2000716806D140FA26C6CEC1F00A26CB612FEA36C5D01F8C7127CA2017C5CA2013C5C 013E1301A2011E5C011F1303A26D6C485AA201075CECC00FA2010391C7FC6E5AA2903801 F03EA20100133CECF87CA2EC7878EC7CF8A2EC3FF0A26E5AA36E5AA36E5A6EC8FC2E3C80 B92F>I<156015F0A21401EB07F190383FFFE0EB7C1FEBF00748486C5AD803C07F484848 7ED80F007FA248497E001E14BC153C003E143E141FA248EB1E1F143EA2143CA2147C00FC 1580147814F8A214F0A21301A214E01303A214C0A21307A21480A2130FA214005B007C15 00131EA2D87E3E5BA2D83E3C133E137CA21378001F5C13F8000F14784913F800075C0003 495AEBE0033901F007802603FC1FC7FCEBFFFEEBC7F0D807C0C8FCA25BA26CC9FC21477C BF2A>59 D<18F017011707A3170FA2171F60173F1737177F176F17EF17CF04017F178F16 03170FEE0707160EA2161C161816381630167016E0A2ED01C016801503ED0700A2150E5D A25D157815705D02018103CFB5FCEC03BF4AB6FCA2020EC71203141E5C14380278810020 5B386001E0EAF0036C4848140126FE1F8081B5C8FC190C49EEFF3C496F13F06C4817E06C 4817806C48EE7E00D8078093C7FC3E407DBB42>65 D67 D<0203B512F0027F14FF49B7 12E0010F16F890273FC3F00713FED978039038007FFF2601E007020F1380D803C0030313 C0D80780030013E0000F177FD81F00EE3FF048EF1FF8003E4A140F5A0078EF07FC00C001 0F1503C7FCA24B1401A3141F5DA3023F16F8A292C8FCF003F0A25C027EED07E0A219C04A 150F1980F01F00495A183E6049481578604D5A49484A5A4D5A050EC7FC4948143C5FEE01 E04948EB07C0043FC8FC91380001FC49EB3FF049B5128048B500FCC9FC4814E04801FCCA FC3E397FB840>II<0307B6 12FE033FEDFF804AB812C0140791260F807EC7FC91263C00FEEC3F004A161E4A49141801 0194C7FC495A01071301A2D90FC05B148014000118130390C75BA34B5AA3150F5EA34B5A A293B512FC4B5C604B14C0037ECAFCA25DA25D1401A24A5AA25D14075D140F5D141F92CB FC5C0006133E003E137E007E137CB413FC6D5AEBC1F0EBF1E06CB45A6C90CCFC6C5AEA07 F0423C7EB83C>III<92B6 12FC021F15F891B712F0010316C090270FF0003CC7FC013EC7127C01785C49130100015D 0003140348485C49130790C7FCC8485AA34B5AA34BC8FCA35D157EA315FE5DA314015DA3 4A5AA314075DA34A5AA25D141F92C9FC4A1406023E141C027E147C027C5C4A495A4A5C49 48495A000FB7C7FC003F5D4815F0B712C0363982B82D>I76 DI<0370EBFF80912601E00713E0912603C0 1F13F891260F007F7F021E9038F03FFE913A7803C00FFF9139F0078003494848486C1380 902603C01E7F902607803EEC7FC049485A011E49143F013E17E0494848141FEBF8035D26 01F007150F00035CEBE00F00075CD9C01EC8FC000F131C49C9FC121FA248CA13C0A34817 1F1980127EA2183F00FE1800A2183E187E187C18FC6017016C5F4D5A6017076C6C4B5A4D C7FC171E6D5D6C6C5D5F6D4A5A6C6CEC03806C6C020FC8FC01FF143E6C01C013F86C9038 F807E06C90B512806C6C49C9FC011F13F0010313803B3D7BBA42>79 D<0203B512F8027FECFF8049B712F0010F8290273FC3F00313FED978039038003FFF2601 E00702071380D803C06F13C0D807801500000F177FD81F00EE3FE0484A141F123E5A0078 010F150F12C0C7FC4B15C0A3021FED1F80A24B1500183EA2023F5D6092C85A4D5A4D5A4A 4A5A027E020EC7FC173C17F84AEB03E0EE3F80DB1FFEC8FC0101EB7FF89138F8FFC0DAF9 FCC9FC02F8CAFC495AA3495AA3495AA3495AA291CBFC5BA2137EA35B13F013C03B3D7FB8 3A>I<0203B512FE027FECFFF049B712FC010F16FF90273FC3F00080D9780302077F2601 E0071401D803C06F6C7ED80780163F000F171FEA1F00484A140F123E5A0078010F5E12C0 C7FC4B4A5AA296C7FC021F5D183E4B5C187860023F4A5A4D5A92C7000FC8FC173EEE03F8 4AEBFFE0DA7E0313804B48C9FC4B7EECFC036F7F6F7F0101147F4A80163F707E495A707E A249481307830403151049486E14F0F101E04A6D6CEB03C0011F933880078070EC0F0049 C8EBC01E716C5A013E92383FF0F0017EEEFFE0017C6F1380496F48C7FC01E0ED07F0443B 7FB846>82 DI<1A801907F10F00023FB712FE49B8 5A010F17F0013F17C0494CC7FC2801E00003F0C9FC48481307485A120F48C7485A5A5AA2 00FE4A5A5A12F01280C8485AA44BCAFCA415FEA44A5AA44A5AA44A5AA4140F5DA35D141F A25D143FA292CBFC5CA2147E14FE5CA2495A5C495A5C0102CCFC41427DBB2D>IIII<0060161800F0163CB3B26C167CA2007C16F8A26CED01F0003F 15036C6CEC07E06C6CEC0FC0D807F0EC3F80D803FE903801FF003A00FFC00FFC6DB55A01 1F14E0010391C7FC9038007FF82E347CB137>91 DI102 D<12FCEAFFC0EA07F0EA01FCEA007E7F80131F80130FB3A7801307 806D7E6D7EEB007EEC1FF0EC07F8EC1FF0EC7E00495A495A495A5C130F5CB3A7131F5C13 3F91C7FC137E485AEA07F0EAFFC000FCC8FC1D537ABD2A>I<14C0EB01E01303A214C013 07A21480130FA2EB1F00A2131E133EA25BA2137813F8A2485AA25B1203A25B1207A2485A A290C7FC5AA2123EA2123C127CA2127812F8A41278127CA2123C123EA27EA27E7FA26C7E A212037FA212017FA26C7EA21378137CA27FA2131E131FA2EB0F80A2130714C0A2130314 E0A21301EB00C0135278BD20>I<126012F07EA21278127CA2123C123EA27EA27E7FA26C 7EA212037FA26C7EA212007FA21378137CA27FA2131E131FA2EB0F80A2130714C0A21303 14E0A414C01307A21480130FA2EB1F00A2131E133EA25BA2137813F8A25B1201A2485AA2 5B1207A2485AA290C7FC5AA2123EA2123C127CA2127812F8A25A126013527CBD20>I<12 6012F0B3B3B3B3A91260045377BD17>I<0070131C00F0131EB3B3B3B3A80070131C1752 77BD2A>I<126012F07EA21278127CA2123C123EA2121E121FA27E7FA212077FA212037F A212017FA212007FA21378137CA2133C133EA2131E131FA27F80A2130780A26D7EA21301 80A2130080A21478147CA2143C143EA2141E141FA2801580A2140715C0A2140315E0A214 0115F0A2140015F8A21578157CA2153C153EA2151E150C1F537BBD2A>110 D112 D114 D<0060166000F016F0B3B3A9B8FCA36C16E02C327BB1 37>116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FM cmr7 7 73 /FM 73 128 df0 DI<1438A3147CA314FEA2497E14BFA2 01037F141FA201067F140FA2010C7F1407A201187F1403A201307F1401A201607F140001 E07F49137EA20001147F497FA248C71380151FA24815C05AD81FC0EB3FE03AFFF001FFFE A2272A7EA92D>3 D6 D<90383FFFFCA2010090C7FC147EA5903803FF80013F13F89038FC7E 7ED803E0EB0F80D80FC0EB07E0D81F00EB01F04815F8007EEC00FCA248157EA6007E15FC A26CEC01F86C15F0D80FC0EB07E0D803E0EB0F80D800FCEB7E0090383FFFF801031380D9 007EC7FCA514FF013F13FCA227287DA72F>8 D<010FB5FCA29038003FC06E5AA400FEED 0FE06C151FD83F80EC3F80001F160001C05C000F157EA813E000075DA3D803F0EB81F8EA 01F8ED83F0D800FCEB87E0013FEB8FC090261FDFBFC7FC903807FFFC9038007FE0EC1F80 A54A7E010FB5FCA22B287DA733>I<903803FF80011F13F090387E00FCD801F8133FD807 E0EB0FC04848EB07E04848EB03F048C7EA01F8A2007EEC00FCA248157EA7007E15FCA36C EC01F8A26C6CEB03F0000F15E0A26C6CEB07C0000315806C6CEB0F00A26C6C131ED8C070 EB1C060178133CD86038EB380C01181330011C13700070151CD87FFCEB7FFC003F15F8A3 27297DA82F>I<1238127C12FE12FFA2127F123B1203A31206A3120C1218123812701220 08127BA713>39 D<1306130C13181330136013E0EA01C0EA0380A2EA07005A120E121EA2 121C123CA35AA512F85AAB7E1278A57EA3121C121EA2120E120F7EEA0380A2EA01C0EA00 E0136013301318130C13060F3B7AAB1A>I<12C012607E7E7E120E7EEA0380A2EA01C013 E0120013F0A213701378A3133CA5133E131EAB133E133CA51378A3137013F0A213E01201 13C0EA0380A2EA0700120E120C5A5A5A5A0F3B7DAB1A>I<140EB3A2B812E0A3C7000EC8 FCB3A22B2B7DA333>43 D45 D<1238127C12FEA3127C123807077B 8613>I48 D<13381378EA01F8121F12FE12E01200B3AB487EB512F8A21526 7BA521>I<13FF000313E0380E03F0381800F848137C48137E00787F12FC6CEB1F80A412 7CC7FC15005C143E147E147C5C495A495A5C495A010EC7FC5B5B903870018013E0EA0180 390300030012065A001FB5FC5A485BB5FCA219267DA521>I<13FF000313E0380F01F838 1C007C0030137E003C133E007E133FA4123CC7123E147E147C5C495AEB07E03801FF8091 C7FC380001E06D7E147C80143F801580A21238127C12FEA21500485B0078133E00705B6C 5B381F01F03807FFC0C690C7FC19277DA521>I<1438A2147814F81301A2130313071306 130C131C131813301370136013C012011380EA03005A120E120C121C5A12305A12E0B612 E0A2C7EAF800A7497E90383FFFE0A21B277EA621>I<0018130C001F137CEBFFF85C5C14 80D819FCC7FC0018C8FCA7137F3819FFE0381F81F0381E0078001C7F0018133EC7FC80A2 1580A21230127C12FCA3150012F00060133E127000305B001C5B380F03E03803FFC0C648 C7FC19277DA521>II<1230123C003FB512E0A215C0481480A239700007000060130E140C48131C5C 5CC75A5C1301495AA249C7FC5B130E131EA3133E133CA2137CA413FCA813781B287DA621 >I<137F3803FFE0380781F8380E007C48131E5A801278A3127C007E131EEA3F80EBE03C 6C6C5A380FFCF03807FFC06C5BC613E0487F38079FFC380F07FEEA1E0348C67E48133FEC 1F8048130FA21407A315001278140E6C5B6C5B380F80F03803FFE0C66CC7FC19277DA521 >I<137F3801FFC03807C1E0380F0070001E1378003E7F003C133E007C131EA200FC131F A41580A4007C133FA2123C003E137F001E135F380F01DF3807FF9F3801FE1FD800101300 1300A2143E123C007E133CA25C5C007C5B383003C0381C0780D80FFFC7FCEA03F819277D A521>I<1238127C12FEA3127C12381200AB1238127C12FEA3127C123807197B9813>I61 D<140EA2141FA34A7EA3EC6FC0A2ECEFE014C7 A290380183F0A390380301F8A201067F1400A249137EA2011C137F01187FA24980013FB5 FCA2903960000FC0A201E080491307A248486D7EA200038115011207D81FC0497ED8FFF8 90383FFFE0A22B2A7EA931>65 D I<91387FC002903903FFF80690390FE01E0E90383F0007017CEB019ED801F0EB00FE4848 147E4848143E5B000F151E48C8FC48150E123EA2007E1506A2127C00FC1500A8127C007E 1506A2123EA2003F150C7E6C7E000715186D14386C6C14306C6C1460D8007CEB01C0013F EB038090390FE01E00903803FFF89038007FC0272A7DA82F>IIII<9138 7FC002903903FFF80690390FE01E0E90383F0007017CEB019ED801F0EB00FE4848147E48 48143E5B000F151E48C8FC48150E123EA2007E1506A2127C00FC92C7FCA792387FFFE012 7C007E02001300167E123EA2123F7E6C7E6C7EA26C7ED801F814FEEA007C013FEB039E90 390FE00F0E903903FFFC029026007FE0C7FC2B2A7DA833>II< B512C0A23807F8006C5AB3B0487EB512C0A212287EA718>I75 DIIIIIII<9038 7F80203903FFF06039078078E0380E000E481307481303007813010070130012F0A21560 A27E1500127C127FEA3FE013FF6C13F06C13FC000313FFC61480010F13C0010013E0EC0F F014031401EC00F8A200C01478A46C1470A26C14F06C14E06CEB01C000EFEB078039E3E0 1F0038C0FFFC38801FF01D2A7DA825>I<007FB7FCA23A7E003F003F0078150F00708100 6081A200E01680481501A5C791C7FCB3A64A7E013FB5FCA229287EA72F>II II<3B7FFF801FFF80A23B07FE0007F8006C48EB03E0000115806C 6C91C7FC017F1306150E6D6C5A90381FC0186D6C5A1570903807F0606D6C5AEB01F9ECFF 806D90C8FC80A26E7E6E7E143F4A7EECE7F0ECC3F8EB018390380381FC49C67E0106137E 49137F011C6D7E496D7E1330496D7E01E06D7E00016E7E1203D80FF0EB07FED8FFFC9038 1FFFE0A22B287EA731>II< 003FB6FCA2EBC00090C712FE003CEB01FC0038EB03F8A248EB07F0EC0FE0A20060EB1FC0 EC3F80A2C7EA7F0014FEA2495A495AA2495A495A495AA2495A90387F0003A213FE485AA2 48481307485AA24848130E485A151E4848133E48C7127E48EB03FE90B5FCA220287DA728 >II93 D<5AEA0380EA07C0EA0FE0EA1EF0EA3C78EA701CEAE00EEAC0060F0978A721 >I98 D100 D<133F3801FFE03803E1F0380F80F8381F007C143E123E007E131E141F127C12FCA2B6FC A200FCC7FCA4127C127E1403123E6C1307380F800E3807C01C3803E0783800FFE0EB3F80 181C7E9A1E>I<90387E03E03901FF9FF03807C3FC380F00F048EBF800001E1378003E13 7CA6001E1378001F13F86C5BEBC3E0380DFF80D81C7EC7FC90C8FCA3121E380FFFF014FC 6C13FF001F1480393E001FC000781307EC03E0481301A40078EB03C0007C13076CEB0F80 390FC07E003803FFF838007FC01C277E9921>103 DI<120EEA3F80A5EA0E00C7FCA7EA078012FFA2121F120FB3121FEAFFF8A20D 287EA713>I<260F81FC137F3BFF8FFF03FFC0903A9C0F8703E03B1FB007CC01F0D80FE0 13D8903AC003F000F8A301805BAF486C486C487E3CFFF83FFE0FFF80A2311A7E9937> 109 D<380F81FC38FF8FFF90389C0F80391FB007C0EA0FE09038C003E0A31380AF391FC0 07F039FFF83FFEA21F1A7E9925>II<380F81FC38FF8FFF9038BC0FC0391FF0 07E0390FC003F0EB800115F8EC00FCA2157C157EA7157C15FCA2EC01F801C013F0EC03E0 9038F007C09038BC1F8090388FFF00EB83F80180C7FCA7487EEAFFF8A21F257E9925>I< 380F07C038FF1FF0EB38F8EA1F71EA0F6113C1EBC0F014005BAF487EEAFFFCA2151A7E99 1A>114 D<3803F840380FFEC0EA3C07EA7803EA7001EAF000A37E6C1300EA7FC013FC6C B4FC6C1380000713C0C613E0130738C003F0130113007EA26C13E0130100F813C038EE07 8038C7FF00EA81FC141C7E9A1A>I<13C0A41201A312031207120F121FB512E0A23807C0 00AC1430A73803E060A23801F0C03800FF80EB3F0014257FA31A>I<39FFF807FEA2390F E001F001C013E0000714C013E000031480EBF00300011400A23800F806A2EB7C0CA2EB7E 1CEB3E18A26D5AA2EB0FE0A36D5AA26D5AA21F1A7F9823>118 D<3BFFF8FFF07FE0A23B 1FC01FC01F80000F90390F800E00A20007150CEC1FC02603E01B5B15E0143B2601F0315B 15F0D9F86013700000156015F89039FCC078E0017CEB7CC0137D90393F803D80153FEC00 1F6D91C7FCA2011E7F010E130EA22B1A7F982F>I<39FFF81FFCA2390FF00FE0D807E013 80D803F013003801F80E00005BEB7C386D5AEB3FE06D5A130F130780497EEB1DF8EB38FC EB707EEBE03E48487E0003EB0F80000714C0001F14E039FFE01FFEA21F197F9823>I<38 3FFFFEA2383E00FCEA3801003013F8387003F0EB07E0EA600F14C0EB1F8038003F00137E 13FE5B3801F806EA03F0EA07E0120FEBC00E381F800C383F001C5A007E137CB512FCA217 197E981E>122 DI<380F8010381FF038383FFFF04813E038E07F C038400F8015067BA621>126 D<3838038038FC07E0EAFE0FA3EAFC073838038013077A A721>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FN cmtt10 10 21 /FN 21 122 df<121FEA3F80EA7FC0EAFFE0A5EA7FC0EA3F80EA1F000B0B708A2C>46 D64 D79 D86 D<3801FFF0000713FE001F6D7E15E0488090 38C01FF81407EC01FC381F80000006C77EC8127EA3ECFFFE131F90B5FC1203120F48EB80 7E383FF800EA7FC090C7FC12FE5AA47E007F14FEEB8003383FE01F6CB612FC6C15FE6C14 BF0001EBFE1F3A003FF007FC27247CA32C>97 DI100 DI104 D<1307EB1FC0A2497EA36D5AA20107C7FC90C8FCA7387FFFC080B5FC7EA2EA0007B3A800 7FB512FCB612FEA36C14FC1F3479B32C>I107 D<387FFFE0B57EA37EEA0003B3B3A500 7FB61280B712C0A36C158022337BB22C>I<3A7F83F007E09039CFFC1FF83AFFDFFE3FFC D87FFF13FF91B57E3A07FE1FFC3E01FCEBF83F496C487E01F013E001E013C0A301C01380 B33B7FFC3FF87FF0027F13FFD8FFFE6D13F8D87FFC4913F0023F137F2D2481A32C>I<39 7FF01FE039FFF87FFC9038F9FFFE01FB7F6CB6FC00019038F03F80ECC01F02807FEC000F 5B5BA25BB3267FFFE0B5FCB500F11480A36C01E0140029247FA32C>II114 D<90387FF8700003B512F8120F5A5A387FC00F387E00034813015AA36CEB00F0007F1400 13F0383FFFC06C13FE6CEBFF80000314E0C66C13F8010113FCEB0007EC00FE0078147F00 FC143F151F7EA26C143F6D133E6D13FE9038F007FC90B5FC15F815E000F8148039701FFC 0020247AA32C>I<131E133FA9007FB6FCB71280A36C1500D8003FC8FCB1ED03C0ED07E0 A5EC800F011FEB1FC0ECE07F6DB51280160001035B6D13F89038003FE0232E7EAD2C>I< 3A7FF003FF80486C487FA3007F7F0001EB000FB3A3151FA2153F6D137F3900FE03FF90B7 FC6D15807F6D13CF902603FE07130029247FA32C>I<3A7FFF01FFFCB514FE148314016C 15FC3A03E0000F80A26D131F00011500A26D5B0000143EA26D137E017C137CA2017E13FC 013E5BA2EB3F01011F5BA21483010F5BA214C701075BA214EF01035BA214FF6D90C7FCA2 6D5A147C27247EA32C>I<3A7FFF01FFFCB5008113FE148314816C010113FC3A03E0000F 806C7E151F6D140012005D6D133E137C017E137E013E137CA2013F13FC6D5BA2EB0F815D A2EB07C1ECC3E0A2EB03E3ECE7C0130114F75DEB00FFA292C7FC80A2143EA2147E147CA2 14FC5CA2EA0C01003F5BEA7F83EB87E0EA7E0F495A387FFF806C90C8FC6C5A6C5AEA07E0 27367EA32C>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FO cmti10 10 72 /FO 72 128 df<04FFEB03F003039038E00FFC923A0FC0F01F1E923A3F00783E0F923A7E 01F87C3FDB7C03EBFC7F03FC14F8DA01F813F905F1137EDC01E1133C913B03F00003F000 A314074B130760A3140F4B130F60A3010FB812C0A3903C001F80001F8000A3023F143F92 C790C7FCA44A5C027E147EA402FE14FE4A5CA413014A13015FA313034A13035FA313074A 495AA44948495AA44948495AA3001CD9038090C8FC007E90380FC03F013E143E00FE011F 5B133C017C5C3AF8780F01E0D878F0EB07C0273FE003FFC9FC390F8000FC404C82BA33> 11 DI< EE7FE0923903FFFC7E92380FC03E92381F000F033EEB3FFE4B137F03FC14FC5D1401173D 4A48EB01F8A21703A24A4814F0A21707A2020F15E05D170FA218C0010FB7FCA3903B001F 80001F80A2173F143F92C71300A25FA24A147E147E17FEA25F14FE4A1301A25FA2010114 035CEFF070A21607010316F04AECE0E0A3EFE1C013074A14C3933803E380EE01E7933800 FF004948143C94C7FCA3495AA3001C90CAFC127E133E12FE133C137CEAF878EA78F0EA3F E0EA0F80374C82BA31>II<130FEB1F80133F 137FEBFF00485A5BEA03F0485A485A485A003EC7FC5A5A12E05A111064B92A>19 D<3901E003C03907F00FE0000F131F01F813F0001F133FA3000F131F3907B00F60380030 00A2017013E0016013C0EBE00101C01380000113030180130000035B3807000E000E5B48 5B485B485B48485A00C05B1C1971B92B>34 D39 D<150C151C153815F0EC01E0EC03C0EC0780EC0F00141E5C147C5C5C495A1303495A5C13 0F49C7FCA2133EA25BA25BA2485AA212035B12075BA2120F5BA2121FA290C8FCA25AA212 3EA2127EA2127CA412FC5AAD1278A57EA3121C121EA2120E7EA26C7E6C7EA212001E5274 BD22>I<140C140E80EC0380A2EC01C015E0A2140015F0A21578A4157C153CAB157CA715 FCA215F8A21401A215F0A21403A215E0A21407A215C0140F1580A2141F1500A2143EA25C A25CA2495AA2495A5C1307495A91C7FC5B133E133C5B5B485A12035B48C8FC120E5A1278 5A12C01E527FBD22>I<4B7E4B7EA21507A25EA2150FA293C8FCA25DA2151EA2153EA215 3CA2157CA21578A2007FB812E0B9FCA27EC7D801F0C8FCA25DA21403A25DA21407A25DA2 140FA292C9FCA25CA2141EA2143EA2141C333275AD40>43 DI<387FFFF8A2B5FCA214F0150579941E>I<120EEA3F80127F12FFA31300127E12 3C0909778819>I<15181538157815F0140114031407EC0FE0141F147FEB03FF90383FEF C0148FEB1C1F13001580A2143FA21500A25CA2147EA214FEA25CA21301A25CA21303A25C A21307A25CA2130FA25CA2131FA25CA2133FA291C7FC497EB61280A31D3877B72A>49 DII<133C137E13FF5AA313FE13FCEA00701300B2120E EA3F80127F12FFA31300127E123C102477A319>58 DI65 D<0107B612FCEFFF8018C0903B000FF0001FF04BEB07F81703021F15FC17014B14 FEA2023F1400A24B1301A2147F18FC92C7120318F84A140718F04AEC0FE0EF1FC00101ED 3F80EF7F004AEB01FEEE07F849B612E05F9139F80007F0EE01FC01076E7E177F4AEC3F80 A2010F16C0171F5CA2131F173F5CA2133FEF7F805C1800017F5D4C5A91C7485A5F49140F EE1FE0494A5A00014AB45AB748C7FC16F816C037397BB83A>II<0103B612FEEFFFC018F0903B 0007F8000FF84BEB03FCEF00FE020F157FF03F804B141F19C0021F150F19E05D1807143F 19F05DA2147FA292C8FCA25C180F5CA2130119E04A151FA2130319C04A153FA201071780 187F4A1600A2010F16FEA24A4A5A60011F15034D5A4A5D4D5A013F4B5A173F4A4AC7FC17 FC017FEC03F84C5A91C7EA1FC04949B45A007F90B548C8FCB712F016803C397CB83F>I< 0107B8FCA3903A000FF000034BEB007F183E141F181E5DA2143FA25D181C147FA2923800 0380A24A130718004A91C7FC5E13015E4A133E167E49B512FEA25EECF8000107147C163C 4A1338A2010F147818E04A13701701011F16C016004A14031880013F150718004A5CA201 7F151E173E91C8123C177C4915FC4C5A4914070001ED7FF0B8FCA25F38397BB838>I<01 07B712FEA3903A000FF000074B1300187C021F153CA25DA2143FA25D1838147FA292C8FC EE03804A130718004A91C7FCA201015CA24A131E163E010314FE91B5FC5EA2903807F800 167C4A1378A2130FA24A1370A2011F14F0A24A90C8FCA2133FA25CA2137FA291CAFCA25B A25B487EB6FCA337397BB836>II<0103B5D8F80FB512E0A390260007F8C7381FE0 004B5DA2020F153F615DA2021F157F96C7FC5DA2023F5D605DA2027F14016092C7FCA24A 1403605CA249B7FC60A202FCC712070103150F605CA20107151F605CA2010F153F605CA2 011F157F95C8FC5CA2013F5D5F5CA2017F14015F91C7FC491403007FD9FE01B512F8B55B A243397CB83E>I<0103B512F8A390390007F8005DA2140FA25DA2141FA25DA2143FA25D A2147FA292C7FCA25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C A2133FA25CA2137FA291C8FC497EB6FCA25C25397CB820>I<0103B500F890387FFFE0A2 1AC090260007F8C7380FFC004B15E061020F4BC7FC183E4B5C18F0021F4A5A4D5A4BEB0F 804DC8FC023F143C5F4B5B4C5A027FEB07C04CC9FCED001E5E4A5BED01FCECFE03150701 01497E151FECFC7C4B7E903903FDE07FDAFFC07F1580ED003F49488014F84A131F83130F 160F4A801607011F81A24A130383133F16014A80A2017F6E7EA291C8FC494A7F007F01FE 011F13FCB55CA243397CB840>75 D<0107B512FCA25E9026000FF8C7FC5D5D141FA25DA2 143FA25DA2147FA292C8FCA25CA25CA21301A25CA21303A25CA21307A25CA2130F170C4A 141CA2011F153C17384A1478A2013F157017F04A14E01601017F140317C091C71207160F 49EC1F80163F4914FF000102071300B8FCA25E2E397BB834>I<902607FFF8923807FFF0 614F13E0D9000FEFF0004F5AA2021F167FF1EFC0141DDA1CFCEC01CF023C16DF9538039F 800238ED071FA20278ED0E3F97C7FC0270151CA202F04B5AF0707E14E0037E14E0010117 FE4D485A02C0EC0380A20103ED0701610280140EA20107ED1C0305385B14006F13704916 0705E05B010EEC01C0A2011E913803800F61011CEC0700A2013C020E131F4C5C1338ED1F B80178163F04F091C8FC01705CA201F04A5B187E00015DD807F816FEB500C09039007FFF FC151E150E4C397AB84A>I<902603FFF891B512E0A281D90007923807F8006F6E5A6102 0F5E81DA0E7F5DA2021E6D1307033F92C7FC141C82DA3C1F5C70130EEC380FA202786D13 1E0307141C147082DAF003143C70133814E0150101016E1378030014705C8201036E13F0 604A1480163F010715C1041F5B91C7FC17E149EC0FE360010E15F31607011E15FF95C8FC 011C80A2013C805F1338160013785F01F8157CEA03FC267FFFE0143CB51538A243397CB8 3E>I I<0107B612F817FF1880903B000FF0003FE04BEB0FF0EF03F8141FEF01FC5DA2023F15FE A25DA2147FEF03FC92C7FCA24A15F817074A15F0EF0FE01301EF1FC04AEC3F80EFFE0001 034A5AEE0FF091B612C04CC7FCD907F8C9FCA25CA2130FA25CA2131FA25CA2133FA25CA2 137FA291CAFCA25BA25B1201B512FCA337397BB838>II<0103B612F017FEEFFF80903B0007F8003FC04BEB0FF01707020FEC03F8EF01 FC5DA2021F15FEA25DA2143FEF03FC5DA2027FEC07F818F092C7120F18E04AEC1FC0EF3F 004A14FEEE01F80101EC0FE091B6128004FCC7FC9138FC003F0103EC0F80834A6D7E8301 071403A25C83010F14075F5CA2011F140FA25CA2133F161F4AECE007A2017F160F180E91 C7FC49020F131C007F01FE153CB5913807F078040313F0CAEAFFE0EF3F80383B7CB83D> I<92383FC00E913901FFF01C020713FC91391FC07E3C91393F001F7C027CEB0FF84A1307 49481303495A4948EB01F0A2495AA2011F15E091C7FCA34915C0A36E90C7FCA2806D7E14 FCECFF806D13F015FE6D6D7E6D14E0010080023F7F14079138007FFC150F15031501A215 00A2167C120EA3001E15FC5EA3003E4A5AA24B5AA2007F4A5A4B5A6D49C7FC6D133ED8F9 F013FC39F8FC03F839F07FFFE0D8E01F138026C003FCC8FC2F3D7ABA2F>I<0007B812E0 A25AD9F800EB001F01C049EB07C0485AD900011403121E001C5C003C1780140312380078 5C00701607140700F01700485CA2140FC792C7FC5DA2141FA25DA2143FA25DA2147FA292 C9FCA25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CEB3FF0007FB512F8B6FC A2333971B83B>I<003FB539800FFFFEA326007F80C7EA7F8091C8EA3F00173E49153CA2 491538A20001167817705BA2000316F05F5BA2000715015F5BA2000F15035F5BA2001F15 0794C7FC5BA2003F5D160E5BA2007F151E161C90C8FCA2163C4815385A16781670A216F0 4B5A5E1503007E4A5A4BC8FC150E6C143E6C6C5B15F0390FC003E03907F01FC00001B5C9 FC38007FFCEB1FE0373B70B83E>III89 D<91B712F0A25B9239E0001FE092C7EA3FC0D903FCEC7F8002F015004A14FE 16014948495A4A495A4C5A49C75B4C5A010E143F011E4A5A011C4AC7FC4B5A5E90C7485A 15074B5A4B5A4B5A5E157F4BC8FC4A5A4A5A4A5A5D140F4A5A4A5A4A5A4AC712E05C1301 4948130149485C495A494813034A5C013F1407495A49C7FC48484AC7FC48485C5B000715 3E4848147E4848EB01FE4848EB07FC4848133F90B6FCB7FC5E34397AB833>I<01181330 013813709038F001E03901C003800180130000035B3807000E000E5B000C1318001C1338 485B00301360A2007013E000605BA238EF01DE38FF81FFA66CC65A003C13781C196AB92B >92 D<14F8EB07FE90381F871C90383E03FE137CEBF801120148486C5A485A120FEBC001 001F5CA2EA3F801403007F5C1300A21407485C5AA2140F5D48ECC1C0A2141F1583168014 3F1587007C017F1300ECFF076C485B9038038F8E391F0F079E3907FE03FC3901F000F022 2677A42A>97 D<133FEA1FFFA3C67E137EA313FE5BA312015BA312035BA31207EBE0F8EB E7FE9038EF0F80390FFC07C013F89038F003E013E0D81FC013F0A21380A2123F1300A214 075A127EA2140F12FE4814E0A2141F15C05AEC3F80A215005C147E5C387801F8007C5B38 3C03E0383E07C0381E1F80D80FFEC7FCEA01F01C3B77B926>I<147F903803FFC090380F C1E090381F0070017E13784913383901F801F83803F003120713E0120FD81FC013F091C7 FC485AA2127F90C8FCA35A5AA45AA3153015381578007C14F0007EEB01E0003EEB03C0EC 0F806CEB3E00380F81F83803FFE0C690C7FC1D2677A426>II<147F903803FFC090 380FC1E090383F00F0017E13785B485A485A485A120F4913F8001F14F0383F8001EC07E0 EC1F80397F81FF00EBFFF891C7FC90C8FC5A5AA55AA21530007C14381578007E14F0003E EB01E0EC03C06CEB0F806CEB3E00380781F83803FFE0C690C7FC1D2677A426>IIIII<150E153F157FA3157E151C1500ABEC1F80EC7FC0ECF1F0 EB01C090380380F813071401130F130E131EEB1C03133C013813F0A2EB0007A215E0A214 0FA215C0A2141FA21580A2143FA21500A25CA2147EA214FEA25CA21301A25CA213035C12 1C387E07E0A238FE0FC05C49C7FCEAF83EEA787CEA3FF0EA0FC0204883B619>IIIII<147F903803FFC090380FC1 F090381F00F8017E137C5B4848137E4848133E0007143F5B120F485AA2485A157F127F90 C7FCA215FF5A4814FEA2140115FC5AEC03F8A2EC07F015E0140F007C14C0007EEB1F8000 3EEB3F00147E6C13F8380F83F03803FFC0C648C7FC202677A42A>I<9039078007C09039 1FE03FF090393CF0787C903938F8E03E9038787FC00170497EECFF00D9F0FE148013E05C EA01E113C15CA2D80003143FA25CA20107147FA24A1400A2010F5C5E5C4B5A131F5EEC80 035E013F495A6E485A5E6E48C7FC017F133EEC70FC90387E3FF0EC0F8001FEC9FCA25BA2 1201A25BA21203A25B1207B512C0A3293580A42A>II<3903C003F0390FF01FFC391E783C0F381C7C703A3C3EE03F8038383FC0EB7F 800078150000701300151CD8F07E90C7FCEAE0FE5BA2120012015BA312035BA312075BA3 120F5BA3121F5BA3123F90C9FC120E212679A423>I<14FE903807FF8090380F83C09038 3E00E04913F00178137001F813F00001130313F0A215E00003EB01C06DC7FC7FEBFFC06C 13F814FE6C7F6D13807F010F13C01300143F141F140F123E127E00FE1480A348EB1F0012 E06C133E00705B6C5B381E03E06CB45AD801FEC7FC1C267AA422>II<13F8D803FEEB01C0D8078FEB03E0390E0F80 07121E121C0038140F131F007815C01270013F131F00F0130000E015805BD8007E133FA2 01FE14005B5D120149137EA215FE120349EBFC0EA20201131E161C15F813E0163CD9F003 133814070001ECF07091381EF8F03A00F83C78E090393FF03FC090390FC00F00272679A4 2D>I<01F0130ED803FC133FD8071EEB7F80EA0E1F121C123C0038143F49131F0070140F A25BD8F07E140000E08013FEC6485B150E12015B151E0003141C5BA2153C000714385B5D A35DA24A5A140300035C6D48C7FC0001130E3800F83CEB7FF8EB0FC0212679A426>I<01 F01507D803FC903903801F80D8071E903907C03FC0D80E1F130F121C123C0038021F131F 49EC800F00701607A249133FD8F07E168000E0ED000313FEC64849130718000001147E5B 03FE5B0003160E495BA2171E00070101141C01E05B173C1738A217781770020314F05F00 03010713016D486C485A000190391E7C07802800FC3C3E0FC7FC90393FF81FFE90390FE0 03F0322679A437>I<903907E007C090391FF81FF89039787C383C9038F03E703A01E01E E0FE3803C01F018013C0D8070014FC481480000E1570023F1300001E91C7FC121CA2C75A A2147EA214FEA25CA21301A24A1370A2010314F016E0001C5B007E1401010714C000FEEC 0380010F1307010EEB0F0039781CF81E9038387C3C393FF03FF03907C00FC027267CA427 >I<13F0D803FCEB01C0D8071EEB03E0D80E1F1307121C123C0038140F4914C01270A249 131FD8F07E148012E013FEC648133F160012015B5D0003147E5BA215FE00075C5BA21401 5DA314035D14070003130FEBF01F3901F87FE038007FF7EB1FC7EB000F5DA2141F003F5C 48133F92C7FC147E147C007E13FC387001F8EB03E06C485A383C1F80D80FFEC8FCEA03F0 233679A428>I<903903C0038090380FF007D91FF81300496C5A017F130E9038FFFE1E90 38F83FFC3901F007F849C65A495B1401C7485A4A5A4AC7FC141E5C5C5C495A495A495A49 C8FC131E5B49131C5B4848133C48481338491378000714F8390FF801F0391FFF07E0383E 1FFFD83C0F5B00785CD8700790C7FC38F003FC38E000F021267BA422>III<001E1338007F13FEEAFF811383A3EB03FC00FE13F8 383800F017096AB72A>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FP cmcsc10 10 50 /FP 50 122 df<121C127FEAFF80A213C0A3127F121C1200A412011380A2120313005A12 06120E5A5A5A12600A1977881B>44 D<121C127FEAFF80A5EA7F00121C090977881B>46 D48 DIII<151C153CA2157C15FCA214011403A21407140F141D141914311471 146114C11301EB038114011307130E130C131813381330136013E0EA01C01380EA03005A 12065A121C5A123012705AB712FEA3C73801FC00AB4A7E49B512FCA327397DB82E>I<00 061406D80780131E9038F801FC90B5FC5D5D15C05D4AC7FC38067FF090C9FCABEB03FC90 381FFF8090387C07E09038E001F03907C000F8497F90C7127E0006147FC8EA3F80A216C0 151FA216E0A4123E127F487EA490C713C048143F126016800070147F6C150015FE6C5C00 0F495A39078007F03903F01FE06CB512806C6C48C7FCEB0FF0233A7BB72E>II<12301238123E003FB612F8A316F05A16E016C00070C7EA0180 00601403ED0700150E00E0140C48141C5D5DC8126015E04A5A4A5A92C7FC5C140EA25C14 3C14381478147014F0A213015C1303A21307A3130F5CA2131FA5133FA96D5A6DC8FC253B 7AB82E>III<150EA315 1FA24B7EA34B7EA3EDDFE0A202017F158FA29138030FF81507A202067F1503020E7FEC0C 01A2021C7FEC1800A24A80167FA24A6D7EA202E0804A131FA2494880160FA249B67EA249 810106C71203A249811601A2498182A2496F7EA20170820160153F13E06D821203D80FFC ED7FF8B56C010FB512E0A33B3C7CBB44>65 DIIIII73 D76 DII<913801FFC0020F13F891387F80FF903A01FC001FC0D903F0EB07E0D90FC0EB01F849 486D7E49C8127E017E81496F7E00018348486F7EA248486F7E000F83491503001F83A248 486F7EA3007F834981A300FF1880AB007F18006D5DA3003F5FA26D1503001F5FA26C6C4B 5AA200075F6D150F6C6C4B5A00015F6C6C4B5A017F4BC7FC6D6C14FE6D6C495A6D6C495A D903F0EB07E0D901FCEB1FC09027007F80FFC8FC91380FFFF8020113C0393D7ABA46>I< B712F816FF17E0C69039C0003FF86D48EB07FCEE01FE707EEF7F80EF3FC0A2EF1FE0A218 F0A718E0A2EF3FC0A2EF7F80EFFF004C5AEE07F8EE3FF091B612C04CC7FC0280C9FCB3A5 497EB612C0A334397DB83E>I82 DI<003FB812FCA3D9C001EB800390C790C7FC007C173E0078171E0070170EA30060 1706A400E01707481703A4C81500B3B0020313C0010FB612F0A338397CB841>II89 D<1407A24A7EA34A7EA3EC37E0A2EC77F01463A2ECC1F8A201017F1480A290380300 7EA301067FA2010E80010C131FA2496D7EA2013FB57EA29038300007496D7EA3496D7EA2 00018149130012036D801207D81FE0903801FF80D8FFF8010F13F8A22D2C7DAB33>97 DI< 91383FC006903901FFF80E90390FE03E1E90381F0007017EEB03BE01F8EB01FE48481300 4848147E0007153E485A001F151E5B003F150E90C8FC5A1606A212FE1600AA007F1506A3 7E6D140E001F150C7F000F151C6C6C1418000315386C6C14706C6C14E0017EEB01C0011F EB078090390FE03E00903801FFF89038003FC0272D7BAB31>IIII< 91383FE003903901FFF807903907E01E0F90391F00078F017EEB01DF496DB4FC48488048 4880484880485A001F815B003F8190C8FC5A82A212FE93C7FCA892383FFFF8A2007F0200 1380EE3F00A27E7F121F7F120F6C7E6C7E6C6C5C6C7E017E5C011FEB01CF903907E00F87 903901FFFE039026003FF0C7FC2D2D7BAB35>III107 DIIIII114 D<017F13603901FFE0E0380780F9380E001F48130748130312780070130100F01300A315 607EA26C14007E127F13C0EA3FFEEBFFE06C13F8000713FE6C7FC61480010F13C01300EC 0FE01407EC03F01401A212C01400A37E15E06C1301A26CEB03C06CEB0780B4EB0F0038F3 E01E38E0FFF838C01FE01C2D7BAB26>I<007FB712C0A23A7E003FC00F007890381F8003 007015011600126000E016E0A2481660A5C71500B3A8EC7FE0011FB57EA22B2B7DAA31> II< 3B7FFF800FFFC0A2000790390003FE006C48EB01F800015D000015C0017F13036D5C6E48 C7FC90381FC0066D6C5A151C6D6C5A903803F83001015BECFCE06D6C5AEC7F80A2143F6E 7E140F4A7E4A7E1433EC63F8ECE1FCECC0FE903801807E0103137F49486C7E0106131F49 80011C6D7E496D7E0130130301708001F06D7E000181000781D81FF8491380B46C4913F8 A22D2B7DAA33>120 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: FQ cmr10 10 98 /FQ 98 128 df0 D<1506150FA24B7EA24B7EA24B 7EA2EDDFF0A29138018FF8A291380307FCA291380603FEA291380E01FF140CDA1C007F14 1802386D7E143002706D7E146002E06D7E5C01016E7E5C01036E7E91C7FC496E7E130601 0E6E7E130C011C6E7F131801386F7E133001706F7E136001E06F7E5B170F484882170748 C97F17030006831701488383481880001FB9FC4818C0A24818E0A2BA12F0A23C3C7CBB45 >II<15E0A34A7EA34A7EA34A7EA34A7EA2 140DEC1DFF14191418A24A7F157FA202607F153FA202C07F151FA2D901807F150FA2D903 007F1507A20106801503A2010E80130C1501011C80131881A24981167FA24981163FA249 81161FA20001821203486C81D81FF84A7EB50107B512E0A3333C7DBB3A>I5 DI<011FB512FE A39026001FFEC8FCEC07F8A8EC3FFE0103B512E0D91FF713FC90397F07F87F01FCEC1F80 D803F8EC0FE0D807F06E7ED80FE06E7E001F82D83FC06E7EA2007F8201808000FF1780A7 007F170001C05C003F5EA2D81FE04A5A000F5ED807F04A5AD803F84A5AD800FCEC1F8001 7F027FC7FC90391FF7FFFC0103B512E09026003FFEC8FCEC07F8A8EC1FFE011FB512FEA3 31397BB83C>8 D<010FB612C0A3D900070180C7FCDA01FEC8FCA7D8FF80ED07FC01E015 1F001F17E001F0153F000F17C001F8157F00071780ACD803FCEDFF00A4D801FE4A5AA200 005E017F4A5A02811307013F5DD91FC1495AD90FE1495AD903F9017FC7FC0100B512FC02 3F13F0020390C8FC6E5AA8913807FF80010FB612C0A336397BB841>III III<133C137EA213FE1201EA03FC13F0EA07E0EA0FC0EA1F80EA1E005A5A5A12C00F0F 6FB92A>19 D<121C127FEAFF80A8EA7F00AB123EAB121CABC7FCA8121C127FEAFF80A5EA 7F00121C093C79BB17>33 D<001C131C007F137F39FF80FF80A26D13C0A3007F137F001C 131C00001300A40001130101801380A20003130301001300485B00061306000E130E485B 485B485B006013601A197DB92A>I<030C1303031E497EA2033E130FA2033C91C7FCA203 7C5BA20378131EA303F8133EA24B133CA20201147CA24B1378A2020314F8A24B5BA30207 1301007FB91280BA12C0A26C1880C7271F0007C0C7FC021E5CA3023E130FA2023C91C8FC A2027C5BA20278131EA302F8133E007FB91280BA12C0A26C1880280003E000F8C8FC4A5B A301071301A202805BA2010F1303A202005BA2491307A2011E5CA3013E130FA2013C91C9 FCA2017C5BA20178131EA20130130C3A4A7BB945>I<121C127FEAFF80A213C0A3127F12 1C1200A412011380A2120313005A1206120E5A5A5A12600A1979B917>39 D<146014E0EB01C0EB0380EB0700130E131E5B5BA25B485AA2485AA212075B120F90C7FC A25A121EA2123EA35AA65AB2127CA67EA3121EA2121F7EA27F12077F1203A26C7EA26C7E 1378A27F7F130E7FEB0380EB01C0EB00E01460135278BD20>I<12C07E12707E7E7E120F 6C7E6C7EA26C7E6C7EA21378A2137C133C133E131EA2131F7FA21480A3EB07C0A6EB03E0 B2EB07C0A6EB0F80A31400A25B131EA2133E133C137C1378A25BA2485A485AA2485A48C7 FC120E5A5A5A5A5A13527CBD20>I<15301578B3A6007FB812F8B912FCA26C17F8C80078 C8FCB3A6153036367BAF41>43 D<121C127FEAFF80A213C0A3127F121C1200A412011380 A2120313005A1206120E5A5A5A12600A19798817>II<121C127F EAFF80A5EA7F00121C0909798817>I48 DIII<1538A2157815F8A2140114031407A2140F141F141B1433147314 6314C313011483EB030313071306130C131C131813301370136013C01201EA038013005A 120E120C5A123812305A12E0B712F8A3C73803F800AB4A7E0103B512F8A325397EB82A> I<0006140CD80780133C9038F003F890B5FC5D5D158092C7FC14FC38067FE090C9FCABEB 07F8EB3FFE9038780F803907E007E090388003F0496C7E12066E7EC87EA28181A21680A4 123E127F487EA490C71300485C12E000605C12700030495A00385C6C1303001E495A6C6C 485A3907E03F800001B5C7FC38007FFCEB1FE0213A7CB72A>II<12301238123E003FB612E0A316C05A168016000070C712060060140E5D1518 00E01438485C5D5DC712014A5A92C7FC5C140E140C141C5CA25CA214F0495AA21303A25C 1307A2130FA3495AA3133FA5137FA96DC8FC131E233B7BB82A>III<121C127FEAFF80A5EA7F00121CC7FCB2121C127FEAFF 80A5EA7F00121C092479A317>I<121C127FEAFF80A5EA7F00121CC7FCB2121C127F5A13 80A4127F121D1201A412031300A25A1206A2120E5A121812385A1260093479A317>I<00 7FB812F8B912FCA26C17F8CCFCAE007FB812F8B912FCA26C17F836167B9F41>61 D63 D<1538A3157CA315FEA34A7EA34A6C7EA202077FEC063FA2020E7FEC0C1FA2021C7FEC18 0FA202387FEC3007A202707FEC6003A202C07F1501A2D901807F81A249C77F167FA20106 810107B6FCA24981010CC7121FA2496E7EA3496E7EA3496E7EA213E0707E1201486C81D8 0FFC02071380B56C90B512FEA3373C7DBB3E>65 DI<913A01FF8001 80020FEBE003027F13F8903A01FF807E07903A03FC000F0FD90FF0EB039F4948EB01DFD9 3F80EB00FF49C8127F01FE153F12014848151F4848150FA248481507A2485A1703123F5B 007F1601A35B00FF93C7FCAD127F6DED0180A3123F7F001F160318006C7E5F6C7E17066C 6C150E6C6C5D00001618017F15386D6C5CD91FE05C6D6CEB03C0D903FCEB0F80902701FF 803FC7FC9039007FFFFC020F13F002011380313D7BBA3C>IIIIIII75 DIIIIIIII<003FB812E0A3D9C003EB001F273E0001FE130348EE01F000781600007017 70A300601730A400E01738481718A4C71600B3B0913807FF80011FB612E0A335397DB83C >IIII<007FB590383FFFFCA3C601F801071380D97FE0D903FCC7FC013FEC 01F06D6C5C5F6D6C5C6D6C13034CC8FC6D6C1306160E6D6C5B6DEB8018163891387FC030 6E6C5A16E06E6C5A91380FF18015FB6EB4C9FC5D14036E7EA26E7F6F7EA24B7E15DF9138 019FF09138038FF8150F91380607FC91380E03FE140C4A6C7EEC38000230804A6D7E14E0 4A6D7E49486D7E130391C76C7E01066E7E130E010C6E7E011C1401013C8101FE822607FF 80010713E0B500E0013FEBFF80A339397EB83E>II<003FB7FCA39039FC0001FE01C0130349495A003EC7FC003C4A5A5E003814 1F00784A5A12704B5A5E006014FF4A90C7FCA24A5A5DC712074A5AA24A5A5D143F4A5AA2 4A5A92C8FC5B495AA2495A5C130F4948EB0180A2495A5C137F495A16034890C7FC5B1203 485AEE0700485A495C001F5D48485C5E4848495A49130FB8FCA329397BB833>II<3901800180000313033907000700000E 130E485B0018131800381338003013300070137000601360A200E013E0485BA400CE13CE 39FF80FF806D13C0A3007F137FA2393F803F80390E000E001A1974B92A>II<13101338137C13FE487E3803C780380783C0 380F01E0381E00F04813780070131C48130E00401304170D77B92A>I96 DIIIII<147E903803FF8090380F C1E0EB1F8790383F0FF0137EA213FCA23901F803C091C7FCADB512FCA3D801F8C7FCB3AB 487E387FFFF8A31C3B7FBA19>III< EA0380EA0FE0487EA56C5AEA0380C8FCAAEA03F012FFA312071203B3AA487EB512C0A312 387EB717>IIII<2703F00FF0EB1FE000FFD93FFCEB7FF8 913AF03F01E07E903BF1C01F83803F3D0FF3800FC7001F802603F70013CE01FE14DC49D9 07F8EB0FC0A2495CA3495CB3A3486C496CEB1FE0B500C1B50083B5FCA340257EA445>I< 3903F00FF000FFEB3FFCECF03F9039F1C01F803A0FF3800FC03803F70013FE496D7EA25B A35BB3A3486C497EB500C1B51280A329257EA42E>II<3903F01FE000 FFEB7FF89038F1E07E9039F3801F803A0FF7000FC0D803FEEB07E049EB03F04914F84913 0116FC150016FEA3167FAA16FEA3ED01FCA26DEB03F816F06D13076DEB0FE001F614C090 39F7803F009038F1E07E9038F0FFF8EC1FC091C8FCAB487EB512C0A328357EA42E>I I<3807E01F00FFEB7FC09038E1E3E09038E387F0380FE707EA03E613EE9038EC03E09038 FC0080491300A45BB3A2487EB512F0A31C257EA421>II<1318A51338A31378A313F8120112031207 001FB5FCB6FCA2D801F8C7FCB215C0A93800FC011580EB7C03017E13006D5AEB0FFEEB01 F81A347FB220>IIIIII<003FB512FCA2EB8003D83E0013F8003CEB07F00038EB0FE012 300070EB1FC0EC3F800060137F150014FE495AA2C6485A495AA2495A495A495AA290387F 000613FEA2485A485A0007140E5B4848130C4848131CA24848133C48C7127C48EB03FC90 B5FCA21F247EA325>III126 D<001C131C007F137F39FF80FF80A5397F007F00001C131C190978B72A>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FR cmr10 10.95 18 /FR 18 121 df<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A3120113 80120313005A120E5A1218123812300B1C798919>44 D<121EEA7F80A2EAFFC0A4EA7F80 A2EA1E000A0A798919>46 D<15074B7EA34B7EA34B7EA34B7EA34B7E15E7A2913801C7FC 15C3A291380381FEA34AC67EA3020E6D7EA34A6D7EA34A6D7EA34A6D7EA34A6D7EA34948 6D7E91B6FCA249819138800001A249C87EA24982010E157FA2011E82011C153FA2013C82 0138151FA2017882170F13FC00034C7ED80FFF4B7EB500F0010FB512F8A33D417DC044> 65 DI<011FB512FCA3D9000713006E5A1401B3B3A6123FEA7F 80EAFFC0A44A5A1380D87F005B007C130700385C003C495A6C495A6C495A2603E07EC7FC 3800FFF8EB3FC026407CBD2F>74 DI97 D100 DI105 D<1478EB01FEA2EB03FFA4EB01 FEA2EB00781400AC147FEB7FFFA313017F147FB3B3A5123E127F38FF807E14FEA214FCEB 81F8EA7F01387C03F0381E07C0380FFF803801FC00185185BD1C>III<3901F801FE00FF903807FFC091381E07E09138 7803F000079038E001F82603F9C07F0001138001FB6D7E91C7FC13FF5BA25BB3A6486C49 7EB5D8F87F13FCA32E287DA733>110 D<14FF010713E090381F81F890387E007E01F813 1F4848EB0F804848EB07C04848EB03E0000F15F04848EB01F8A2003F15FCA248C812FEA4 4815FFA96C15FEA36C6CEB01FCA3001F15F86C6CEB03F0A26C6CEB07E06C6CEB0FC06C6C EB1F80D8007EEB7E0090383F81FC90380FFFF0010090C7FC282A7EA82D>I<3901F807E0 00FFEB1FF8EC787CECE1FE3807F9C100031381EA01FB1401EC00FC01FF1330491300A35B B3A5487EB512FEA31F287EA724>114 D118 D120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FS cmbx10 10.95 28 /FS 28 122 df40 D<127012F8127C7EEA3F806C7E6C7E12076C7E7F6C7E6C 7EA2137F80133F806D7EA280130FA280130780A36D7EA4807FA51580B01500A55B5CA449 5AA35C130F5CA2131F5CA2495A5C137F91C7FC13FEA2485A485A5B485A120F485A485A00 3EC8FC5A5A1270195A7AC329>I44 D46 D48 D<903803FF80013F13F890B512FE00036E7E4881260FF80F7F261FC0037F4848C67F486C 6D7E6D6D7E487E6D6D7EA26F1380A46C5A6C5A6C5A0007C7FCC8FC4B1300A25E153F5E4B 5AA24B5A5E4A5B4A5B4A48C7FC5D4A5AEC1FE04A5A4A5A9139FF000F80EB01FC495A4948 EB1F00495AEB1F8049C7FC017E5C5B48B7FC485D5A5A5A5A5AB7FC5EA4293C7BBB34>50 D59 D77 D85 DII<903807FFC0013F13F848B6FC48812607FE037F26 0FF8007F6DEB3FF0486C806F7EA36F7EA26C5A6C5AEA01E0C8FC153F91B5FC130F137F39 01FFFE0F4813E0000F1380381FFE00485A5B485A12FF5BA4151F7F007F143F6D90387BFF 806C6C01FB13FE391FFF07F36CEBFFE100031480C6EC003FD91FF890C7FC2F2B7DA933> 97 D99 D101 DI<903A03FF8007F0013F9038F83FF8499038FCFFFC48B712FE 48018313F93A07FC007FC34848EB3FE1001FEDF1FC4990381FF0F81700003F81A7001F5D A26D133F000F5D6C6C495A3A03FF83FF8091B5C7FC4814FC01BF5BD80F03138090CAFCA2 487EA27F13F06CB6FC16F016FC6C15FF17806C16C06C16E01207001F16F0393FE0000348 48EB003F49EC1FF800FF150F90C81207A56C6CEC0FF06D141F003F16E001F0147FD81FFC 903801FFC02707FF800F13006C90B55AC615F8013F14E0010101FCC7FC2F3D7DA834>I< EA01F8487E487E487E481380A66C13006C5A6C5A6C5AC8FCA913FFB5FCA512077EB3ABB5 12F8A515407CBF1D>105 D<13FFB5FCA512077EB092380FFFFEA5DB01FEC7FC4B5AED07 F0ED1FE04B5A4B5A4BC8FCEC03FC4A5A4A5A141F4A7EECFFFCA2818102E77F02C37F1481 02007F826F7E6F7E151F6F7E826F7F6F7F816F7FB5D8FC07EBFFC0A5323F7DBE37>107 D<01FFD91FF8ECFFC0B590B5010713F80203DAC01F13FE4A6E487FDA0FE09026F07F077F 91261F003FEBF8010007013EDAF9F0806C0178ECFBC04A6DB4486C7FA24A92C7FC4A5CA3 4A5CB3A4B5D8FE07B5D8F03FEBFF80A551297CA858>109 D<01FFEB1FF8B5EBFFFE0203 6D7E4A80DA0FE07F91381F007F0007013C806C5B4A6D7E5CA25CA35CB3A4B5D8FE0FB512 E0A533297CA83A>II<01FFEBFFE0 B5000713FC021FEBFF80027F80DAFF8113F09139FC007FF8000701F06D7E6C496D7E4A13 0F4A6D7E1880A27013C0A38218E0AA4C13C0A318805E18005E6E5C6E495A6E495A02FCEB FFF0DAFF035B92B55A029F91C7FC028713FC028113C00280C9FCACB512FEA5333B7DA83A >I<3901FE01FE00FF903807FF804A13E04A13F0EC3F1F91387C3FF8000713F8000313F0 EBFFE0A29138C01FF0ED0FE091388007C092C7FCA391C8FCB3A2B6FCA525297DA82B> 114 D<90383FFC1E48B512BE000714FE5A381FF00F383F800148C7FC007E147EA200FE14 3EA27E7F6D90C7FC13F8EBFFE06C13FF15C06C14F06C806C806C806C80C61580131F1300 020713C014000078147F00F8143F151F7EA27E16806C143F6D140001E013FF9038F803FE 90B55A15F0D8F87F13C026E00FFEC7FC222B7DA929>III119 D121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FT cmbx12 14.4 36 /FT 36 124 df45 D<91380FFFC091B512FC0107ECFF80011F15 E090263FF8077F9026FF800113FC4848C76C7ED803F86E7E491680D807FC8048B416C080 486D15E0A4805CA36C17C06C5B6C90C75AD801FC1680C9FC4C13005FA24C5A4B5B4B5B4B 13C04B5BDBFFFEC7FC91B512F816E016FCEEFF80DA000713E0030113F89238007FFE707E 7013807013C018E07013F0A218F8A27013FCA218FEA2EA03E0EA0FF8487E487E487EB57E A318FCA25E18F891C7FC6C17F0495C6C4816E001F04A13C06C484A1380D80FF84A13006C B44A5A6CD9F0075BC690B612F06D5D011F1580010302FCC7FCD9001F1380374F7ACD43> 51 D66 D<932601FFFCEC01C0047FD9FFC013030307B600F81307033F03FE131F92B8EA803F0203 DAE003EBC07F020F01FCC7383FF0FF023F01E0EC0FF94A01800203B5FC494848C9FC4901 F8824949824949824949824949824990CA7E494883A2484983485B1B7F485B481A3FA248 49181FA3485B1B0FA25AA298C7FC5CA2B5FCAE7EA280A2F307C07EA36C7FA21B0F6C6D19 80A26C1A1F6C7F1C006C6D606C6D187EA26D6C606D6D4C5A6D6D16036D6D4C5A6D6D4C5A 6D01FC4C5A6D6DEE7F806D6C6C6C4BC7FC6E01E0EC07FE020F01FEEC1FF80203903AFFE0 01FFF0020091B612C0033F93C8FC030715FCDB007F14E0040101FCC9FC525479D261>I< BB12FEA5D8000701F8C700077FF0007F191F190785858586861B80A21A1FA31A0FA41BC0 06F81307A497C7FCA31701A317031707170F177F92B6FCA59238F8007F170F1707170317 01A31700A795C9FCB3B812F8A54A517CD055>70 D73 D76 DII<93380FFFC00303B6FC031F15E092B712 FC0203D9FC0013FF020F01C0010F13C0023F90C7000313F0DA7FFC02007F902601FFF0ED 3FFE49496F7E49496F7F49496F7F4990C96C7F4948707F4948707F01FF854A177F488648 49717EA24849711380A2481BC04A83481BE0A24A83481BF0A3481BF8A291CB7EA3B51AFC AF6C1BF8A26E5FA36C1BF0A36C6D4D13E0A36C1BC06E5F6C1B806E5F6CDB01FE16006C6D 902607FF80495A4C13E06C6D013F6D495A017F91267F03F85C6D6C90277C00FC015B6D6C 49D97E035B6D01806E485B6D6D48D91F8F5B6D01E0039F90C7FC6D01F06EB45A6DD9FCF8 5DDA3FFF6E13F0020F6D4913C0020301FF90B5C8FC020091B512FC031F180C0303181EDB 001FEBE3FE93C7EA01FF74133E74137E7413FEF2F8077290B5FC1CFCA285A21CF8A2851C F07314E0A27314C0731480731400735B9638007FF8F21FE0576A79D265>81 DI<91260FFF80130791B500 F85B010702FF5B011FEDC03F49EDF07F9026FFFC006D5A4801E0EB0FFD4801800101B5FC 4848C87E48488149150F001F824981123F4981007F82A28412FF84A27FA26D82A27F7F6D 93C7FC14C06C13F014FF15F86CECFF8016FC6CEDFFC017F06C16FC6C16FF6C17C06C836C 836D826D82010F821303010082021F16801400030F15C0ED007F040714E01600173F050F 13F08383A200788200F882A3187FA27EA219E07EA26CEFFFC0A27F6D4B13806D17006D5D 01FC4B5A01FF4B5A02C04A5A02F8EC7FF0903B1FFFC003FFE0486C90B65AD8FC0393C7FC 48C66C14FC48010F14F048D9007F90C8FC3C5479D24B>I<003FBC1280A59126C0003F90 38C0007F49C71607D87FF8060113C001E08449197F49193F90C8171FA2007E1A0FA3007C 1A07A500FC1BE0481A03A6C994C7FCB3B3AC91B912F0A553517BD05E>I87 D<001FBA12C01AE0A40380C714C002 F8C75A02C0178091C8481400495D495F494B5B495D495F48484B5B5F495F94B55A5E90C8 5D4C91C7FC5E60003E4B5B5E604C5B5EC95C93B55A5D604B91C8FC5D5F4B5B5D5F4B5B5D 5F92B55A5C5F4A91C9FC5C5E4A5B5C4CEC03E04A5B5C5E91B55A5B4C14074991C8FC4918 C05D495B5B4B150F495B5B4B151F90B55A48183F5D4891C9127F4818FF4A5D48495D485F 4A5D4849033F1380484CB5FC4A143FBBFCA47E435279D152>90 D97 DI<913801FFF8021FEBFF80 91B612F0010315FC010F9038C00FFE903A1FFE0001FFD97FFC491380D9FFF05B4817C048 495B5C5A485BA2486F138091C7FC486F1300705A4892C8FC5BA312FFAD127F7FA27EA2EF 03E06C7F17076C6D15C07E6E140F6CEE1F806C6DEC3F006C6D147ED97FFE5C6D6CEB03F8 010F9038E01FF0010390B55A01001580023F49C7FC020113E033387CB63C>I<4DB47E04 07B5FCA5EE001F1707B3A4913801FFE0021F13FC91B6FC010315C7010F9038E03FE74990 380007F7D97FFC0101B5FC49487F4849143F484980485B83485B5A91C8FC5AA3485AA412 FFAC127FA36C7EA37EA26C7F5F6C6D5C7E6C6D5C6C6D49B5FC6D6C4914E0D93FFED90FEF EBFF80903A0FFFC07FCF6D90B5128F0101ECFE0FD9003F13F8020301C049C7FC41547CD2 4B>I<913803FFC0023F13FC49B6FC010715C04901817F903A3FFC007FF849486D7E4948 6D7E4849130F48496D7E48178048497F18C0488191C7FC4817E0A248815B18F0A212FFA4 90B8FCA318E049CAFCA6127FA27F7EA218E06CEE01F06E14037E6C6DEC07E0A26C6DEC0F C06C6D141F6C6DEC3F806D6CECFF00D91FFEEB03FE903A0FFFC03FF8010390B55A010015 C0021F49C7FC020113F034387CB63D>IIII<137F497E000313E0487FA2487FA76C5BA26C5B C613806DC7FC90C8FCADEB3FF0B5FCA512017EB3B3A6B612E0A51B547BD325>I108 DII<913801FFE0021F13FE91B612C0010315F0010F9038807FFC90 3A1FFC000FFED97FF86D6C7E49486D7F48496D7F48496D7F4A147F48834890C86C7EA248 83A248486F7EA3007F1880A400FF18C0AC007F1880A3003F18006D5DA26C5FA26C5F6E14 7F6C5F6C6D4A5A6C6D495B6C6D495B6D6C495BD93FFE011F90C7FC903A0FFF807FFC6D90 B55A010015C0023F91C8FC020113E03A387CB643>I<903A3FF001FFE0B5010F13FE033F EBFFC092B612F002F301017F913AF7F8007FFE0003D9FFE0EB1FFFC602806D7F92C76C7F 4A824A6E7F4A6E7FA2717FA285187F85A4721380AC1A0060A36118FFA2615F616E4A5BA2 6E4A5B6E4A5B6F495B6F4990C7FC03F0EBFFFC9126FBFE075B02F8B612E06F1480031F01 FCC8FC030313C092CBFCB1B612F8A5414D7BB54B>I<90397FE003FEB590380FFF80033F 13E04B13F09238FE1FF89139E1F83FFC0003D9E3E013FEC6ECC07FECE78014EF150014EE 02FEEB3FFC5CEE1FF8EE0FF04A90C7FCA55CB3AAB612FCA52F367CB537>114 D<903903FFF00F013FEBFE1F90B7FC120348EB003FD80FF81307D81FE0130148487F4980 127F90C87EA24881A27FA27F01F091C7FC13FCEBFFC06C13FF15F86C14FF16C06C15F06C 816C816C81C681013F1580010F15C01300020714E0EC003F030713F015010078EC007F00 F8153F161F7E160FA27E17E07E6D141F17C07F6DEC3F8001F8EC7F0001FEEB01FE9039FF C00FFC6DB55AD8FC1F14E0D8F807148048C601F8C7FC2C387CB635>I<143EA6147EA414 FEA21301A313031307A2130F131F133F13FF5A000F90B6FCB8FCA426003FFEC8FCB3A9EE 07C0AB011FEC0F8080A26DEC1F0015806DEBC03E6DEBF0FC6DEBFFF86D6C5B021F5B0203 13802A4D7ECB34>II<007FB500F090387FFFFEA5C66C 48C7000F90C7FC6D6CEC07F86D6D5C6D6D495A6D4B5A6F495A6D6D91C8FC6D6D137E6D6D 5B91387FFE014C5A6E6C485A6EEB8FE06EEBCFC06EEBFF806E91C9FCA26E5B6E5B6F7E6F 7EA26F7F834B7F4B7F92B5FCDA01FD7F03F87F4A486C7E4A486C7E020F7FDA1FC0804A48 6C7F4A486C7F02FE6D7F4A6D7F495A49486D7F01076F7E49486E7E49486E7FEBFFF0B500 FE49B612C0A542357EB447>120 DI 123 D E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 93 1 93 96 bop 1699 790 a FQ(CHAPTER)41 b(5)1446 1089 y FT(Mo)t(dular)k(F) -11 b(unctor)605 1372 y FQ(Giv)n(en)37 b(a)f(mo)r(dular)h(tensor)f (category)f FL(C)5 b FQ(,)39 b(in)e(the)g(previous)f(c)n(hapter)g(w)n (e)h(constructed)456 1471 y(a)d(3-dimensional)g(T)-7 b(op)r(ological)34 b(Quan)n(tum)h(Field)h(Theory)e(\(3D)h(TQFT\).)h (Moreo)n(v)n(er,)e(this)456 1571 y(3D)29 b(TQFT)g(w)n(as)g(based)g(on)g (an)g(extended)h(notion)f(of)g(a)h(manifold)f(\(a)g(usual)g(manifold)h (with)456 1671 y(additional)25 b(data\).)36 b(In)26 b(this)g(c)n (hapter,)f(w)n(e)g(will)h(sho)n(w)f(that)h(the)g(notion)f(of)h(a)f(mo)r (dular)g(tensor)456 1770 y(category)e(\(MTC\))k(is)e(essen)n(tially)g (equiv)-5 b(alen)n(t)25 b(to)h(some)f(geometric)g(construction)f(in)i (dimen-)456 1870 y(sion)k(2.)46 b(The)31 b(righ)n(t)f(notion)h(here)f (is)h(that)g(of)g(a)f(mo)r(dular)g(functor,)i(whic)n(h)f(w)n(as)f(in)n (tro)r(duced)456 1969 y(b)n(y)h(Segal)f(\(see)h([)p FK(S)p FQ(]\).)48 b(Our)31 b(exp)r(osition)f(mostly)h(follo)n(ws)f(the)i(pap)r (ers)f([)p FK(S,)k(MS1,)g(MS2)o(,)h(T)p FQ(])456 2069 y(and)27 b(folklore)f(of)i(mathematical)f(ph)n(ysicists.)1505 2258 y FK(5.1.)47 b(Mo)s(dular)31 b(functor)605 2408 y FP(Definition)h FQ(5.1.1)p FP(.)40 b FQ(A)18 b(\()p FO(top)l(olo)l(gic)l(al)p FQ(\))24 b FJ(d)p FO(-dimensional)f(mo)l (dular)f(functor)28 b FQ(\(MF)19 b(for)e(short\))456 2507 y(is)27 b(the)h(follo)n(wing)f(collection)g(of)g(data:)605 2607 y(\(i\))21 b(A)f(v)n(ector)f(space)h FJ(\034)9 b FQ(\()p FJ(N)g FQ(\))21 b(assigned)e(to)h(an)n(y)f(orien)n(ted)g (compact)h FJ(d)p FQ(-manifold)g FJ(N)29 b FQ(without)456 2706 y(b)r(oundary)-7 b(.)605 2809 y(\(ii\))37 b(An)g(isomorphism)e FJ(f)1432 2821 y FE(\003)1479 2809 y FQ(:)c FJ(\034)9 b FQ(\()p FJ(N)1677 2821 y FM(1)1715 2809 y FQ(\))1813 2762 y FE(\030)1784 2809 y FL(\000)-39 b(!)37 b FJ(\034)9 b FQ(\()p FJ(N)2074 2821 y FM(2)2112 2809 y FQ(\))37 b(of)f(v)n(ector)f(spaces)h(assigned)f(to)h(ev)n(ery)456 2915 y(homeomorphism)26 b FJ(f)18 b FQ(:)28 b FJ(N)1256 2927 y FM(1)1344 2868 y FE(\030)1316 2915 y FL(\000)-40 b(!)23 b FJ(N)1514 2927 y FM(2)1551 2915 y FQ(,)28 b(whic)n(h)f(dep)r (ends)h(only)g(on)f(the)h(isotop)n(y)e(class)h(of)g FJ(f)9 b FQ(.)605 3017 y(\(iii\))34 b(Isomorphisms)d FJ(\034)9 b FQ(\()p FL(;)p FQ(\))1515 2970 y FE(\030)1486 3017 y FL(\000)-39 b(!)32 b FJ(k)s FQ(,)i FJ(\034)9 b FQ(\()p FJ(N)1874 3029 y FM(1)1934 3017 y FL(t)23 b FJ(N)2079 3029 y FM(2)2116 3017 y FQ(\))2209 2970 y FE(\030)2180 3017 y FL(\000)-39 b(!)32 b FJ(\034)9 b FQ(\()p FJ(N)2465 3029 y FM(1)2503 3017 y FQ(\))22 b FL(\012)g FJ(\034)9 b FQ(\()p FJ(N)2788 3029 y FM(2)2826 3017 y FQ(\),)35 b(where)d FJ(k)k FQ(is)d(the)456 3117 y(base)27 b(\014eld.)456 3217 y(These)g(data)g(ha)n(v)n(e)f(to)i(satisfy)f(the)h(follo)n(wing)f (axioms:)612 3337 y FK(Multiplicativit)m(y:)40 b FQ(\()p FJ(f)9 b(g)s FQ(\))1491 3349 y FE(\003)1552 3337 y FQ(=)22 b FJ(f)1680 3349 y FE(\003)1718 3337 y FJ(g)1758 3349 y FE(\003)1796 3337 y FQ(,)28 b(id)1916 3349 y FE(\003)1977 3337 y FQ(=)23 b(id.)612 3437 y FK(F)-8 b(unctorialit)m(y:)41 b FQ(the)28 b(isomorphisms)e(\(iii\))j(are)d(functorial.)612 3536 y FK(Compatibilit)m(y:)38 b FQ(the)23 b(isomorphisms)f(of)g(part)h (\(iii\))g(are)f(compatible)g(with)h(the)h(canon-)711 3636 y(ical)38 b(isomorphisms)f FJ(N)d FL(t)26 b(;)40 b FQ(=)g FJ(N)9 b FQ(,)41 b FJ(N)1979 3648 y FM(1)2041 3636 y FL(t)26 b FJ(N)2189 3648 y FM(2)2267 3636 y FQ(=)40 b FJ(N)2439 3648 y FM(2)2501 3636 y FL(t)26 b FJ(N)2649 3648 y FM(1)2686 3636 y FQ(,)41 b(\()p FJ(N)2849 3648 y FM(1)2912 3636 y FL(t)26 b FJ(N)3060 3648 y FM(2)3097 3636 y FQ(\))f FL(t)h FJ(N)3302 3648 y FM(3)3380 3636 y FQ(=)711 3736 y FJ(N)778 3748 y FM(1)834 3736 y FL(t)18 b FQ(\()p FJ(N)1006 3748 y FM(2)1062 3736 y FL(t)h FJ(N)1203 3748 y FM(3)1240 3736 y FQ(\).)612 3835 y FK(Normalization:)39 b FQ(W)-7 b(e)41 b(ha)n(v)n(e)e(an)h(isomorphism)g FJ(\034)9 b FQ(\()p FJ(S)2394 3805 y FI(d)2433 3835 y FQ(\))45 b(=)g FJ(k)s FQ(,)f(where)c FJ(S)3042 3805 y FI(d)3121 3835 y FQ(is)g(the)i FJ(d)p FQ(-)711 3935 y(dimensional)27 b(sphere.)605 4088 y(Detailed)g(statemen)n(t)g(of)g(the)h(functorialit) n(y)e(and)h(compatibilit)n(y)f(axioms)g(can)h(b)r(e)g(found)456 4188 y(in)g(Remark)g(4.2.2,)g(where)g(the)h(same)f(conditions)g(app)r (ear)f(in)i(the)g(de\014nition)g(of)g(TQFT.)605 4341 y FP(Remark)k FQ(5.1.2)p FP(.)39 b FQ(An)n(y)20 b(\()p FJ(d)r FQ(+)r(1\)D)e(TQFT)h(\(see)g(De\014nition)h(4.2.1\))e(giv)n(es)g (a)h FJ(d)p FQ(-dimensional)456 4441 y(MF,)26 b(b)r(ecause)g(the)g (axioms)f(of)h(a)g(MF,)h(except)f(for)f(the)i(requiremen)n(t)e(that)h FJ(f)2906 4453 y FE(\003)2970 4441 y FQ(dep)r(ends)h(only)456 4541 y(on)34 b(the)h(isotop)n(y)e(class)h(of)h FJ(f)9 b FQ(,)36 b(are)e(con)n(tained)g(in)g(the)h(axioms)f(of)h(a)f(TQFT,)g (and)h(this)g(last)456 4640 y(condition)27 b(is)g(satis\014ed)h(b)n(y)f (Theorem)g(4.2.3.)605 4740 y(This)f(mo)r(dular)f(functor)g(is)h FO(unitary)p FQ(:)36 b(in)26 b(addition)f(to)h(the)g(data)f(ab)r(o)n(v) n(e,)g(there)h(are)e(func-)456 4842 y(torial)40 b(isomorphisms)g FJ(\034)9 b FQ(\()p 1300 4775 60 4 v(\006)q(\))1468 4795 y FE(\030)1439 4842 y FL(\000)-39 b(!)46 b FJ(\034)9 b FQ(\(\006\))1763 4812 y FE(\003)1802 4842 y FQ(,)46 b(where)p 2124 4775 V 40 w(\006)c(is)f(the)h(manifold)f(\006)h(with)g (opp)r(osite)456 4942 y(orien)n(tation,)26 b(whic)n(h)h(are)g (compatible)g(with)i(the)e(isomorphisms)g(of)g(part)g(\(iii\).)605 5095 y FP(Definition)32 b FQ(5.1.3)p FP(.)40 b FQ(\(i\))28 b(W)-7 b(e)28 b(de\014ne)g(a)f(category)f(\000)h(with:)612 5216 y FK(Ob)5 b(jects:)41 b FJ(d)p FQ(-manifolds.)1917 5365 y FM(93)p eop %%Page: 94 2 94 97 bop 456 226 a FM(94)1043 b(5.)29 b(MODULAR)g(FUNCTOR)612 425 y FK(Morphisms:)38 b FQ(Mor)1295 437 y FM(\000)1340 425 y FQ(\()p FJ(N)1439 437 y FM(1)1476 425 y FJ(;)14 b(N)1580 437 y FM(2)1617 425 y FQ(\))23 b(=)j(isotop)n(y)e(classes)h (of)h(orien)n(tation-preserving)c(home-)711 532 y(omorphisms)27 b FJ(N)1241 544 y FM(1)1329 485 y FE(\030)1301 532 y FL(\000)-40 b(!)23 b FJ(N)1499 544 y FM(2)1536 532 y FQ(.)456 662 y(This)34 b(is)g(a)g(symmetric)g(tensor)g(category)e(with) j(the)g(\\tensor)e(pro)r(duct")h(giv)n(en)f(b)n(y)h(disjoin)n(t)456 762 y(union,)d(and)f(the)h(unit)h(giv)n(en)d(b)n(y)i FL(;)p FQ(.)45 b(\(Note)31 b(that)g(this)g(category)d(is)j(not)f (additiv)n(e:)43 b(one)30 b(can)456 862 y(not)d(add)h (homeomorphisms!\))605 961 y(\(ii\))35 b(F)-7 b(or)34 b(a)g(manifold)g FJ(N)9 b FQ(,)36 b(its)f FO(mapping)i(class)g(gr)l (oup)j FQ(\000\()p FJ(N)9 b FQ(\))35 b(is)f(the)h(group)e(of)i(isotop)n (y)456 1068 y(classes)26 b(of)h(homeomorphisms)g FJ(N)1598 1021 y FE(\030)1569 1068 y FL(\000)-39 b(!)23 b FJ(N)9 b FQ(.)37 b(In)28 b(other)f(w)n(ords,)f(\000\()p FJ(N)9 b FQ(\))23 b(:=)g(Mor)2895 1080 y FM(\000)2940 1068 y FQ(\()p FJ(N)t(;)14 b(N)9 b FQ(\).)605 1233 y(The)32 b(category)e(\000)i(is)g(a)g FO(gr)l(oup)l(oid)p FQ(,)i(i.e.,)g(a)d (category)f(in)i(whic)n(h)g(ev)n(ery)f(morphism)h(is)g(in-)456 1332 y(v)n(ertible.)75 b(One)40 b(easily)g(sees)g(that)g FJ(d)p FQ(-dimensional)g(mo)r(dular)g(functor)h(is)f(the)h(same)f(as)g (a)456 1432 y(represen)n(tation)24 b(of)i(the)g(group)r(oid)f(\000,)h (i.e.,)h(a)e(tensor)g(functor)h(\000)d FL(!)g(V)7 b FJ(ec)2751 1444 y FI(f)2793 1432 y FQ(\()p FJ(k)s FQ(\).)37 b(This)26 b(explains)456 1531 y(the)i(origin)e(of)i(the)g(term)f(\\mo)r(dular)g (functor".)605 1631 y(In)34 b(particular,)g(b)n(y)f(5.1.1\(ii\),)h(ev)n (ery)f(MF)h(de\014nes)f(a)g(represen)n(tation)f(of)i(the)g(mapping)456 1731 y(class)26 b(group)h(\000\()p FJ(N)9 b FQ(\))28 b(of)f(an)n(y)g FJ(d)p FQ(-manifold)g FJ(N)37 b FQ(on)27 b(the)h(v)n(ector)e(space)h FJ(\034)9 b FQ(\()p FJ(N)g FQ(\).)605 1830 y(F)-7 b(rom)19 b(no)n(w)g(on,)j(let)e(us)f(assume)g (that)h FJ(d)k FQ(=)e(2.)34 b(Then)20 b(ev)n(ery)e(connected)i(compact) f(orien)n(ted)456 1930 y(surface)j(is)i(determined)f(up)h(to)f (homeomorphism)g(b)n(y)g(its)g(gen)n(us)g FJ(g)s FQ(,)h(and)f (de\014ning)h(a)f(mo)r(dular)456 2030 y(functor)32 b(is)g(equiv)-5 b(alen)n(t)33 b(to)f(de\014ning)h(for)f(ev)n(ery)f FJ(g)j FL(\025)c FQ(0)j(a)f(represen)n(tation)e(of)j(the)g(mapping)456 2129 y(class)c(group)h(\000)944 2141 y FI(g)983 2129 y FQ(.)46 b(W)-7 b(e)31 b(quote)g(here)f(some)g(classical)g(results)g (regarding)f(the)i(mapping)f(class)456 2229 y(groups.)605 2393 y FP(Theorem)i FQ(5.1.4)e(\(Dehn\))p FP(.)42 b FO(L)l(et)35 b FQ(\006)g FO(b)l(e)g(a)h(c)l(omp)l(act)g(oriente)l(d)g(surfac)l(e,)i (and)d(let)g FJ(c)h FO(b)l(e)f(a)456 2493 y(simple)e(close)l(d)h(curve) f(on)f FQ(\006)p FO(.)48 b(De\014ne)32 b(the)g FQ(Dehn)g(t)n(wist)g FJ(t)2312 2505 y FI(c)2374 2493 y FL(2)d FQ(\000\(\006\))k FO(by)g(Figur)l(e)g FQ(5.1)p FO(.)3174 2463 y FM(1)3258 2493 y FO(Then)456 2593 y(the)d(elements)f FJ(t)965 2605 y FI(c)1029 2593 y FO(gener)l(ate)h(the)f(mapping)j(class)e(gr)l(oup)g FQ(\000\(\006\))p FO(.)1050 3586 y @beginspecial 0 @llx 0 @lly 216 @urx 95 @ury 2160 @rwi @setspecial %%BeginDocument: figures/dehn.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: dehn.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Sun Jun 6 11:53:21 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 216 95 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -32.0 101.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 2673 m -1000 -1000 l 5132 -1000 l 5132 2673 l cp clip 0.06000 0.06000 sc % Ellipse n 1332 890 783 783 0 360 DrawEllipse gs col7 0.75 shd ef gr % Ellipse n 3337 890 783 783 0 360 DrawEllipse gs col7 0.75 shd ef gr % Ellipse n 3347 907 388 388 0 360 DrawEllipse gs col7 1.00 shd ef gr 15.000 slw % Ellipse n 3367 912 595 595 0 360 DrawEllipse gs col-1 s gr % Ellipse n 1362 912 595 595 0 360 DrawEllipse gs col-1 s gr % Polyline 7.500 slw n 560 925 m 945 925 l gs col-1 s gr 0.000 slw % Ellipse n 1342 907 388 388 0 360 DrawEllipse gs col7 1.00 shd ef gr % Polyline 7.500 slw n 1726 915 m 1734 915 l gs col-1 s gr /Times-Italic ff 180.00 scf sf 1900 600 m gs 1 -1 sc (c) col-1 sh gr % Polyline n 1730 915 m 2105 905 l gs col-1 s gr % Polyline gs clippath 2381 885 m 2453 900 l 2381 915 l 2495 915 l 2495 885 l cp clip n 2170 900 m 2480 900 l gs col-1 s gr gr % arrowhead n 2381 885 m 2453 900 l 2381 915 l 2393 900 l 2381 885 l cp gs 0.00 setgray ef gr col-1 s % Polyline n 2560 930 m 2561 932 l 2563 936 l 2566 944 l 2571 956 l 2578 972 l 2588 992 l 2598 1017 l 2611 1044 l 2625 1074 l 2640 1106 l 2655 1138 l 2671 1170 l 2687 1201 l 2704 1230 l 2720 1258 l 2736 1283 l 2752 1306 l 2768 1327 l 2784 1346 l 2802 1364 l 2820 1380 l 2838 1394 l 2857 1407 l 2877 1420 l 2898 1433 l 2920 1445 l 2943 1458 l 2966 1470 l 2991 1482 l 3016 1494 l 3041 1506 l 3067 1518 l 3093 1530 l 3119 1541 l 3146 1552 l 3172 1563 l 3198 1572 l 3223 1581 l 3248 1590 l 3273 1597 l 3297 1603 l 3321 1608 l 3344 1612 l 3367 1614 l 3390 1615 l 3414 1614 l 3439 1611 l 3463 1606 l 3488 1600 l 3513 1592 l 3538 1583 l 3563 1573 l 3589 1562 l 3615 1551 l 3640 1538 l 3666 1525 l 3691 1512 l 3716 1499 l 3741 1485 l 3764 1471 l 3787 1458 l 3809 1444 l 3830 1431 l 3850 1417 l 3868 1403 l 3885 1389 l 3900 1375 l 3915 1358 l 3928 1341 l 3940 1322 l 3950 1302 l 3959 1281 l 3966 1259 l 3973 1237 l 3979 1214 l 3985 1190 l 3989 1166 l 3994 1143 l 3998 1119 l 4002 1096 l 4006 1074 l 4010 1053 l 4014 1033 l 4017 1014 l 4020 996 l 4023 980 l 4025 965 l 4026 946 l 4026 930 l 4025 916 l 4023 905 l 4020 895 l 4016 887 l 4013 880 l 4008 873 l 4003 866 l 3997 857 l 3990 847 l 3982 835 l 3972 821 l 3960 805 l 3950 793 l 3939 780 l 3928 766 l 3915 751 l 3902 735 l 3888 718 l 3874 700 l 3859 681 l 3844 663 l 3829 644 l 3814 625 l 3798 607 l 3782 589 l 3765 572 l 3748 556 l 3731 541 l 3713 527 l 3695 515 l 3675 504 l 3655 495 l 3636 488 l 3615 482 l 3594 476 l 3571 472 l 3547 468 l 3522 464 l 3497 461 l 3470 459 l 3443 457 l 3416 455 l 3388 453 l 3360 452 l 3333 451 l 3306 450 l 3280 450 l 3255 450 l 3231 451 l 3208 452 l 3186 454 l 3166 457 l 3147 460 l 3130 465 l 3111 472 l 3093 481 l 3076 492 l 3061 504 l 3047 518 l 3034 533 l 3022 549 l 3010 566 l 2998 583 l 2987 600 l 2977 617 l 2967 634 l 2957 651 l 2948 667 l 2940 682 l 2932 697 l 2925 711 l 2920 725 l 2915 743 l 2914 761 l 2914 780 l 2917 801 l 2922 824 l 2928 848 l 2936 872 l 2943 895 l 2951 916 l 2957 933 l 2961 945 l 2964 952 l 2965 955 l gs col-1 s gr % Polyline n 4120 915 m 4119 912 l 4116 906 l 4111 895 l 4105 878 l 4096 858 l 4085 833 l 4074 807 l 4062 779 l 4050 752 l 4039 727 l 4028 703 l 4018 682 l 4008 663 l 3999 646 l 3990 630 l 3981 615 l 3971 600 l 3962 586 l 3953 573 l 3945 559 l 3936 547 l 3928 534 l 3919 522 l 3911 509 l 3902 497 l 3892 485 l 3881 472 l 3869 459 l 3856 446 l 3841 433 l 3825 420 l 3811 409 l 3795 398 l 3779 387 l 3762 375 l 3744 363 l 3725 351 l 3706 337 l 3686 324 l 3665 311 l 3645 297 l 3624 284 l 3603 271 l 3583 259 l 3562 248 l 3541 237 l 3521 228 l 3501 220 l 3480 213 l 3460 208 l 3440 205 l 3419 203 l 3399 203 l 3377 204 l 3356 207 l 3334 210 l 3311 214 l 3288 220 l 3265 225 l 3242 232 l 3218 238 l 3195 245 l 3172 253 l 3150 260 l 3127 268 l 3106 276 l 3085 284 l 3065 292 l 3046 301 l 3027 310 l 3010 320 l 2992 332 l 2974 345 l 2958 359 l 2942 374 l 2926 390 l 2911 407 l 2896 424 l 2881 441 l 2867 459 l 2853 477 l 2839 495 l 2826 513 l 2813 531 l 2801 548 l 2791 566 l 2781 584 l 2772 602 l 2765 620 l 2759 638 l 2755 657 l 2751 676 l 2748 695 l 2746 714 l 2744 733 l 2743 753 l 2741 772 l 2740 792 l 2740 812 l 2740 831 l 2742 851 l 2744 871 l 2748 892 l 2753 912 l 2760 933 l 2769 954 l 2780 975 l 2790 991 l 2802 1008 l 2815 1025 l 2829 1043 l 2845 1062 l 2862 1081 l 2879 1101 l 2898 1121 l 2917 1142 l 2937 1164 l 2958 1185 l 2978 1206 l 2999 1228 l 3020 1248 l 3041 1268 l 3062 1288 l 3083 1306 l 3103 1324 l 3123 1340 l 3143 1354 l 3163 1367 l 3182 1378 l 3201 1387 l 3220 1395 l 3241 1401 l 3262 1405 l 3284 1408 l 3306 1408 l 3329 1407 l 3352 1404 l 3375 1400 l 3399 1395 l 3424 1390 l 3448 1383 l 3472 1376 l 3496 1369 l 3520 1361 l 3544 1353 l 3566 1346 l 3588 1338 l 3609 1331 l 3629 1324 l 3648 1317 l 3665 1310 l 3681 1302 l 3695 1295 l 3712 1284 l 3727 1272 l 3740 1258 l 3752 1244 l 3761 1228 l 3770 1212 l 3777 1196 l 3784 1179 l 3790 1162 l 3796 1145 l 3801 1129 l 3807 1113 l 3811 1097 l 3815 1083 l 3818 1069 l 3820 1055 l 3820 1040 l 3818 1025 l 3813 1009 l 3806 992 l 3796 973 l 3786 954 l 3774 935 l 3762 917 l 3751 900 l 3742 887 l 3736 878 l 3732 873 l 3730 870 l gs col-1 s gr /Times-Italic ff 180.00 scf sf 3900 600 m gs 1 -1 sc (c) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1488 3786 a FP(Figure)i(5.1.)41 b FQ(Dehn)28 b(t)n(wist.)605 4068 y(This)37 b(theorem)g(w)n(as)f(later)g(re\014ned)h (b)n(y)g(Lic)n(k)n(orish)e([)p FK(Li)p FQ(],)40 b(who)d(suggested)f(a)h (\014nite)g(set)456 4168 y(of)h(Dehn)i(t)n(wists)f(generating)e (\000\(\006\).)71 b(Finally)-7 b(,)42 b(an)c(approac)n(h)f(allo)n(wing) h(one)g(to)h(describ)r(e)456 4267 y(the)34 b(generators)d(and)i (relations)g(in)g(\000\(\006\))i(w)n(as)d(giv)n(en)h(in)h([)p FK(HT)p FQ(].)55 b(F)-7 b(or)33 b(surfaces)f(of)i(gen)n(us)f FJ(g)456 4367 y FQ(with)26 b(0)g(or)f(1)h(b)r(oundary)g(comp)r(onen)n (ts)f(\(or)h(mark)n(ed)f(p)r(oin)n(ts\),)i(the)f(ideas)g(of)g([)p FK(HT)p FQ(])h(w)n(ere)e(fully)456 4466 y(dev)n(elop)r(ed)g(in)h([)p FK(W)-8 b(a)5 b(j)q FQ(],)27 b(where)e(a)h(complete)g(set)g(of)g (generators)e(and)h(relations)g(for)h(\000)3152 4478 y FI(g)3213 4466 y FL(\021)d FQ(\000)3353 4478 y FI(g)r(;)p FM(0)456 4566 y FQ(and)k(\000)669 4578 y FI(g)r(;)p FM(1)788 4566 y FQ(is)h(written.)605 4731 y FP(Example)j FQ(5.1.5)p FP(.)40 b FQ(Let)33 b FJ(g)h FQ(=)d(1,)i(i.e.,)h(let)f(\006)g(b)r(e)g (a)f(t)n(w)n(o-dimensional)f(torus.)52 b(Then,)34 b(b)n(y)456 4830 y(Theorem)26 b(4.1.3,)g(\000)1079 4842 y FM(1)1139 4830 y FL(')d FQ(SL)1325 4842 y FM(2)1362 4830 y FQ(\()p FH(Z)p FQ(\),)f(whic)n(h)27 b(can)g(b)r(e)h(describ)r(ed)f(as)f(the)i (group)e(with)i(generators)p 456 4958 499 4 v 605 5026 a Fp(1)640 5050 y Fo(Here)i(w)n(e)h(put)g(some)e(auxiliary)h(lines)g (on)h(the)g(surface)g(to)g(demonstrate)g(the)g(action)h(of)e(the)h (home-)456 5133 y(omorphisms.)50 b(These)31 b(lines)g(are)g(for)f (illustration)g(purp)r(oses)h(only)-6 b(.)53 b(Note)32 b(that)g Fm(c)f Fo(is)f(not)i(required)e(to)i(b)r(e)456 5216 y(orien)n(ted.)p eop %%Page: 95 3 95 98 bop 1539 226 a FM(5.1.)29 b(MODULAR)g(FUNCTOR)995 b(95)456 425 y FJ(s;)14 b(t)38 b FQ(and)h(relations)e(\()p FJ(st)p FQ(\))1254 395 y FM(3)1334 425 y FQ(=)k FJ(s)1479 395 y FM(2)1516 425 y FJ(;)14 b(s)1592 395 y FM(4)1671 425 y FQ(=)41 b(1)d(\(whic)n(h)h(implies)g FJ(s)2470 395 y FM(2)2507 425 y FJ(t)j FQ(=)f FJ(ts)2754 395 y FM(2)2791 425 y FQ(\).)71 b(It)39 b(can)f(also)g(b)r(e)456 525 y(generated)26 b(b)n(y)h(the)h(elemen)n(ts)1322 705 y FJ(t)1352 717 y FI(a)1415 705 y FQ(=)23 b FJ(t)g FQ(=)1643 587 y Fy(\022)1704 654 y FQ(1)83 b(1)1704 754 y(0)g(1)1870 587 y Fy(\023)1945 705 y FJ(;)97 b(t)2095 717 y FI(b)2152 705 y FQ(=)2239 587 y Fy(\022)2300 654 y FQ(1)83 b(0)2300 754 y(1)g(1)2466 587 y Fy(\023)2541 705 y FJ(;)456 884 y FQ(whic)n(h)23 b(corresp)r(ond)g(to)g(Dehn)i(t)n(wists)f(around)f (the)h(meridian)f(and)h(the)g(parallel)f(of)h(the)g(torus.)605 1026 y(It)h(turns)f(out)h(that)g(for)f FJ(d)f FQ(=)g(2)h(the)h(notion)f (of)h(mo)r(dular)f(functor)g(can)h(b)r(e)g(generalized)e(b)n(y)456 1126 y(allo)n(wing)j(surfaces)g(with)i(\\holes",)e(i.e.,)i(with)g(b)r (oundary)-7 b(.)605 1267 y FP(Definition)32 b FQ(5.1.6)p FP(.)40 b FQ(An)24 b FO(extende)l(d)i(surfac)l(e)31 b FQ(is)24 b(a)f(compact)g(orien)n(ted)h(surface)f(\006,)h(p)r(ossi-)456 1369 y(bly)18 b(with)h(b)r(oundary)-7 b(,)20 b(together)d(with)i(an)f (orien)n(tation-preserving)d(parameterization)h FJ(\031)3246 1381 y FI(i)3283 1369 y FQ(:)28 b(\()p FJ(@)5 b FQ(\006\))3507 1381 y FI(i)3586 1322 y FE(\030)3558 1369 y FL(\000)-39 b(!)456 1469 y FJ(S)512 1439 y FM(1)575 1469 y FQ(of)25 b(ev)n(ery)g(b)r(oundary)g(circle.)36 b(Here)25 b(\()p FJ(@)5 b FQ(\006\))1873 1481 y FI(i)1927 1469 y FQ(is)26 b(considered)f(with)h(the)g(orien)n(tation)f(induced)456 1569 y(from)i(\006,)h(and)f FJ(S)980 1539 y FM(1)1040 1569 y FQ(=)c FL(f)p FJ(z)i FL(2)f FH(C)44 b FL(j)23 b(j)p FJ(z)t FL(j)f FQ(=)h(1)p FL(g)k FQ(with)h(the)g(coun)n(terclo)r (c)n(kwise)d(orien)n(tation.)605 1668 y(By)e(a)f FO(genus)30 b FQ(of)23 b(an)f(extended)i(surface,)f(w)n(e)f(will)h(mean)g(the)h (gen)n(us)e(of)h(the)g(closed)f(surface)456 1768 y FJ(cl)r FQ(\(\006\))29 b(obtained)g(b)n(y)g(\\patc)n(hing)f(the)i(holes)e(of)h (\006",)h(i.e.,)g(gluing)e(a)h(disk)g(to)g(ev)n(ery)f(b)r(oundary)456 1868 y(circle.)605 1967 y(A)21 b FO(home)l(omorphism)29 b FQ(of)20 b(extended)g(surfaces)f FJ(f)f FQ(:)28 b(\006)2259 1920 y FE(\030)2231 1967 y FL(\000)-40 b(!)24 b FQ(\006)2423 1937 y FE(0)2466 1967 y FQ(is)c(an)g(orien)n(tation-preserving)456 2067 y(homeomorphism)26 b(whic)n(h)h(also)g(preserv)n(es)f (parameterizations.)605 2169 y(Finally)-7 b(,)32 b(for)e(an)h(extended) g(surface)g(\(\006)p FJ(;)14 b(\031)1973 2181 y FI(i)2010 2169 y FQ(:)29 b(\()p FJ(@)5 b FQ(\006\))2235 2181 y FI(i)2320 2122 y FE(\030)2292 2169 y FL(\000)-40 b(!)29 b FJ(S)2485 2139 y FM(1)2522 2169 y FQ(\))i(w)n(e)g(de\014ne)g(the)h (op)r(eration)456 2271 y(of)27 b FO(orientation)k(r)l(eversal)37 b FQ(b)n(y)27 b(\()p 1441 2205 60 4 v(\006)q FJ(;)14 b FL(\000)p 1604 2226 75 4 v FJ(\031)1651 2283 y FI(i)1678 2271 y FQ(\))28 b(\()p FK(note)k(the)f(min)m(us)f(sign!)p FQ(\).)605 2413 y(The)f(notion)g(of)g(isotop)n(y)f(of)i(homeomorphisms) d(is)i(trivially)g(generalized)f(to)h(this)g(case,)456 2513 y(as)d(w)n(ell)i(as)e(the)i(notion)f(of)h(disjoin)n(t)f(union.)37 b(Th)n(us,)27 b(w)n(e)g(can)g(de\014ne)h(the)g(extended)g(group)r(oid) 456 2612 y FL(T)7 b FJ(eich)27 b FQ(similarly)f(to)i(De\014nition)g (5.1.3\(i\).)605 2754 y FP(Definition)k FQ(5.1.7)p FP(.)40 b FQ(\(i\))29 b(The)h(\()p FO(extende)l(d)p FQ(\))f FO(T)-6 b(eichm)q(\177)-43 b(ul)t(ler)33 b(gr)l(oup)l(oid)39 b FL(T)7 b FJ(eich)29 b FQ(is)g(the)g(cate-)456 2854 y(gory)d(with)j(ob)5 b(jects)28 b(extended)g(surfaces,)g(and)g (morphisms)f(isotop)n(y)g(classes)g(of)h(homeomor-)456 2953 y(phisms)f(of)h(extended)g(surfaces)e(\(see)i(De\014nition)g (5.1.6\).)605 3053 y(\(ii\))23 b(F)-7 b(or)22 b(an)n(y)f(extended)i (surface)e(\006,)j(its)e FO(mapping)k(class)g(gr)l(oup)i FQ(\000\(\006\))23 b(is)f(the)g(group)g(of)g(all)456 3160 y(isotop)n(y)j(classes)g(of)i(homeomorphisms)e(\006)1864 3113 y FE(\030)1836 3160 y FL(\000)-40 b(!)23 b FQ(\006.)37 b(\(Sometimes)27 b(the)f(name)h(\\mapping)e(class)456 3259 y(group")c(is)h(used)h(for)f(the)h(smaller)f(group)f(\000)1815 3229 y FE(0)1838 3259 y FQ(\(\006\))j(of)e(all)h(isotop)n(y)e(classes)g (of)i(homeomorphisms)456 3366 y(\006)567 3319 y FE(\030)539 3366 y FL(\000)-40 b(!)23 b FQ(\006)g(whic)n(h)h(act)f(trivially)f(on)h (the)g(set)h(of)f(connected)g(comp)r(onen)n(ts)f(of)h(the)h(b)r (oundary)-7 b(.\))35 b(If)456 3466 y(\006)23 b(is)h(a)f(surface)g(of)h (gen)n(us)f FJ(g)j FQ(with)e FJ(n)g FQ(b)r(oundary)f(comp)r(onen)n(ts,) h(w)n(e)f(will)h(denote)g(\000\(\006\))f FL(\021)g FQ(\000)3322 3478 y FI(g)r(;n)3421 3466 y FQ(.)605 3607 y(Again,)j(it)g(can)g(b)r(e) g(sho)n(wn)f(that)i(\000)1693 3577 y FE(0)1716 3607 y FQ(\(\006\))f(is)g(generated)f(b)n(y)g(Dehn)i(t)n(wists)f(\(a)g (complete)f(set)456 3707 y(of)d(relations)g(for)g(\000)1052 3677 y FE(0)1052 3728 y FI(g)r(;n)1174 3707 y FQ(is)h(giv)n(en)e(in)i ([)p FK(Ge1)p FQ(],)h([)p FK(Luo)p FQ(],)g([)p FK(Ge2)p FQ(]\),)g(and)e(\000)2567 3719 y FI(g)r(;n)2689 3707 y FQ(is)h(generated)e(b)n(y)i(Dehn)456 3815 y(t)n(wists)k(and)g(the)h (\\braiding)f(op)r(eration")f(sho)n(wn)h(in)g(Figure)g(5.2.)2521 3785 y FM(2)1233 4477 y @beginspecial 0 @llx 0 @lly 172 @urx 62 @ury 1720 @rwi @setspecial %%BeginDocument: figures/braiding.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: braiding.fig %%Creator: fig2dev Version 3.1 Patchlevel 2 %%CreationDate: Tue Sep 9 13:13:13 1997 %%For: kirillov@severi (Alexander Kirillov) %Magnification: 1.00 %%Orientation: Portrait %%BoundingBox: 0 0 172 62 %%Pages: 0 %%BeginSetup %%IncludeFeature: *PageSize Letter %%EndSetup %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -27.0 85.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n 0 792 m 0 0 l 612 0 l 612 792 l cp clip 0.06000 0.06000 sc % Ellipse n 2785 902 510 510 0 360 DrawEllipse gs col7 0.75 shd ef gr 7.500 slw % Interp Spline gs n 3295 895 m 3256.6 852.4 3241.4 832.7 3234 816 curveto 3228.9 804.5 3231.4 776.7 3225 765 curveto 3203.2 725.1 3139.2 661.8 3095 645 curveto 3027.5 619.3 2896.3 598.7 2825 650 curveto 2785.7 678.2 2787.3 758.4 2775 790 curveto 2766.5 811.9 2759.7 866.2 2735 885 curveto 2719.4 896.9 2697.9 899.6 2649 896 curveto gs col7 0.75 shd ef gr gs col-1 s gr gr % Interp Spline gs n 2275 905 m 2344.9 1055.6 2383.6 1117.3 2430 1152 curveto 2507.1 1209.6 2662.5 1302.1 2780 1250 curveto 2834.2 1226.0 2846.8 1140.5 2855 1100 curveto 2862.9 1061.2 2824.8 982.9 2845 940 curveto 2851.4 926.4 2865.2 916.4 2900 900 curveto gs col7 0.75 shd ef gr gs col-1 s gr gr 0.000 slw % Ellipse n 975 902 510 510 0 360 DrawEllipse gs col7 0.75 shd ef gr 7.500 slw % Interp Spline gs n 2410 885 m 2374.3 896.3 2361.3 906.0 2358 924 curveto 2344.2 1000.0 2418.0 1067.8 2469 1098 curveto 2515.1 1125.2 2606.7 1128.2 2655 1110 curveto 2693.4 1095.5 2739.9 1033.8 2760 1005 curveto 2790.7 961.0 2815.9 841.5 2855 799 curveto 2885.5 765.9 2956.6 712.5 3009 712 curveto 3064.6 711.5 3143.6 755.7 3174 801 curveto 3190.8 826.0 3207.3 873.1 3185 904 curveto 3176.7 915.5 3164.2 918.2 3135 915 curveto gs col7 0.75 shd ef gr gs col-1 s gr gr % Ellipse n 1202 905 117 117 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col-1 s gr % Ellipse n 727 905 117 117 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col-1 s gr % Polyline n 855 905 m 1080 905 l gs 0.00 setgray ef gr gs col-1 s gr % Polyline n 465 900 m 605 900 l gs 0.00 setgray ef gr gs col-1 s gr % Polyline gs clippath 1950 911 m 2022 925 l 1950 941 l 2064 940 l 2064 910 l cp clip n 1624 930 m 2049 925 l gs col-1 s gr gr % arrowhead n 1950 911 m 2022 925 l 1950 941 l 1962 926 l 1950 911 l cp gs 0.00 setgray ef gr col-1 s % Ellipse n 2537 905 117 117 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col-1 s gr % Ellipse n 3012 905 117 117 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col-1 s gr % Polyline n 1330 910 m 1495 910 l gs 0.00 setgray ef gr gs col-1 s gr /Times-Roman ff 180.00 scf sf 2972 949 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 180.00 scf sf 2496 949 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 180.00 scf sf 1176 964 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 180.00 scf sf 707 954 m gs 1 -1 sc (1) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1531 4678 a FP(Figure)32 b(5.2.)40 b FQ(Braiding.)605 4864 y(It)31 b(will)h(b)r(e)f(useful)h(in)f(the)g(future)h(to)f(giv)n (e)f(an)g(alternativ)n(e)g(de\014nition)i(of)e(an)h(extended)456 4964 y(surface.)41 b(W)-7 b(e)29 b(giv)n(e)g(b)r(elo)n(w)f(t)n(w)n(o)h (suc)n(h)g(de\014nitions.)42 b(Both)29 b(of)g(them)h(are)e(equiv)-5 b(alen)n(t)29 b(to)g(De\014-)456 5064 y(nition)e(5.1.6)g(in)h(the)g (follo)n(wing)e(sense:)p 456 5122 499 4 v 605 5192 a Fp(2)640 5216 y Fo(See)e(the)h(fo)r(otnote)g(on)f(page)h(94.)p eop %%Page: 96 4 96 99 bop 456 226 a FM(96)1043 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FP(Pr)n(oposition)i FQ(5.1.8)p FP(.)40 b FO(The)22 b(extende)l(d)f(gr)l(oup)l(oids)i FL(T)7 b FJ(eich)p FO(,)23 b(de\014ne)l(d)e(by)h(De\014nitions)28 b FQ(5.1.6)p FO(,)456 525 y FQ(5.1.9)c FO(and)34 b FQ(5.1.10)p FO(,)25 b(ar)l(e)h(e)l(quivalent)f(as)h(c)l(ate)l(gories,)i(and)e(this)g(e)l (quivalenc)l(e)g(pr)l(eserves)g(the)g(op-)456 624 y(er)l(ation)k(of)g (orientation)h(r)l(eversal.)605 782 y FP(Definition)h FQ(5.1.9)p FP(.)40 b FQ(An)d FO(extende)l(d)i(surfac)l(e)44 b FQ(is)37 b(an)g(orien)n(ted)g(compact)g(surface)f(with)456 882 y(b)r(oundary)26 b(and)i(with)g(a)f(sp)r(eci\014ed)h(p)r(oin)n(t)g FJ(p)1843 894 y FI(i)1898 882 y FQ(on)f(ev)n(ery)g(comp)r(onen)n(t)g (of)g(the)h(b)r(oundary)-7 b(.)605 981 y(A)39 b FO(home)l(omorphism)47 b FQ(of)38 b(extended)h(surfaces)e(is)h(an)g(orien)n(tation-preserving) c(homeo-)456 1081 y(morphism)27 b(\006)c FL(!)g FQ(\006)1093 1051 y FE(0)1144 1081 y FQ(whic)n(h)k(maps)h(mark)n(ed)e(p)r(oin)n(ts)h (to)h(mark)n(ed)e(p)r(oin)n(ts.)605 1180 y FO(Orientation)i(r)l (eversal)35 b FQ(is)25 b(de\014ned)h(in)f(the)h(ob)n(vious)e(w)n(a)n(y) -7 b(,)25 b(b)n(y)g(rev)n(ersing)e(the)j(orien)n(tation)456 1280 y(of)h(\006)h(while)g(lea)n(ving)e(the)i(p)r(oin)n(ts)f FJ(p)1570 1292 y FI(i)1626 1280 y FQ(unc)n(hanged.)605 1437 y FP(Definition)32 b FQ(5.1.10)p FP(.)39 b FQ(An)19 b FO(extende)l(d)j(surfac)l(e)j FQ(is)19 b(an)f(orien)n(ted)g(compact)g (surface)g(\006)g(with-)456 1537 y(out)i(b)r(oundary)-7 b(,)22 b(with)f(mark)n(ed)f(p)r(oin)n(ts)h FJ(z)1734 1549 y FI(i)1761 1537 y FQ(,)h(and)f(with)g(non-zero)f(tangen)n(t)g(v)n (ectors)f FJ(v)3084 1549 y FI(i)3133 1537 y FQ(attac)n(hed)456 1637 y(to)27 b(eac)n(h)g(mark)n(ed)f(p)r(oin)n(t.)605 1736 y(A)21 b FO(home)l(omorphism)29 b FQ(of)20 b(extended)h(surfaces)e (is)h(an)g(orien)n(tation-preserving)d(homeomor-)456 1836 y(phism)30 b(\006)e FL(!)h FQ(\006)963 1806 y FE(0)1016 1836 y FQ(whic)n(h)i(maps)f(mark)n(ed)g(p)r(oin)n(ts)g(to)g(mark)n(ed)g (p)r(oin)n(ts,)h(and)g(mark)n(ed)e(tangen)n(t)456 1936 y(v)n(ectors)d(to)h(mark)n(ed)g(tangen)n(t)g(v)n(ectors.)605 2039 y FO(Orientation)j(r)l(eversal)37 b FQ(is)28 b(de\014ned)g(b)n(y)p 1855 1967 333 4 v 27 w(\(\006)p FJ(;)14 b(z)2023 2051 y FI(i)2050 2039 y FJ(;)g(v)2127 2051 y FI(i)2155 2039 y FQ(\))23 b(=)g(\()p 2330 1972 60 4 v(\006)p FJ(;)14 b(z)2466 2051 y FI(i)2493 2039 y FJ(;)g FL(\000)p FJ(v)2635 2051 y FI(i)2663 2039 y FQ(\).)605 2139 y(This)28 b(de\014nition)g(is)f (analogous)e(to)j(De\014nition)g(4.4.1.)605 2296 y FP(Pr)n(oof)j(of)h (Pr)n(oposition)f FQ(5.1.8)p FP(.)39 b FQ(T)-7 b(o)18 b(establish)g(the)h(equiv)-5 b(alence)18 b(of)g(De\014nitions)h(5.1.6) 456 2396 y(and)29 b(5.1.9,)h(note)f(that)h(a)g(parameterization)e(of)h (a)h(b)r(oundary)f(circle)g(giv)n(es)g(a)g(distinguished)456 2498 y(p)r(oin)n(t)h FJ(p)717 2510 y FI(i)773 2498 y FQ(=)e FJ(\031)916 2462 y FE(\000)p FM(1)913 2521 y FI(i)1005 2498 y FQ(\(i\).)47 b(Since)31 b(the)g(set)f(of)h(all)f(homeomorphisms) f FJ(S)2591 2468 y FM(1)2685 2451 y FE(\030)2656 2498 y FL(\000)-39 b(!)28 b FJ(S)2849 2468 y FM(1)2917 2498 y FQ(preserving)h(ori-)456 2597 y(en)n(tation)i(and)h(the)g (distinguished)g(p)r(oin)n(t)g(i)e FL(2)g FJ(S)2021 2567 y FM(1)2090 2597 y FQ(is)i(con)n(tractible,)g(this)g(is)f(an)h(equiv)-5 b(alence)456 2697 y(of)25 b(categories.)34 b(Similarly)-7 b(,)25 b(to)g(establish)g(the)h(equiv)-5 b(alence)24 b(of)i(De\014nitions)f(5.1.6)f(and)h(5.1.10,)456 2797 y(note)i(that)g(giv)n(en)g(\006)g(as)g(in)h(De\014nition)g(5.1.6,)e(w)n (e)h(can)g(glue)g(to)g(\006)g FJ(n)h FQ(copies)e(of)i(the)f(standard) 456 2896 y(disk)h FJ(D)f FQ(=)e FL(f)p FJ(z)j FL(2)d FH(C)46 b FL(j)26 b(j)p FJ(z)t FL(j)e(\024)h FQ(1)p FL(g)j FQ(\(with)h(rev)n(ersed)e(orien)n(tation\),)h(using)h(the)g(iden)n (ti\014cations)g(of)456 2996 y(the)f(b)r(oundary)f(circles)g(of)h(\006) g(with)h FJ(S)1652 2966 y FM(1)1689 2996 y FQ(.)38 b(This)28 b(giv)n(es)e(a)i(new)g(surface)f FJ(cl)r FQ(\(\006\))h(without)g(b)r (ound-)456 3095 y(ary)-7 b(,)31 b(with)g(mark)n(ed)f(p)r(oin)n(ts)h (images)f(of)h(0)d FL(2)h FJ(D)r FQ(,)j(and)f(tangen)n(t)g(v)n(ectors)e (images)h(of)h(the)h(unit)456 3195 y(v)n(ector)26 b(going)h(along)g (the)h(real)g(axis)f(in)h FJ(D)r FQ(.)38 b(As)29 b(b)r(efore,)e(it)i (is)f(easy)f(to)h(c)n(hec)n(k)f(that)h(this)h(giv)n(es)456 3295 y(an)e(equiv)-5 b(alence)27 b(of)h(categories.)p 3384 3295 4 57 v 3388 3242 50 4 v 3388 3295 V 3437 3295 4 57 v 605 3464 a FP(Examples)j FQ(5.1.11)p FP(.)39 b FQ(\(i\))28 b(Let)g(\006)f(b)r(e)h(a)f(t)n(w)n(o-dimensional)f(torus)g (\\with)i(one)f(puncture":)456 3564 y FJ(@)5 b FQ(\006)45 b FL(')g FJ(S)776 3534 y FM(1)854 3564 y FQ(and)c(\006)g(has)f(gen)n (us)g(1.)77 b(Then)41 b(the)h(mapping)f(class)f(group)g(\000)2926 3576 y FM(1)p FI(;)p FM(1)3061 3564 y FQ(=)45 b(\000\(\006\))d(is)456 3663 y(generated)27 b(b)n(y)i(the)g(elemen)n(ts)f FJ(s;)14 b(t)29 b FQ(with)g(the)g(relations)f(\()p FJ(st)p FQ(\))2377 3633 y FM(3)2439 3663 y FQ(=)d FJ(s)2568 3633 y FM(2)2605 3663 y FJ(;)14 b(s)2681 3633 y FM(2)2747 3663 y FQ(is)29 b(cen)n(tral)e(\(compare)456 3763 y(with)37 b(Example)f(5.1.5\).)63 b(Moreo)n(v)n(er,)36 b FJ(s)1736 3733 y FM(4)1810 3763 y FQ(is)g(the)h(in)n(v)n(erse)f(of)g(the)h(Dehn)h(t)n(wist)e(around)g (the)456 3863 y(puncture.)41 b(The)30 b(easiest)e(w)n(a)n(y)g(to)h(c)n (hec)n(k)f(this)i(is)f(to)g(use)g(the)g(realization)f(of)h(the)h(torus) e(with)456 3962 y(one)f(puncture)h(as)f(the)g(quotien)n(t)h FH(R)1585 3932 y FM(2)1628 3962 y FJ(=)p FH(Z)1731 3932 y FM(2)1790 3962 y FQ(with)g(a)f(non-zero)f(tangen)n(t)h(v)n(ector)g (at)g(the)h(origin.)605 4062 y(\(ii\))35 b(Let)f(\006)965 4074 y FI(n)1044 4062 y FQ(=)f FH(R)1196 4032 y FM(2)1240 4062 y FQ(,)i(with)g FJ(n)f FQ(mark)n(ed)f(p)r(oin)n(ts)h(on)f(the)i FJ(x)p FQ(-axis)e(and)h(with)h(the)f(tangen)n(t)456 4162 y(v)n(ector)d FJ(v)750 4174 y FI(i)811 4162 y FQ(going)h(along)g(this)i (axis)e(in)h(p)r(ositiv)n(e)g(direction)g(\(all)g(suc)n(h)f(surfaces)g (are)g(canoni-)456 4261 y(cally)c(isomorphic\).)41 b(This)29 b(surface)g(is)g(not)g(compact,)h(so)e(it)i(do)r(es)f(not)g(formally)f (satisfy)h(our)456 4361 y(de\014nition,)g(but)h(let)f(us)f(ignore)g (this.)41 b(Then)28 b(the)i(group)d(\000\(\006\))j(is)e(isomorphic)g (to)g(the)i(group)456 4460 y FJ(F)12 b(B)584 4472 y FI(n)654 4460 y FQ(of)25 b(all)f(framed)h(braids)f(with)h FJ(n)g FQ(strands.)35 b(This)25 b(group)f(is)h(a)g(semidirect)f(pro)r(duct)h (of)g(the)456 4560 y(usual)31 b(braid)g(group)f FJ(B)1200 4572 y FI(n)1277 4560 y FQ(and)h FH(Z)1504 4530 y FI(n)1575 4560 y FQ(\(see)g(De\014nition)h(1.2.1\).)48 b(In)32 b(general,)f(there)h(is)f(indeed)h(a)456 4660 y(relationship)25 b(b)r(et)n(w)n(een)h(the)g(group)f(\000\(\006\),)i(where)f(\006)g(is)g (an)g(extended)g(surface)f(with)i FJ(n)f FQ(holes,)456 4759 y(and)d(the)i(framed)f(braid)f(group)g FJ(F)12 b(B)1602 4771 y FI(n)1647 4759 y FQ(\()p FJ(cl)r FQ(\(\006\)\),)25 b(where)f FJ(cl)r FQ(\(\006\))g(is)g(the)g(closed)g(surface)f(obtained) 456 4859 y(b)n(y)k(patc)n(hing)g(the)h(holes)f(of)g(\006.)37 b(This)28 b(relationship)f(is)g(studied)h(in)g(detail)g(in)g([)p FK(B2)o FQ(].)605 5016 y(The)d(most)f(imp)r(ortan)n(t)g(di\013erence)g (b)r(et)n(w)n(een)h(extended)f(surfaces)g(and)g(usual)g(surfaces)g(is) 456 5116 y(that)f(extended)g(surfaces)e(can)i(b)r(e)g(glued)f(\(or)g (sew)n(ed\))h(together)f(along)f(the)i(b)r(oundary)f(circles.)456 5216 y(Therefore,)j(if)h(w)n(e)f(additionally)h(require)e(a)i(mo)r (dular)f(functor)h(to)g(b)r(eha)n(v)n(e)f(nicely)g(under)h(this)p eop %%Page: 97 5 97 100 bop 1539 226 a FM(5.1.)29 b(MODULAR)g(FUNCTOR)995 b(97)456 425 y FQ(op)r(eration,)32 b(w)n(e)f(could)h(de\014ne)g FJ(\034)9 b FQ(\(\006\))34 b(b)n(y)d(gluing)h(\006)g(from)f(simpler)h (pieces.)50 b(This)32 b(motiv)-5 b(ates)456 525 y(the)28 b(follo)n(wing)e(de\014nition.)605 677 y FP(Definition)32 b FQ(5.1.12)p FP(.)39 b FQ(Let)25 b FL(C)30 b FQ(b)r(e)25 b(an)g(ab)r(elian)f(category)f(o)n(v)n(er)g(a)i(\014eld)g FJ(k)s FQ(,)g(and)g(let)g FJ(R)h FQ(b)r(e)f(a)456 777 y(symmetric)d(ob)5 b(ject)23 b(in)g(ind)p FL(\000C)1423 747 y Fv(\002)p FM(2)1535 777 y FQ(\(see)f(Section)h(2.4\).)35 b(Then)23 b(a)g FL(C)5 b FO(-extende)l(d)24 b(mo)l(dular)i(functor)456 877 y FQ(is)h(the)h(follo)n(wing)f(collection)g(of)g(data:)605 976 y(\(i\))19 b(T)-7 b(o)18 b(ev)n(ery)f(extended)i(surface)e(\006)i (is)f(assigned)f(a)h(p)r(olylinear)g(functor)g FJ(\034)9 b FQ(\(\006\))g(:)29 b FL(C)3117 946 y Fv(\002)p FI(\031)3208 954 y FF(0)3240 946 y FM(\()p FI(@)t FM(\006\))3405 976 y FL(!)456 1076 y(V)7 b FJ(ec)589 1088 y FI(f)631 1076 y FQ(,)32 b(where)f FJ(\031)977 1088 y FM(0)1015 1076 y FQ(\()p FJ(@)5 b FQ(\006\))32 b(is)f(the)h(set)f(of)g(b)r(oundary)g (comp)r(onen)n(ts)g(\(or)g(punctures,)h(dep)r(ending)456 1175 y(on)c(the)i(p)r(oin)n(t)f(of)g(view\))g(of)g(\006.)41 b(In)29 b(other)f(w)n(ords,)g(for)h(ev)n(ery)e(c)n(hoice)h(of)h(ob)5 b(jects)29 b FJ(W)3119 1187 y FI(a)3185 1175 y FL(2)c(C)34 b FQ(at-)456 1275 y(tac)n(hed)24 b(to)i(ev)n(ery)e(b)r(oundary)g(comp)r (onen)n(t)h(of)g(\006)h(\(so,)f FJ(a)g FQ(runs)g(through)g(the)g(set)g (of)h(connected)456 1375 y(comp)r(onen)n(ts)32 b(of)h FJ(@)5 b FQ(\006\))33 b(is)f(assigned)g(a)g(\014nite-dimensional)h(v)n (ector)f(space)g FJ(\034)9 b FQ(\(\006;)14 b FL(f)p FJ(W)3139 1387 y FI(a)3180 1375 y FL(g)p FQ(\),)34 b(and)456 1474 y(this)27 b(assignmen)n(t)g(is)h(functorial)f(in)h FJ(W)1680 1486 y FI(a)1720 1474 y FQ(.)605 1576 y(\(ii\))f(T)-7 b(o)26 b(ev)n(ery)e(homeomorphism)h FJ(f)18 b FQ(:)28 b(\006)1923 1529 y FE(\030)1895 1576 y FL(\000)-40 b(!)23 b FQ(\006)2086 1546 y FE(0)2136 1576 y FQ(is)j(assigned)e(a)i (functorial)g(isomorphism)456 1683 y FJ(f)497 1695 y FE(\003)544 1683 y FQ(:)h FJ(\034)9 b FQ(\(\006\))816 1636 y FE(\030)788 1683 y FL(\000)-40 b(!)23 b FJ(\034)9 b FQ(\(\006)1056 1653 y FE(0)1081 1683 y FQ(\).)605 1790 y(\(iii\))28 b(F)-7 b(unctorial)28 b(isomorphisms)e FJ(\034)9 b FQ(\()p FL(;)p FQ(\))1886 1743 y FE(\030)1858 1790 y FL(\000)-40 b(!)23 b FJ(k)s FQ(,)28 b FJ(\034)9 b FQ(\()p FJ(N)2230 1802 y FM(1)2286 1790 y FL(t)19 b FJ(N)2427 1802 y FM(2)2464 1790 y FQ(\))2548 1743 y FE(\030)2519 1790 y FL(\000)-39 b(!)23 b FJ(\034)9 b FQ(\()p FJ(N)2795 1802 y FM(1)2833 1790 y FQ(\))19 b FL(\012)f FJ(\034)9 b FQ(\()p FJ(N)3111 1802 y FM(2)3148 1790 y FQ(\).)605 1890 y(\(iv\))19 b FK(Gluing)h(isomorphism:)27 b FQ(Let)19 b FJ(c)k FL(\032)f FQ(\006)d(b)r(e)g(a)f(closed)f(curv)n(e)h(without)g (self-in)n(tersections)456 1989 y(and)j FJ(p)g FQ(b)r(e)h(a)f(mark)n (ed)f(p)r(oin)n(t)i(on)f FJ(c)p FQ(.)35 b(Cutting)22 b(\006)f(along)f FJ(c)p FQ(,)j(w)n(e)e(obtain)g(a)g(new)h(surface)e (\006)3157 1959 y FE(0)3202 1989 y FQ(\(whic)n(h)456 2089 y(ma)n(y)k(b)r(e)i(connected)f(or)f(not\).)36 b(\006)1499 2059 y FE(0)1548 2089 y FQ(has)24 b(a)h(natural)f(structure)h(of)g(an)g (extended)g(surface)g(in)g(the)456 2188 y(sense)k(of)i(De\014nition)g (5.1.9)e(whic)n(h)h(has)f(the)i(same)f(b)r(oundary)f(comp)r(onen)n(ts)h (as)g(\006)g(plus)g(t)n(w)n(o)456 2288 y(more)f(comp)r(onen)n(ts)g FJ(c)1161 2300 y FM(1)1198 2288 y FQ(,)h FJ(c)1287 2300 y FM(2)1324 2288 y FQ(,)h(whic)n(h)f(come)f(from)g(the)h(circle)f FJ(c)h FQ(\(with)h(mark)n(ed)d(p)r(oin)n(ts)i FJ(p)3275 2300 y FM(1)3312 2288 y FQ(,)g FJ(p)3407 2300 y FM(2)456 2388 y FQ(coming)d(from)g FJ(p)p FQ(\).)784 3109 y @beginspecial 0 @llx 0 @lly 308 @urx 66 @ury 3080 @rwi @setspecial %%BeginDocument: figures/sivp.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: sivp.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Mon Jun 7 09:34:41 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 308 66 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -14.0 89.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8383 m -1000 -1000 l 27808 -1000 l 27808 8383 l cp clip 0.01200 0.01200 sc 30.000 slw % Ellipse n 21590 4762 375 1612 0 360 DrawEllipse gs col-1 s gr % Ellipse n 5475 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 19155 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 21975 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 60.000 slw n 16515 4545 m 16635 4335 l gs col-1 s gr % Polyline 30.000 slw gs clippath 13467 4785 m 13899 4875 l 13467 4965 l 14025 4965 l 14025 4785 l cp clip n 11490 4875 m 13980 4875 l gs col-1 s gr gr % arrowhead n 13467 4785 m 13899 4875 l 13467 4965 l 13539 4875 l 13467 4785 l cp gs 0.00 setgray ef gr col-1 s % Polyline n 1200 2700 m 1202 2700 l 1206 2701 l 1213 2703 l 1225 2705 l 1242 2709 l 1265 2713 l 1294 2719 l 1328 2726 l 1369 2734 l 1415 2744 l 1465 2754 l 1521 2765 l 1580 2777 l 1642 2790 l 1706 2803 l 1771 2816 l 1837 2829 l 1902 2842 l 1967 2855 l 2031 2867 l 2093 2880 l 2154 2892 l 2212 2903 l 2268 2914 l 2322 2924 l 2374 2934 l 2424 2943 l 2472 2952 l 2517 2961 l 2561 2969 l 2603 2976 l 2644 2983 l 2683 2990 l 2722 2997 l 2759 3003 l 2795 3009 l 2830 3014 l 2865 3020 l 2900 3025 l 2934 3030 l 2968 3035 l 3002 3040 l 3036 3044 l 3070 3049 l 3105 3053 l 3139 3058 l 3174 3062 l 3209 3066 l 3245 3070 l 3281 3074 l 3318 3077 l 3355 3081 l 3393 3084 l 3431 3088 l 3470 3091 l 3509 3094 l 3549 3097 l 3589 3099 l 3629 3102 l 3671 3105 l 3712 3107 l 3754 3109 l 3796 3111 l 3838 3113 l 3881 3115 l 3924 3116 l 3967 3118 l 4011 3119 l 4055 3120 l 4099 3121 l 4143 3122 l 4187 3123 l 4232 3123 l 4278 3124 l 4323 3124 l 4370 3125 l 4416 3125 l 4464 3125 l 4513 3125 l 4550 3125 l 4589 3125 l 4629 3125 l 4669 3125 l 4710 3124 l 4752 3124 l 4794 3123 l 4838 3123 l 4883 3122 l 4929 3121 l 4975 3120 l 5023 3119 l 5071 3118 l 5121 3117 l 5171 3115 l 5222 3114 l 5275 3112 l 5328 3110 l 5382 3108 l 5436 3105 l 5492 3103 l 5548 3100 l 5604 3097 l 5662 3094 l 5719 3090 l 5777 3087 l 5836 3083 l 5894 3079 l 5953 3074 l 6012 3070 l 6071 3065 l 6130 3060 l 6189 3055 l 6248 3049 l 6307 3044 l 6365 3038 l 6423 3032 l 6481 3025 l 6539 3019 l 6596 3012 l 6652 3005 l 6709 2998 l 6764 2991 l 6820 2983 l 6875 2975 l 6929 2967 l 6983 2958 l 7037 2950 l 7091 2941 l 7144 2932 l 7197 2922 l 7250 2913 l 7301 2903 l 7352 2893 l 7403 2882 l 7454 2872 l 7506 2860 l 7557 2849 l 7610 2837 l 7663 2824 l 7716 2811 l 7771 2797 l 7827 2783 l 7883 2768 l 7941 2752 l 8001 2736 l 8061 2719 l 8124 2701 l 8188 2683 l 8253 2663 l 8321 2643 l 8390 2622 l 8461 2600 l 8534 2578 l 8608 2555 l 8684 2531 l 8762 2506 l 8841 2480 l 8921 2455 l 9002 2428 l 9084 2402 l 9165 2375 l 9247 2348 l 9328 2321 l 9408 2294 l 9487 2268 l 9563 2242 l 9637 2217 l 9707 2194 l 9774 2171 l 9836 2150 l 9894 2130 l 9947 2112 l 9995 2096 l 10038 2081 l 10075 2068 l 10106 2057 l 10132 2048 l 10154 2041 l 10170 2035 l 10182 2031 l 10191 2028 l 10196 2026 l 10199 2025 l 10200 2025 l gs col-1 s gr % Polyline n 1200 7350 m 1202 7349 l 1205 7348 l 1213 7345 l 1224 7340 l 1240 7333 l 1261 7324 l 1288 7313 l 1321 7300 l 1360 7284 l 1404 7265 l 1453 7245 l 1507 7223 l 1565 7199 l 1626 7173 l 1689 7147 l 1755 7120 l 1821 7093 l 1888 7066 l 1954 7039 l 2020 7012 l 2084 6986 l 2147 6960 l 2208 6936 l 2267 6912 l 2323 6890 l 2378 6868 l 2430 6848 l 2480 6828 l 2528 6809 l 2574 6792 l 2617 6775 l 2659 6760 l 2699 6745 l 2738 6731 l 2775 6717 l 2811 6705 l 2845 6693 l 2879 6681 l 2912 6670 l 2944 6660 l 2975 6650 l 3013 6638 l 3050 6627 l 3087 6616 l 3124 6606 l 3160 6596 l 3197 6586 l 3233 6577 l 3269 6568 l 3305 6560 l 3341 6551 l 3378 6544 l 3414 6536 l 3451 6529 l 3487 6523 l 3524 6516 l 3560 6510 l 3597 6505 l 3633 6500 l 3669 6495 l 3705 6490 l 3741 6486 l 3777 6482 l 3813 6478 l 3848 6475 l 3884 6471 l 3919 6468 l 3954 6466 l 3988 6463 l 4023 6461 l 4058 6458 l 4093 6456 l 4128 6454 l 4164 6452 l 4200 6450 l 4231 6448 l 4263 6447 l 4295 6445 l 4329 6443 l 4363 6441 l 4397 6440 l 4433 6438 l 4470 6436 l 4507 6435 l 4546 6433 l 4585 6431 l 4625 6430 l 4666 6428 l 4708 6427 l 4751 6425 l 4795 6424 l 4839 6423 l 4883 6422 l 4929 6420 l 4974 6419 l 5020 6419 l 5066 6418 l 5113 6417 l 5159 6416 l 5206 6416 l 5252 6416 l 5299 6415 l 5345 6415 l 5391 6415 l 5436 6415 l 5482 6416 l 5526 6416 l 5571 6417 l 5615 6418 l 5659 6418 l 5703 6419 l 5746 6421 l 5789 6422 l 5832 6423 l 5875 6425 l 5916 6427 l 5957 6429 l 5999 6431 l 6040 6433 l 6082 6435 l 6125 6438 l 6168 6440 l 6211 6443 l 6255 6446 l 6300 6450 l 6344 6453 l 6390 6457 l 6435 6461 l 6481 6465 l 6528 6469 l 6574 6473 l 6621 6478 l 6668 6483 l 6714 6488 l 6761 6493 l 6808 6498 l 6854 6503 l 6900 6509 l 6946 6514 l 6991 6520 l 7036 6526 l 7080 6532 l 7123 6538 l 7166 6543 l 7208 6550 l 7249 6556 l 7290 6562 l 7329 6568 l 7368 6574 l 7406 6580 l 7443 6587 l 7479 6593 l 7515 6599 l 7549 6606 l 7584 6612 l 7617 6618 l 7650 6625 l 7690 6633 l 7730 6641 l 7769 6650 l 7808 6659 l 7847 6667 l 7886 6676 l 7924 6686 l 7963 6695 l 8002 6705 l 8041 6715 l 8079 6725 l 8118 6735 l 8157 6745 l 8196 6756 l 8234 6766 l 8273 6777 l 8311 6788 l 8349 6798 l 8387 6809 l 8424 6819 l 8461 6830 l 8497 6840 l 8533 6850 l 8569 6860 l 8603 6870 l 8638 6880 l 8672 6889 l 8705 6899 l 8738 6908 l 8771 6916 l 8803 6925 l 8836 6934 l 8868 6942 l 8900 6950 l 8931 6958 l 8962 6965 l 8993 6973 l 9025 6980 l 9058 6987 l 9092 6995 l 9126 7002 l 9163 7010 l 9200 7018 l 9239 7026 l 9280 7034 l 9323 7042 l 9368 7051 l 9415 7060 l 9464 7069 l 9514 7078 l 9567 7088 l 9620 7098 l 9675 7108 l 9730 7117 l 9786 7127 l 9840 7137 l 9893 7146 l 9943 7155 l 9991 7164 l 10034 7171 l 10073 7178 l 10107 7184 l 10135 7189 l 10157 7193 l 10174 7196 l 10186 7198 l 10194 7199 l 10198 7200 l 10200 7200 l gs col-1 s gr % Polyline n 5100 3150 m 5101 3151 l 5104 3154 l 5112 3162 l 5123 3173 l 5135 3185 l 5147 3197 l 5158 3208 l 5168 3218 l 5177 3227 l 5188 3238 l 5196 3246 l 5206 3256 l 5216 3266 l 5227 3278 l 5238 3290 l 5250 3303 l 5262 3317 l 5273 3331 l 5284 3345 l 5294 3359 l 5304 3373 l 5313 3388 l 5320 3400 l 5327 3413 l 5334 3427 l 5340 3442 l 5347 3458 l 5354 3474 l 5360 3491 l 5366 3509 l 5372 3527 l 5377 3545 l 5382 3562 l 5387 3580 l 5391 3597 l 5395 3615 l 5398 3631 l 5402 3647 l 5405 3664 l 5408 3682 l 5412 3701 l 5415 3721 l 5418 3741 l 5421 3762 l 5425 3784 l 5428 3806 l 5430 3828 l 5433 3849 l 5436 3871 l 5438 3892 l 5440 3914 l 5443 3935 l 5444 3954 l 5446 3974 l 5448 3995 l 5450 4016 l 5452 4038 l 5454 4060 l 5455 4084 l 5457 4107 l 5459 4130 l 5461 4154 l 5462 4177 l 5464 4199 l 5465 4221 l 5466 4241 l 5467 4261 l 5468 4280 l 5469 4298 l 5470 4315 l 5471 4334 l 5472 4352 l 5472 4370 l 5473 4388 l 5473 4405 l 5474 4423 l 5474 4441 l 5474 4458 l 5475 4474 l 5475 4491 l 5475 4506 l 5475 4521 l 5475 4535 l 5475 4549 l 5475 4562 l 5475 4575 l 5475 4590 l 5475 4605 l 5475 4620 l 5475 4637 l 5475 4653 l 5475 4670 l 5475 4688 l 5475 4705 l 5475 4722 l 5475 4738 l 5475 4755 l 5475 4770 l 5475 4785 l 5475 4800 l 5475 4815 l 5475 4830 l 5475 4846 l 5475 4862 l 5475 4880 l 5475 4898 l 5474 4916 l 5474 4935 l 5474 4955 l 5473 4974 l 5472 4994 l 5472 5013 l 5471 5033 l 5470 5053 l 5469 5068 l 5468 5085 l 5467 5102 l 5466 5120 l 5465 5139 l 5464 5159 l 5462 5179 l 5461 5200 l 5460 5221 l 5458 5242 l 5457 5263 l 5455 5284 l 5454 5304 l 5452 5323 l 5451 5342 l 5450 5360 l 5449 5378 l 5448 5395 l 5446 5414 l 5445 5432 l 5444 5451 l 5442 5470 l 5441 5490 l 5440 5509 l 5438 5529 l 5436 5549 l 5435 5569 l 5433 5588 l 5431 5607 l 5429 5626 l 5427 5644 l 5425 5662 l 5422 5680 l 5420 5698 l 5417 5715 l 5414 5734 l 5411 5753 l 5408 5772 l 5404 5792 l 5400 5813 l 5395 5834 l 5390 5856 l 5386 5877 l 5381 5898 l 5375 5918 l 5370 5937 l 5365 5955 l 5360 5973 l 5355 5989 l 5350 6005 l 5344 6022 l 5338 6039 l 5331 6056 l 5324 6073 l 5317 6090 l 5309 6107 l 5301 6123 l 5292 6139 l 5284 6154 l 5276 6168 l 5267 6181 l 5259 6194 l 5251 6206 l 5243 6218 l 5234 6229 l 5225 6240 l 5215 6252 l 5205 6264 l 5193 6278 l 5179 6292 l 5164 6308 l 5148 6325 l 5133 6341 l 5120 6355 l 5109 6365 l 5103 6372 l 5100 6375 l gs col-1 s gr % Polyline [120] 0 sd n 5100 3150 m 5097 3153 l 5091 3160 l 5081 3171 l 5067 3185 l 5052 3202 l 5037 3220 l 5022 3237 l 5009 3253 l 4997 3268 l 4987 3283 l 4978 3297 l 4970 3311 l 4963 3325 l 4956 3338 l 4950 3352 l 4944 3367 l 4938 3383 l 4932 3400 l 4926 3417 l 4920 3436 l 4914 3455 l 4908 3475 l 4903 3495 l 4897 3515 l 4892 3535 l 4887 3555 l 4882 3574 l 4877 3593 l 4873 3613 l 4868 3630 l 4864 3648 l 4860 3666 l 4855 3685 l 4850 3705 l 4845 3726 l 4840 3747 l 4835 3769 l 4830 3791 l 4825 3813 l 4820 3836 l 4816 3859 l 4811 3881 l 4806 3903 l 4802 3924 l 4798 3946 l 4794 3967 l 4790 3988 l 4787 4007 l 4783 4026 l 4780 4046 l 4776 4066 l 4773 4088 l 4770 4110 l 4766 4132 l 4763 4155 l 4760 4179 l 4756 4203 l 4753 4227 l 4750 4251 l 4747 4275 l 4744 4298 l 4742 4322 l 4739 4345 l 4737 4367 l 4734 4389 l 4732 4411 l 4730 4433 l 4728 4454 l 4726 4476 l 4724 4499 l 4722 4522 l 4720 4546 l 4719 4570 l 4717 4595 l 4715 4620 l 4714 4646 l 4712 4671 l 4711 4697 l 4710 4722 l 4708 4747 l 4708 4772 l 4707 4796 l 4706 4819 l 4706 4841 l 4705 4863 l 4705 4884 l 4705 4905 l 4705 4926 l 4705 4946 l 4706 4967 l 4706 4988 l 4707 5009 l 4708 5031 l 4708 5053 l 4710 5076 l 4711 5098 l 4712 5120 l 4714 5143 l 4715 5165 l 4717 5187 l 4719 5208 l 4720 5229 l 4722 5249 l 4724 5268 l 4726 5288 l 4728 5306 l 4730 5325 l 4732 5346 l 4735 5367 l 4737 5388 l 4740 5410 l 4743 5432 l 4746 5455 l 4749 5478 l 4753 5501 l 4756 5524 l 4760 5547 l 4763 5570 l 4767 5592 l 4770 5613 l 4774 5634 l 4777 5653 l 4781 5672 l 4784 5690 l 4788 5708 l 4791 5727 l 4795 5746 l 4800 5765 l 4804 5784 l 4809 5803 l 4813 5822 l 4818 5841 l 4823 5860 l 4828 5879 l 4833 5896 l 4838 5914 l 4843 5930 l 4848 5945 l 4853 5960 l 4858 5974 l 4863 5988 l 4868 6003 l 4874 6018 l 4879 6033 l 4886 6048 l 4892 6064 l 4898 6080 l 4905 6095 l 4912 6111 l 4918 6126 l 4924 6140 l 4931 6154 l 4936 6167 l 4942 6180 l 4948 6193 l 4954 6207 l 4960 6221 l 4967 6236 l 4973 6252 l 4980 6267 l 4987 6282 l 4994 6297 l 5001 6311 l 5007 6324 l 5013 6336 l 5019 6347 l 5025 6358 l 5032 6369 l 5039 6380 l 5047 6390 l 5057 6402 l 5067 6414 l 5079 6427 l 5089 6438 l 5096 6446 l 5099 6449 l 5100 6450 l gs col-1 s gr [] 0 sd % Polyline n 15600 7350 m 15602 7349 l 15605 7348 l 15613 7345 l 15624 7340 l 15640 7333 l 15661 7324 l 15688 7313 l 15721 7300 l 15760 7284 l 15804 7265 l 15853 7245 l 15907 7223 l 15965 7199 l 16026 7173 l 16089 7147 l 16155 7120 l 16221 7093 l 16288 7066 l 16354 7039 l 16420 7012 l 16484 6986 l 16547 6960 l 16608 6936 l 16667 6912 l 16723 6890 l 16778 6868 l 16830 6848 l 16880 6828 l 16928 6809 l 16974 6792 l 17017 6775 l 17059 6760 l 17099 6745 l 17138 6731 l 17175 6717 l 17211 6705 l 17245 6693 l 17279 6681 l 17312 6670 l 17344 6660 l 17375 6650 l 17415 6637 l 17455 6625 l 17494 6614 l 17533 6603 l 17571 6593 l 17609 6583 l 17647 6573 l 17685 6564 l 17723 6555 l 17760 6547 l 17797 6539 l 17834 6531 l 17871 6524 l 17908 6517 l 17944 6511 l 17980 6505 l 18015 6500 l 18050 6495 l 18084 6490 l 18118 6485 l 18151 6481 l 18183 6478 l 18215 6474 l 18246 6471 l 18276 6468 l 18306 6465 l 18336 6463 l 18364 6461 l 18393 6459 l 18421 6456 l 18449 6454 l 18478 6453 l 18506 6451 l 18534 6449 l 18563 6447 l 18593 6445 l 18623 6443 l 18654 6441 l 18687 6439 l 18721 6437 l 18756 6434 l 18793 6432 l 18832 6430 l 18873 6427 l 18916 6425 l 18961 6422 l 19008 6419 l 19056 6417 l 19105 6414 l 19154 6411 l 19203 6408 l 19251 6405 l 19297 6403 l 19340 6400 l 19380 6398 l 19414 6396 l 19444 6394 l 19468 6393 l 19487 6392 l 19500 6391 l 19508 6390 l 19513 6390 l 19515 6390 l gs col-1 s gr % Polyline n 15585 2700 m 15587 2700 l 15591 2701 l 15598 2703 l 15610 2705 l 15627 2709 l 15650 2713 l 15679 2719 l 15713 2726 l 15754 2734 l 15800 2744 l 15850 2754 l 15906 2765 l 15965 2777 l 16027 2790 l 16091 2803 l 16156 2816 l 16222 2829 l 16287 2842 l 16352 2855 l 16416 2867 l 16478 2880 l 16539 2892 l 16597 2903 l 16653 2914 l 16707 2924 l 16759 2934 l 16809 2943 l 16857 2952 l 16902 2961 l 16946 2969 l 16988 2976 l 17029 2983 l 17068 2990 l 17107 2997 l 17144 3003 l 17180 3009 l 17215 3014 l 17250 3020 l 17285 3025 l 17325 3031 l 17365 3037 l 17405 3042 l 17445 3048 l 17484 3053 l 17524 3058 l 17564 3063 l 17604 3068 l 17644 3072 l 17684 3077 l 17725 3081 l 17765 3085 l 17805 3089 l 17846 3093 l 17886 3097 l 17926 3100 l 17965 3104 l 18004 3107 l 18043 3110 l 18081 3113 l 18119 3116 l 18156 3118 l 18192 3121 l 18227 3123 l 18262 3125 l 18296 3127 l 18329 3128 l 18361 3130 l 18393 3131 l 18424 3133 l 18454 3134 l 18484 3135 l 18513 3136 l 18543 3138 l 18575 3139 l 18608 3140 l 18640 3141 l 18673 3141 l 18706 3142 l 18741 3143 l 18776 3144 l 18812 3144 l 18850 3145 l 18889 3146 l 18930 3146 l 18973 3147 l 19017 3147 l 19063 3147 l 19111 3148 l 19159 3148 l 19208 3149 l 19255 3149 l 19302 3149 l 19346 3149 l 19387 3149 l 19423 3150 l 19454 3150 l 19480 3150 l 19499 3150 l 19514 3150 l 19523 3150 l 19528 3150 l 19530 3150 l gs col-1 s gr % Polyline n 21600 3135 m 21602 3135 l 21608 3135 l 21618 3134 l 21633 3134 l 21654 3133 l 21680 3132 l 21711 3130 l 21746 3129 l 21784 3127 l 21824 3125 l 21865 3124 l 21905 3122 l 21945 3120 l 21983 3119 l 22020 3117 l 22055 3116 l 22088 3114 l 22120 3113 l 22150 3112 l 22179 3110 l 22207 3109 l 22234 3108 l 22261 3107 l 22288 3106 l 22315 3105 l 22340 3104 l 22366 3103 l 22392 3102 l 22418 3101 l 22445 3100 l 22473 3099 l 22501 3097 l 22530 3096 l 22559 3095 l 22589 3093 l 22620 3092 l 22651 3090 l 22682 3089 l 22713 3087 l 22745 3085 l 22776 3083 l 22807 3081 l 22839 3079 l 22869 3077 l 22900 3074 l 22930 3072 l 22959 3069 l 22988 3067 l 23017 3064 l 23045 3061 l 23073 3059 l 23100 3056 l 23128 3053 l 23155 3049 l 23182 3046 l 23210 3042 l 23238 3038 l 23266 3034 l 23295 3030 l 23325 3026 l 23355 3021 l 23385 3016 l 23416 3011 l 23447 3006 l 23479 3000 l 23511 2995 l 23543 2989 l 23574 2983 l 23606 2977 l 23638 2971 l 23669 2965 l 23700 2960 l 23730 2954 l 23760 2948 l 23790 2942 l 23819 2936 l 23847 2930 l 23875 2924 l 23903 2919 l 23930 2913 l 23958 2908 l 23981 2903 l 24005 2898 l 24030 2892 l 24054 2887 l 24080 2882 l 24105 2876 l 24132 2871 l 24159 2865 l 24186 2858 l 24215 2852 l 24244 2845 l 24274 2838 l 24304 2831 l 24335 2823 l 24367 2816 l 24400 2808 l 24433 2799 l 24466 2790 l 24500 2782 l 24534 2772 l 24569 2763 l 24604 2753 l 24639 2743 l 24675 2733 l 24710 2723 l 24746 2712 l 24783 2701 l 24819 2690 l 24856 2679 l 24893 2667 l 24931 2655 l 24970 2643 l 25000 2633 l 25031 2623 l 25062 2612 l 25094 2601 l 25128 2590 l 25162 2578 l 25198 2566 l 25235 2553 l 25274 2540 l 25314 2526 l 25356 2511 l 25400 2495 l 25446 2479 l 25495 2461 l 25545 2443 l 25598 2424 l 25652 2404 l 25709 2384 l 25768 2362 l 25829 2340 l 25891 2317 l 25955 2294 l 26019 2270 l 26084 2247 l 26148 2223 l 26211 2200 l 26273 2177 l 26332 2155 l 26388 2135 l 26440 2116 l 26488 2098 l 26530 2082 l 26568 2068 l 26600 2057 l 26626 2047 l 26646 2039 l 26662 2034 l 26673 2029 l 26680 2027 l 26683 2026 l 26685 2025 l gs col-1 s gr % Ellipse n 19548 4762 375 1612 0 360 DrawEllipse gs col-1 s gr % Polyline n 21600 6360 m 21602 6360 l 21608 6360 l 21617 6361 l 21632 6361 l 21652 6362 l 21678 6363 l 21709 6364 l 21745 6366 l 21784 6367 l 21826 6369 l 21869 6371 l 21913 6373 l 21957 6374 l 22000 6376 l 22041 6378 l 22080 6380 l 22117 6381 l 22153 6383 l 22187 6385 l 22218 6386 l 22249 6388 l 22278 6389 l 22305 6391 l 22332 6393 l 22359 6394 l 22384 6396 l 22410 6398 l 22437 6399 l 22465 6401 l 22493 6403 l 22521 6405 l 22549 6408 l 22578 6410 l 22608 6412 l 22637 6415 l 22667 6417 l 22698 6420 l 22729 6423 l 22760 6426 l 22790 6429 l 22821 6431 l 22852 6434 l 22882 6437 l 22912 6440 l 22942 6443 l 22971 6446 l 22999 6449 l 23027 6452 l 23055 6454 l 23081 6457 l 23108 6460 l 23134 6462 l 23160 6465 l 23186 6468 l 23212 6470 l 23238 6473 l 23265 6476 l 23292 6479 l 23320 6481 l 23348 6484 l 23377 6487 l 23405 6490 l 23435 6493 l 23464 6497 l 23493 6500 l 23523 6503 l 23552 6506 l 23581 6509 l 23609 6512 l 23637 6516 l 23665 6519 l 23691 6522 l 23718 6525 l 23743 6528 l 23768 6531 l 23791 6534 l 23815 6537 l 23838 6540 l 23860 6543 l 23886 6546 l 23912 6549 l 23938 6553 l 23964 6557 l 23990 6561 l 24017 6565 l 24043 6569 l 24070 6573 l 24097 6577 l 24124 6582 l 24150 6586 l 24176 6591 l 24202 6595 l 24227 6600 l 24252 6604 l 24275 6609 l 24298 6613 l 24320 6618 l 24342 6622 l 24362 6626 l 24383 6631 l 24403 6635 l 24424 6640 l 24446 6645 l 24467 6650 l 24490 6655 l 24512 6661 l 24535 6667 l 24558 6673 l 24582 6679 l 24605 6685 l 24629 6692 l 24653 6698 l 24676 6705 l 24699 6712 l 24722 6718 l 24744 6725 l 24766 6732 l 24788 6738 l 24809 6745 l 24829 6751 l 24850 6758 l 24869 6763 l 24888 6770 l 24908 6776 l 24928 6782 l 24948 6789 l 24970 6796 l 24992 6803 l 25015 6810 l 25038 6818 l 25061 6825 l 25086 6833 l 25110 6840 l 25134 6848 l 25159 6856 l 25183 6863 l 25208 6870 l 25232 6877 l 25256 6884 l 25279 6891 l 25303 6897 l 25326 6904 l 25350 6910 l 25372 6916 l 25394 6921 l 25417 6927 l 25441 6933 l 25465 6939 l 25491 6945 l 25517 6951 l 25544 6957 l 25571 6963 l 25599 6969 l 25628 6976 l 25657 6982 l 25687 6988 l 25716 6994 l 25746 7000 l 25776 7006 l 25805 7012 l 25834 7018 l 25863 7023 l 25891 7029 l 25919 7034 l 25947 7040 l 25975 7045 l 26003 7050 l 26028 7055 l 26054 7060 l 26081 7064 l 26109 7069 l 26137 7075 l 26167 7080 l 26199 7086 l 26233 7091 l 26268 7098 l 26306 7104 l 26346 7111 l 26389 7119 l 26432 7126 l 26477 7134 l 26523 7142 l 26567 7149 l 26610 7157 l 26649 7164 l 26684 7170 l 26714 7175 l 26738 7179 l 26755 7182 l 26766 7183 l 26772 7185 l 26775 7185 l gs col-1 s gr /Times-Roman ff 450.00 scf sf 21735 7050 m gs 1 -1 sc (2) col-1 sh gr /Symbol ff 900.00 scf sf 15900 5100 m gs 1 -1 sc (S) col-1 sh gr /Times-Roman ff 600.00 scf sf 12180 4635 m gs 1 -1 sc (cut) col-1 sh gr /Symbol ff 900.00 scf sf 1500 5100 m gs 1 -1 sc (S) col-1 sh gr /Times-Italic ff 750.00 scf sf 5760 4920 m gs 1 -1 sc (p) col-1 sh gr /Times-Italic ff 750.00 scf sf 4815 7095 m gs 1 -1 sc (c) col-1 sh gr /Times-Italic ff 750.00 scf sf 22275 4920 m gs 1 -1 sc (p) col-1 sh gr /Times-Italic ff 750.00 scf sf 19275 6975 m gs 1 -1 sc (c) col-1 sh gr /Times-Italic ff 750.00 scf sf 21375 6975 m gs 1 -1 sc (c) col-1 sh gr /Times-Italic ff 750.00 scf sf 18360 4920 m gs 1 -1 sc (p) col-1 sh gr /Times-Roman ff 450.00 scf sf 18690 5145 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 450.00 scf sf 22650 5115 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 450.00 scf sf 19605 7050 m gs 1 -1 sc (1) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1325 3309 a FP(Figure)32 b(5.3.)40 b FQ(Cutting)28 b(of)g(a)f(surface.)605 3512 y(Then)h(w)n(e)f(are)g(giv)n(en)f(a)i (functorial)f(isomorphism)1244 3654 y FJ(\034)9 b FQ(\(\006)1381 3620 y FE(0)1405 3654 y FQ(;)14 b FL(f)p FJ(W)1562 3666 y FI(a)1602 3654 y FL(g)p FJ(;)g(R)1745 3620 y FM(\(1\))1834 3654 y FJ(;)g(R)1935 3620 y FM(\(2\))2023 3654 y FQ(\))2107 3607 y FE(\030)2079 3654 y FL(\000)-40 b(!)23 b FJ(\034)9 b FQ(\(\006;)14 b FL(f)p FJ(W)2504 3666 y FI(a)2545 3654 y FL(g)p FQ(\))p FJ(;)-2186 b FQ(\(5.1.1\))456 3795 y(where)27 b(w)n(e)g(use)g(the)h(notation)f(of)h(Section)g(2.4.)605 3894 y(The)g(ab)r(o)n(v)n(e)e(data)h(ha)n(v)n(e)f(to)i(satisfy)f(the)h (follo)n(wing)f(axioms:)612 4014 y FK(Multiplicativit)m(y:)40 b FQ(\()p FJ(f)9 b(g)s FQ(\))1491 4026 y FE(\003)1552 4014 y FQ(=)22 b FJ(f)1680 4026 y FE(\003)1718 4014 y FJ(g)1758 4026 y FE(\003)1796 4014 y FQ(,)28 b(id)1916 4026 y FE(\003)1977 4014 y FQ(=)23 b(id.)612 4114 y FK(F)-8 b(unctorialit)m(y:)41 b FQ(all)28 b(isomorphisms)e(in)i(parts)e (\(iii\),)j(\(iv\))f(ab)r(o)n(v)n(e)e(are)h(functorial)g(in)h(\006.)612 4213 y FK(Compatibilit)m(y:)38 b FQ(all)21 b(isomorphisms)f(in)h(parts) f(\(iii\),)j(\(iv\))f(ab)r(o)n(v)n(e)d(are)h(compatible)h(with)711 4313 y(eac)n(h)27 b(other.)612 4412 y FK(Normalization:)39 b FJ(\034)9 b FQ(\()p FJ(S)1407 4382 y FM(2)1445 4412 y FQ(\))23 b(=)f FJ(k)s FQ(.)605 4565 y(As)39 b(b)r(efore,)i(w)n(e)d (lea)n(v)n(e)f(it)j(to)e(the)h(reader)e(to)i(write)f(the)h(explicit)g (statemen)n(ts)f(of)h(the)456 4665 y(functorialit)n(y)g(and)i (compatibilit)n(y)f(axioms,)j(taking)d(as)f(an)i(example)f(the)h (de\014nitions)f(in)456 4764 y(Section)33 b(4.2.)55 b(F)-7 b(rom)34 b(no)n(w)f(on,)i(w)n(e)f(will)g(alw)n(a)n(ys)e(w)n(ork)g(with) i(extended)h(mo)r(dular)e(functors)456 4864 y(\(unless)27 b(otherwise)g(sp)r(eci\014ed\).)605 5016 y FP(Definition)32 b FQ(5.1.13)p FP(.)39 b FQ(A)27 b FL(C)5 b FQ(-extended)25 b(MF)h(is)g(called)g FO(non-de)l(gener)l(ate)g FQ(if)h(for)e(ev)n(ery)g (ob-)456 5116 y(ject)37 b FJ(V)58 b FL(2)40 b FQ(Ob)13 b FL(C)42 b FQ(there)37 b(exists)g(an)g(extended)g(surface)f(\006)i (and)f FL(f)p FJ(W)2661 5128 y FI(a)2701 5116 y FL(g)h(\032)h FQ(Ob)14 b FL(C)41 b FQ(suc)n(h)c(that)456 5216 y FJ(\034)9 b FQ(\(\006;)14 b FJ(V)5 b(;)14 b FL(f)p FJ(W)840 5228 y FI(a)880 5216 y FL(g)p FQ(\))23 b FL(6)p FQ(=)g(0.)p eop %%Page: 98 6 98 101 bop 456 226 a FM(98)1043 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FQ(The)f(main)f(goal)g(of)g(this)h(c)n(hapter)f(is)h(to)f(sho)n (w)g(that)h FO(for)j(a)f(given)g Fl(semisimple)h FO(ab)l(elian)456 525 y(c)l(ate)l(gory)41 b FL(C)k FO(de\014ning)40 b(a)h(non-de)l(gener) l(ate)g FL(C)5 b FO(-extende)l(d)39 b(MF)i(is)g(essential)t(ly)h(e)l (quivalent)e(to)456 624 y(de\014ning)26 b(a)g(structur)l(e)f(of)i(a)f (mo)l(dular)h(tensor)f(c)l(ate)l(gory)g(on)g FL(C)5 b FQ(,)25 b(with)f(the)g(ob)5 b(ject)23 b FJ(R)h FQ(=)3187 562 y Fy(L)3293 624 y FJ(V)3341 636 y FI(i)3380 624 y Fw(\002)456 724 y FJ(V)522 694 y FE(\003)504 746 y FI(i)561 724 y FQ(,)33 b(where)e FL(f)p FJ(V)951 736 y FI(i)979 724 y FL(g)h FQ(are)f(represen)n(tativ)n(es)f(of)i(the)g(equiv)-5 b(alence)32 b(classes)e(of)i(simple)h(ob)5 b(jects)31 b(in)456 824 y FL(C)5 b FQ(.)36 b(The)28 b(precise)f(statemen)n(ts)g (are)g(giv)n(en)f(in)i(Theorems)f(5.4.1)f(and)h(5.5.1.)605 923 y(Finally)-7 b(,)28 b(let)g(us)f(in)n(tro)r(duce)g(the)h(notion)g (of)f(a)g(unitary)h(MF.)605 1075 y FP(Definition)k FQ(5.1.14)p FP(.)39 b FQ(An)27 b(extended)f(mo)r(dular)f(functor)h(is)g(called)f FO(unitary)7 b FQ(,)27 b(if)g(in)f(addi-)456 1177 y(tion)j(to)h(the)g (data)f(ab)r(o)n(v)n(e,)g(w)n(e)h(are)f(also)f(giv)n(en)h(functorial)g (isomorphisms)g FJ(\034)9 b FQ(\()p 2958 1110 60 4 v(\006)q(\))3106 1130 y FE(\030)3078 1177 y FL(\000)-40 b(!)27 b FJ(\034)9 b FQ(\(\006\))3382 1147 y FE(\003)3421 1177 y FQ(,)456 1279 y(where)p 694 1213 V 25 w(\006)26 b(is)f(the)i(manifold)f(\006)f (with)i(opp)r(osite)e(orien)n(tation.)35 b(These)26 b(isomorphisms)e(m) n(ust)i(b)r(e)456 1379 y(compatible)i(with)h(the)g(isomorphisms)e FJ(f)1775 1391 y FE(\003)1841 1379 y FQ(and)i(the)g(isomorphisms)e(of)h (part)g(\(iii\))i(of)e(De\014ni-)456 1479 y(tion)h(5.1.12)f(in)i(the)g (natural)f(w)n(a)n(y)-7 b(.)42 b(Also,)30 b(w)n(e)f(require)f(the)j (follo)n(wing)d(compatibilit)n(y)h(of)h(the)456 1578 y(unitary)d(structure)h(with)g(the)g(gluing)g(isomorphism.)37 b(Let)28 b FL(h)p FJ(;)14 b FL(i)2457 1590 y FM(\006)2518 1578 y FQ(:)28 b FJ(\034)9 b FQ(\(\006\))20 b FL(\012)e FJ(\034)9 b FQ(\()p 2918 1512 V(\006)q(\))24 b FL(!)g FJ(k)31 b FQ(b)r(e)d(the)456 1681 y(pairing)33 b(induced)j(b)n(y)e(the) h(isomorphism)f FJ(\034)9 b FQ(\(\006\))36 b FL(')f FJ(\034)9 b FQ(\()p 2208 1614 V(\006)q(\))2301 1651 y FE(\003)2339 1681 y FQ(.)59 b(Let)35 b(\006)p FJ(;)14 b FQ(\006)2734 1651 y FE(0)2792 1681 y FQ(b)r(e)35 b(as)g(in)g(part)f(\(iv\))456 1783 y(of)f(De\014nition)h(5.1.12,)f(and)g(for)f FJ(f)41 b FL(2)33 b FJ(\034)9 b FQ(\(\006\))p FJ(;)14 b(g)36 b FL(2)d FJ(\034)9 b FQ(\()p 2134 1716 V(\006)q(\),)35 b(write)e FJ(f)41 b FQ(=)2682 1721 y Fy(P)2783 1783 y FJ(f)2824 1795 y FI(i)2851 1783 y FQ(,)35 b FJ(g)g FQ(=)3081 1721 y Fy(P)3182 1783 y FJ(g)3222 1795 y FI(i)3283 1783 y FQ(with)456 1897 y FJ(f)497 1909 y FI(i)547 1897 y FL(2)23 b FJ(\034)9 b FQ(\(\006)762 1867 y FE(0)787 1897 y FQ(;)14 b FJ(A)886 1909 y FI(i)913 1897 y FJ(;)g(B)1013 1909 y FI(i)1041 1897 y FQ(\),)28 b FJ(g)1164 1909 y FI(i)1214 1897 y FL(2)c FJ(\034)9 b FQ(\()p 1370 1831 V(\006)1431 1844 y FE(0)1454 1897 y FQ(;)14 b FJ(B)1554 1909 y FI(i)1581 1897 y FJ(;)g(A)1680 1909 y FI(i)1708 1897 y FQ(\),)28 b(using)h(\(5.1.1\))o(.)37 b(Then:)1516 2052 y FL(h)p FJ(f)t(;)14 b(g)s FL(i)1705 2064 y FM(\006)1780 2052 y FQ(=)1867 1973 y Fy(X)2001 2052 y FJ(a)2045 2064 y FI(i)2073 2052 y FL(h)p FJ(f)2146 2064 y FI(i)2173 2052 y FJ(;)g(g)2250 2064 y FI(i)2277 2052 y FL(i)2309 2064 y FM(\006)2356 2048 y Fx(0)456 2052 y FQ(\(5.1.2\))456 2202 y(for)27 b(some)g(non-zero)f(constan)n(ts)g FJ(a)1539 2214 y FI(i)1594 2202 y FQ(whic)n(h)i(do)f(not)h(dep)r(end)g(on)f (\006.)-2964 b Fq(?!)1531 2383 y FK(5.2.)47 b(The)32 b(Lego)f(game)605 2532 y FQ(Let)d(us)f(denote)h(b)n(y)f FJ(S)1294 2544 y FM(0)p FI(;n)1420 2532 y FQ(\\the)g(standard)g(sphere) g(with)h FJ(n)f FQ(holes":)793 2674 y FJ(S)844 2686 y FM(0)p FI(;n)965 2674 y FQ(=)22 b FH(C)15 b(P)1158 2640 y FM(1)1219 2674 y FL(n)j(f)p FJ(D)1390 2686 y FM(1)1426 2674 y FJ(;)c(:)g(:)g(:)g(;)g(D)1680 2686 y FI(n)1725 2674 y FL(g)p FJ(;)96 b(D)1955 2686 y FI(j)2013 2674 y FQ(=)22 b FL(f)p FJ(z)k FL(j)d(j)p FJ(z)f FL(\000)c FJ(z)2459 2686 y FI(j)2494 2674 y FL(j)23 b FJ(<)g(")p FL(g)p FJ(;)96 b(z)2867 2686 y FM(1)2927 2674 y FJ(<)22 b FL(\001)14 b(\001)g(\001)23 b FJ(<)g(z)3261 2686 y FI(n)3306 2674 y FJ(;)-2873 b FQ(\(5.2.1\))456 2813 y(where)26 b FJ(")d(>)f FQ(0)k(is)h(small)f(enough)g(so)g(that)h(the)g(disks)f FJ(D)2192 2825 y FI(j)2254 2813 y FQ(do)g(not)h(in)n(tersect,)f(and)h (let)g(us)f(mark)456 2913 y(on)h(eac)n(h)h(b)r(oundary)f(circle)h(a)f (p)r(oin)n(t)i FJ(p)1680 2925 y FI(j)1739 2913 y FQ(=)23 b FJ(z)1866 2925 y FI(j)1920 2913 y FL(\000)18 b FJ(")p FQ(i.)38 b(This)28 b(endo)n(ws)g FJ(S)2657 2925 y FM(0)p FI(;n)2783 2913 y FQ(with)g(the)h(structure)456 3012 y(of)37 b(an)f(extended)i(surface)e(whic)n(h)h(is)g(indep)r(enden)n(t)h (of)f(the)g(c)n(hoice)f(of)h FJ(z)2811 3024 y FI(j)2846 3012 y FJ(;)14 b(")37 b FQ(\(i.e.,)j(surfaces)456 3112 y(obtained)22 b(for)h(di\013eren)n(t)g(c)n(hoices)f(of)h FJ(z)1642 3124 y FI(j)1677 3112 y FJ(;)14 b(")22 b FQ(are)h (canonically)e(homeomorphic\).)35 b(Note)23 b(that)g(the)456 3212 y(set)31 b(of)g(b)r(oundary)f(comp)r(onen)n(ts)g(of)h(the)h (standard)e(sphere)g(is)h(naturally)f(indexed)h(b)n(y)g(n)n(um-)456 3311 y(b)r(ers)f(1)p FJ(;)14 b(:)g(:)g(:)f(;)h(n)p FQ(;)31 b(w)n(e)f(will)h(use)f(b)r(old)h(n)n(um)n(b)r(ers)f(for)g(denoting)g (these)g(b)r(oundary)g(comp)r(onen)n(ts:)456 3411 y FJ(\031)503 3423 y FM(0)540 3411 y FQ(\()p FJ(@)5 b(S)672 3423 y FM(0)p FI(;n)770 3411 y FQ(\))23 b(=)g FL(f)p FK(1)p FJ(;)14 b(:)g(:)g(:)f(;)h FK(n)p FL(g)p FQ(.)605 3510 y(Ob)n(viously)-7 b(,)28 b(ev)n(ery)g(extended)h(surface)f(\006)h(can)f (b)r(e)h(obtained)g(b)n(y)g(gluing)f(together)g(stan-)456 3610 y(dard)20 b(spheres.)33 b(Therefore,)21 b(using)g(the)g(gluing)f (axiom)g(w)n(e)g(can)h(de\014ne)g(the)g(v)n(ector)e(space)h FJ(\034)9 b FQ(\(\006\))456 3710 y(once)25 b(w)n(e)h(kno)n(w)f FJ(\034)9 b FQ(\()p FJ(S)1107 3722 y FM(0)p FI(;n)1206 3710 y FQ(\).)37 b(Ho)n(w)n(ev)n(er,)24 b(the)i(same)g(surface)f(\006)h (can)g(b)r(e)g(obtained)g(b)n(y)g(gluing)f(the)456 3809 y(standard)31 b(spheres)g(in)h(man)n(y)g(w)n(a)n(ys,)f(and)h(in)h (order)d(for)i FJ(\034)9 b FQ(\(\006\))33 b(to)f(b)r(e)h(correctly)d (de\014ned)j(w)n(e)456 3909 y(need)21 b(to)g(construct)g(canonical)g (isomorphisms)f(b)r(et)n(w)n(een)h(the)h(resulting)f(v)n(ector)f (spaces.)34 b(This)456 4009 y(leads)27 b(to)g(the)h(follo)n(wing)f (problem.)605 4160 y FP(Definition)32 b FQ(5.2.1)p FP(.)40 b FQ(Let)31 b(\006)g(b)r(e)g(an)g(extended)g(surface.)46 b(A)32 b FO(p)l(ar)l(ameterization)h FQ(of)e(\006)g(is)456 4260 y(the)d(follo)n(wing)e(collection)h(of)h(data,)f(considered)f(up)i (to)g(isotop)n(y:)605 4359 y(\(i\))g(A)g(\014nite)g(set)f FJ(C)i FQ(=)23 b FL(f)p FJ(c)1405 4371 y FM(1)1442 4359 y FJ(;)14 b(:)g(:)g(:)f FL(g)27 b FQ(of)h(simple)f(non-in)n(tersecting) f(closed)h(curv)n(es)f(\(cuts\))i(on)456 4459 y(\006,)f(with)h(one)g(p) r(oin)n(t)f(mark)n(ed)g(on)g(ev)n(ery)f(cut)i(\(the)h(cuts)e(do)h(not)f (ha)n(v)n(e)g(to)g(b)r(e)h(ordered\).)605 4566 y(\(ii\))k(A)f (collection)f(of)h(homeomorphisms)e FJ( )2023 4578 y FI(a)2073 4566 y FQ(:)f(\006)2184 4578 y FI(a)2281 4519 y FE(\030)2253 4566 y FL(\000)-40 b(!)29 b FJ(S)2441 4578 y FM(0)p FI(;n)2535 4586 y FG(a)2575 4566 y FQ(,)j(where)e(\006) 2933 4578 y FI(a)3004 4566 y FQ(are)g(the)h(con-)456 4665 y(nected)d(comp)r(onen)n(ts)f(of)g(\006)19 b FL(n)f FJ(C)6 b FQ(.)605 4765 y(W)-7 b(e)28 b(denote)g(the)g(set)f(of)h(all)f (parameterizations)e(of)j(\006)g(b)n(y)f FJ(M)9 b FQ(\(\006\).)605 4917 y(Our)21 b(goal)f(is)h(to)h(construct)f(some)g(n)n(um)n(b)r(er)g (of)h(edges)e(\(\\mo)n(v)n(es"\))g(and)h(2-cells)g(\(\\relations)456 5016 y(among)34 b(mo)n(v)n(es"\))h(whic)n(h)g(w)n(ould)h(turn)g FJ(M)9 b FQ(\(\006\))36 b(in)n(to)f(a)h(connected)f(and)h (simply-connected)456 5116 y(2-complex.)46 b(This)31 b(problem)g(w)n(as)f(\014rst)h(considered)f(b)n(y)h(Mo)r(ore)f(and)h (Seib)r(erg)g([)p FK(MS1)p FQ(],)h(who)456 5216 y(conjectured)20 b(a)f(set)i(of)f(mo)n(v)n(es)f(and)h(relations.)33 b(Ho)n(w)n(ev)n(er,) 20 b(their)g(pap)r(er)g(con)n(tains)f(certain)h(gaps)p eop %%Page: 99 7 99 102 bop 1599 226 a FM(5.2.)29 b(THE)g(LEGO)g(GAME)1054 b(99)456 425 y FQ(making)33 b(it)i(not)f(rigorous)e(ev)n(en)i(b)n(y)g (the)h(ph)n(ysicists)f(standards.)56 b(An)35 b(accurate)e(pro)r(of)g(w) n(as)456 525 y(recen)n(tly)d(found)i(indep)r(enden)n(tly)g(b)n(y)f(the) h(authors)e([)p FK(BK)p FQ(],)j(and)e(b)n(y)g([)p FK(F)m(G)q FQ(].)48 b(Our)31 b(exp)r(osition)456 624 y(follo)n(ws)26 b(the)i(pap)r(er)f([)p FK(BK)p FQ(])h(with)g(minor)f(c)n(hanges.)605 724 y(De\014ne)h(the)g(homeomorphisms)1661 869 y FJ(z)13 b FQ(:)27 b FJ(S)1814 881 y FM(0)p FI(;n)1964 822 y FE(\030)1935 869 y FL(\000)-39 b(!)23 b FJ(S)2118 881 y FM(0)p FI(;n)2216 869 y FJ(;)1668 1014 y(b)9 b FQ(:)27 b FJ(S)1814 1026 y FM(0)p FI(;)p FM(3)1956 967 y FE(\030)1927 1014 y FL(\000)-39 b(!)23 b FJ(S)2110 1026 y FM(0)p FI(;)p FM(3)456 940 y FQ(\(5.2.2\))456 1156 y(as)30 b(follo)n(ws:)41 b FJ(z)34 b FQ(is)d(rotation)e(of)i(the)g(sphere)f(whic)n(h)g(preserv)n(es)f(the) h(real)g(axis)g(and)g(induces)h(a)456 1256 y(cyclic)26 b(p)r(erm)n(utation)h(of)f(the)i(holes)e FK(1)d FL(7!)g FK(2)f FL(7!)h(\001)14 b(\001)g(\001)23 b(7!)g FK(n)h FL(7!)f FK(1)p FQ(,)j(and)h FJ(b)g FQ(is)f(the)h(braiding)f(of)h(the) 456 1356 y(2nd)g(and)g(3rd)g(punctures,)h(as)f(sho)n(wn)g(in)g(Figure)g (5.2.)605 1455 y(Also,)h(for)g FJ(k)s(;)14 b(l)25 b FL(\025)e FQ(0,)28 b(denote)g(b)n(y)g FJ(S)1693 1467 y FM(0)p FI(;k)q FM(+1)1890 1455 y FL(t)1945 1467 y FI(k)q FM(+1)p FI(;)p FM(1)2141 1455 y FJ(S)2192 1467 y FM(0)p FI(;l)p FM(+1)2383 1455 y FQ(the)h(surface)e(obtained)h(b)n(y)g(iden-)456 1555 y(tifying)36 b(the)g(\()p FJ(k)27 b FQ(+)d(1\)-st)35 b(hole)h(of)g FJ(S)1609 1567 y FM(0)p FI(;k)q FM(+1)1822 1555 y FQ(with)h(the)f(\014rst)f(hole)h(of)g FJ(S)2688 1567 y FM(0)p FI(;l)p FM(+1)2850 1555 y FQ(,)i(and)e(de\014ne)g(the)456 1655 y(map)1324 1797 y FJ(\013)1377 1809 y FI(k)q(;l)1468 1797 y FQ(:)28 b FJ(S)1570 1809 y FM(0)p FI(;k)q FM(+1)1766 1797 y FL(t)1821 1809 y FI(k)q FM(+1)p FI(;)p FM(1)2017 1797 y FJ(S)2068 1809 y FM(0)p FI(;l)p FM(+1)2253 1797 y FL(!)c FJ(S)2411 1809 y FM(0)p FI(;k)q FM(+)p FI(l)456 1797 y FQ(\(5.2.3\))456 1939 y(b)n(y)i(the)h(condition)f(that)h(it)g (maps)f(the)h(\014rst)f(hole)g(of)h FJ(S)2183 1951 y FM(0)p FI(;k)q FM(+1)2387 1939 y FQ(to)f(the)h(\014rst)g(hole)f(of)g FJ(S)3118 1951 y FM(0)p FI(;k)q FM(+)p FI(l)3311 1939 y FQ(and)456 2039 y(preserv)n(es)f(the)j(real)f(axis)g(\(these)h(prop)r (erties)e(de\014ne)i FJ(\013)2214 2051 y FI(k)q(;l)2324 2039 y FQ(uniquely)f(up)h(to)g(isotop)n(y\).)605 2139 y(No)n(w,)37 b(let)e(us)g(de\014ne)h(the)f(follo)n(wing)f(edges)h (\(\\simple)g(mo)n(v)n(es"\))e(in)j FJ(M)9 b FQ(\(\006\).)59 b(T)-7 b(o)35 b(a)n(v)n(oid)456 2238 y(confusion,)h(w)n(e)f(will)g (write)g FJ(E)14 b FQ(:)30 b FJ(M)1578 2250 y FM(1)1650 2238 y Fw( )36 b FJ(M)1850 2250 y FM(2)1922 2238 y FQ(if)f(the)h(edge)e FJ(E)40 b FQ(connects)35 b(parameterizations)456 2338 y FJ(M)537 2350 y FM(1)573 2338 y FJ(;)14 b(M)691 2350 y FM(2)728 2338 y FQ(.)612 2459 y FK(Z-mo)m(v)m(e)31 b(\(rotation\):)41 b FQ(If)21 b FJ(M)31 b FQ(=)23 b(\()p FJ(C)q(;)14 b FL(f)p FJ( )1928 2471 y FI(a)1969 2459 y FL(g)p FQ(\))22 b FL(2)i FJ(M)9 b FQ(\(\006\))20 b(and)h(\006)2593 2471 y FI(i)2641 2459 y FQ(is)f(one)g(of)g(the)h(connected)711 2558 y(comp)r(onen)n(ts)27 b(of)h(\006)18 b FL(n)g FJ(C)6 b FQ(,)28 b(then)g(w)n(e)f(de\014ne)h(an)g(edge)1324 2701 y FJ(Z)g FL(\021)23 b FJ(Z)1554 2713 y FI(i)1591 2701 y FQ(:)k FJ(M)32 b Fw( )23 b FQ(\()p FJ(C)q(;)14 b FL(f)p FJ( )2085 2713 y FI(a)2126 2701 y FJ(;)g(z)21 b FL(\016)d FJ( )2337 2713 y FI(i)2365 2701 y FL(g)2407 2713 y FI(a)p FE(6)p FM(=)p FI(i)2521 2701 y FQ(\))p FJ(:)612 2848 y FK(B-mo)m(v)m(e)30 b(\(braiding\):)41 b FQ(If)31 b FJ(M)36 b FQ(=)28 b(\()p FJ(C)q(;)14 b FL(f)p FJ( )1968 2860 y FI(a)2008 2848 y FL(g)p FQ(\))28 b FL(2)g FJ(M)9 b FQ(\(\006\))31 b(and)f(\006)2662 2860 y FI(i)2720 2848 y FQ(is)h(a)f(connected)g(com-)711 2948 y(p)r(onen)n(t)e(of)f (\006)19 b FL(n)f FJ(C)34 b FQ(whic)n(h)27 b(has)g(three)h(holes,)f (then)h(w)n(e)f(de\014ne)h(an)f(edge)1322 3090 y FJ(B)g FL(\021)22 b FJ(B)1562 3102 y FI(i)1599 3090 y FQ(:)28 b FJ(M)k Fw( )23 b FQ(\()p FJ(C)q(;)14 b FL(f)p FJ( )2094 3102 y FI(a)2134 3090 y FJ(;)g(b)k FL(\016)g FJ( )2339 3102 y FI(i)2367 3090 y FL(g)2409 3102 y FI(a)p FE(6)p FM(=)p FI(i)2523 3090 y FQ(\))p FJ(:)612 3237 y FK(F-mo)m(v)m(e)30 b(\(fusion\):)41 b FQ(If)k FJ(M)60 b FQ(=)51 b(\()p FJ(C)q(;)14 b FL(f)p FJ( )1923 3249 y FI(a)1964 3237 y FL(g)p FQ(\))51 b FL(2)h FJ(M)9 b FQ(\(\006\))45 b(and)f FJ(c)51 b FL(2)h FJ(C)f FQ(separates)43 b(t)n(w)n(o)711 3337 y(di\013eren)n(t)36 b(comp)r(onen)n(ts)g(\006)1573 3349 y FI(i)1601 3337 y FJ(;)14 b FQ(\006)1698 3349 y FI(j)1732 3337 y FQ(,)39 b(with)d FJ(k)27 b FQ(+)d(1)36 b(and)g FJ(l)25 b FQ(+)f(1)36 b(holes)f(resp)r(ectiv)n(ely)-7 b(,)38 b(and)711 3436 y FJ( )765 3448 y FI(i)793 3436 y FQ(\()p FJ(c)p FQ(\))23 b(=)g FK(k)c FQ(+)f FK(1)p FJ(;)c( )1295 3448 y FI(j)1330 3436 y FQ(\()p FJ(c)p FQ(\))23 b(=)g FK(1)p FQ(,)k(then)h(w)n(e)g (de\014ne)f(an)h(edge)1035 3579 y FJ(F)35 b FL(\021)23 b FJ(F)1264 3591 y FI(c)1307 3579 y FQ(:)28 b FJ(M)k Fw( )23 b FQ(\()p FJ(C)i FL(n)18 b(f)p FJ(c)p FL(g)p FJ(;)c FL(f)p FJ( )2006 3591 y FI(a)2044 3579 y FJ(;)g(\013)2134 3591 y FI(k)q(l)2215 3579 y FL(\016)k FQ(\()p FJ( )2361 3591 y FI(i)2407 3579 y FL(t)h FJ( )2535 3591 y FI(j)2570 3579 y FQ(\))p FL(g)2644 3591 y FI(a)p FE(6)p FM(=)p FI(i;j)2809 3579 y FQ(\))p FJ(:)605 3721 y FQ(Before)37 b(describing)f(the)i(relations,)g(it)g(is)g(con)n(v)n(enien)n(t)e(to)h (in)n(tro)r(duce)g(some)g(notation.)456 3821 y(First)h(of)g(all,)i(let) e(us)g(place)g(on)g(eac)n(h)f(of)h(the)g(standard)f(spheres)h FJ(S)2687 3833 y FM(0)p FI(;n)2823 3821 y FQ(the)g(graph)f FJ(m)3295 3833 y FM(0)3370 3821 y FQ(as)456 3920 y(sho)n(wn)32 b(in)h(Figure)g(5.4)f(\(for)h FJ(n)e FQ(=)h(4\).)53 b(This)33 b(graph)f(has)g(one)h(in)n(ternal)f(v)n(ertex,)i(mark)n(ed)e(b)n(y)456 4020 y(a)f(star;)h(all)g(other)f(v)n(ertices)f(are)h(1-v)-5 b(alen)n(t)30 b(and)i(coincide)f(with)h(the)g(mark)n(ed)e(p)r(oin)n(ts) i(on)f(the)456 4120 y(b)r(oundary)24 b(comp)r(onen)n(ts)h(of)h FJ(S)1426 4132 y FM(0)p FI(;n)1524 4120 y FQ(.)36 b(The)25 b(graph)g(has)g(a)g(distinguished)g(edge|the)g(one)h(whic)n(h)456 4219 y(connects)31 b(the)h(v)n(ertex)e FL(\003)h FQ(with)h(the)g(b)r (oundary)f(comp)r(onen)n(t)h FK(1)p FQ(;)h(in)f(the)g(\014gure,)g(this) g(edge)f(is)456 4319 y(mark)n(ed)f(b)n(y)h(an)f(arro)n(w.)46 b(Also,)32 b(this)f(graph)f(has)h(a)g(natural)f(cyclic)h(order)f(on)h (the)g(set)h(of)f(all)456 4419 y(edges,)26 b(giv)n(en)f(b)n(y)h FK(1)d FJ(<)g FL(\001)14 b(\001)g(\001)23 b FJ(<)f FK(n)h FJ(<)g FK(1)p FQ(.)36 b(Whenev)n(er)26 b(w)n(e)g(dra)n(w)f(suc)n(h)i(a) f(graph)f(in)i(the)f(plane,)h(w)n(e)456 4518 y(will)g(alw)n(a)n(ys)f (do)h(it)h(in)g(suc)n(h)g(a)f(w)n(a)n(y)f(that)i(this)g(order)e (coincides)h(with)h(the)g(clo)r(c)n(kwise)f(order.)605 4618 y(Ev)n(ery)38 b(parameterization)f FJ(M)48 b FQ(of)39 b(a)g(giv)n(en)f(surface)h(\006)g(giv)n(es)f(rise)g(to)i(a)e(graph)g FJ(m)43 b FQ(=)456 4655 y Fy(S)539 4717 y FJ( )596 4687 y FE(\000)p FM(1)593 4738 y FI(a)685 4717 y FQ(\()p FJ(m)790 4729 y FM(0)827 4717 y FQ(\))28 b(on)f(\006,)g(whic)n(h)g(w)n(e)g(call) g(the)g FO(marking)k(gr)l(aph)k FQ(of)27 b FJ(M)9 b FQ(.)36 b(It)28 b(is)f(easy)f(to)h(sho)n(w)f(that)i(a)456 4817 y(parameterization)e(is)h(uniquely)h(determined)h(b)n(y)e FJ(C)35 b FQ(and)27 b FJ(m)p FQ(;)i(therefore,)e(these)h(graphs)e(giv)n (e)456 4917 y(a)h(w)n(a)n(y)g(to)i(visualize)e(the)i (parameterizations.)36 b(In)29 b(some)e(cases,)h(w)n(e)f(will)i(dra)n (w)e(suc)n(h)h(graphs)456 5016 y(on)i(\006)g(to)g(illustrate)g(a)f (certain)h(sequence)g(of)g(mo)n(v)n(es.)43 b(Ho)n(w)n(ev)n(er,)29 b(in)h(man)n(y)g(cases)f(it)i(su\016ces)456 5116 y(just)j(to)g(dra)n(w) f(the)i(corresp)r(onding)d(graphs)g(on)i(the)g(plane,)i(and)e(then)g (the)h(mo)n(v)n(es)d(can)i(b)r(e)456 5216 y(reconstructed)26 b(uniquely)-7 b(.)p eop %%Page: 100 8 100 103 bop 456 226 a FM(100)1010 b(5.)29 b(MODULAR)g(FUNCTOR)1417 927 y @beginspecial 0 @llx 0 @lly 128 @urx 65 @ury 1280 @rwi @setspecial %%BeginDocument: figures/stmark.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: stmark.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Mon Jun 7 10:11:26 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 128 65 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.5000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -143.0 131.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 5359 m -1000 -1000 l 10008 -1000 l 10008 5359 l cp clip 0.03000 0.03000 sc % Arc 7.500 slw gs n 6900.0 2775.0 300.0 180.0 0.0 arcn gs col-1 s gr gr % Arc gs n 8100.0 2775.0 300.0 180.0 0.0 arcn gs col-1 s gr gr % Arc gs n 6900.0 2162.5 2187.5 163.7 16.3 arcn gs col-1 s gr gr % Ellipse n 5100 2775 300 225 0 360 DrawEllipse gs col-1 s gr % Ellipse n 6300 2775 300 225 0 360 DrawEllipse gs col-1 s gr % Ellipse n 7500 2775 300 225 0 360 DrawEllipse gs col-1 s gr % Ellipse n 8700 2775 300 225 0 360 DrawEllipse gs col-1 s gr % Ellipse n 6300 3000 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7500 3000 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Arc gs n 5700.0 2775.0 300.0 180.0 0.0 arcn gs col-1 s gr gr % Ellipse n 8700 3000 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr /Times-Bold ff 270.00 scf sf 8625 2400 m gs 1 -1 sc (4) col-1 sh gr % Ellipse n 5100 3000 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline [15 30] 30 sd n 8700 3000 m 8698 3001 l 8694 3004 l 8687 3008 l 8676 3016 l 8660 3026 l 8640 3039 l 8614 3055 l 8585 3074 l 8551 3096 l 8514 3119 l 8475 3144 l 8434 3170 l 8392 3196 l 8350 3223 l 8308 3249 l 8267 3274 l 8227 3298 l 8188 3322 l 8151 3344 l 8115 3364 l 8081 3384 l 8049 3402 l 8018 3419 l 7988 3436 l 7959 3451 l 7931 3465 l 7904 3478 l 7878 3491 l 7852 3503 l 7826 3514 l 7800 3525 l 7772 3536 l 7745 3547 l 7717 3557 l 7689 3568 l 7659 3577 l 7629 3587 l 7598 3596 l 7566 3606 l 7532 3615 l 7496 3624 l 7459 3634 l 7420 3643 l 7379 3652 l 7336 3662 l 7292 3672 l 7247 3681 l 7202 3691 l 7158 3700 l 7114 3709 l 7073 3717 l 7035 3724 l 7001 3731 l 6972 3737 l 6947 3741 l 6929 3745 l 6915 3747 l 6907 3749 l 6902 3750 l 6900 3750 l gs col-1 s gr [] 0 sd % Polyline [15 30] 30 sd n 6300 3000 m 6302 3003 l 6306 3009 l 6312 3020 l 6322 3036 l 6335 3056 l 6350 3081 l 6367 3107 l 6384 3135 l 6402 3163 l 6420 3191 l 6437 3217 l 6453 3241 l 6468 3263 l 6482 3284 l 6496 3304 l 6510 3323 l 6523 3340 l 6536 3358 l 6550 3375 l 6563 3391 l 6576 3406 l 6589 3423 l 6604 3439 l 6619 3457 l 6636 3475 l 6654 3495 l 6674 3516 l 6695 3538 l 6717 3562 l 6741 3587 l 6765 3612 l 6790 3638 l 6814 3662 l 6837 3685 l 6856 3706 l 6873 3722 l 6885 3735 l 6893 3743 l 6898 3748 l 6900 3750 l gs col-1 s gr [] 0 sd % Polyline [15 30] 30 sd n 7500 3000 m 7498 3003 l 7494 3009 l 7488 3020 l 7478 3036 l 7465 3056 l 7450 3081 l 7433 3107 l 7416 3135 l 7398 3163 l 7380 3191 l 7363 3217 l 7347 3241 l 7332 3263 l 7318 3284 l 7304 3304 l 7290 3323 l 7277 3340 l 7264 3358 l 7250 3375 l 7237 3391 l 7224 3406 l 7211 3423 l 7196 3439 l 7181 3457 l 7164 3475 l 7146 3495 l 7126 3516 l 7105 3538 l 7083 3562 l 7059 3587 l 7035 3612 l 7010 3638 l 6986 3662 l 6963 3685 l 6944 3706 l 6927 3722 l 6915 3735 l 6907 3743 l 6902 3748 l 6900 3750 l gs col-1 s gr [] 0 sd % Polyline [15 30] 30 sd gs clippath 5300 3187 m 5144 3029 l 5350 3112 l 5112 2954 l 5063 3029 l cp clip n 5100 3000 m 5124 3016 l 5140 3026 l 5160 3039 l 5186 3055 l 5215 3074 l 5249 3096 l 5286 3119 l 5325 3144 l 5366 3170 l 5408 3196 l 5450 3223 l 5492 3249 l 5533 3274 l 5573 3298 l 5612 3322 l 5649 3344 l 5685 3364 l 5719 3384 l 5751 3402 l 5782 3419 l 5812 3436 l 5841 3451 l 5869 3465 l 5896 3478 l 5922 3491 l 5948 3503 l 5974 3514 l 6000 3525 l 6028 3536 l 6055 3547 l 6083 3557 l 6111 3568 l 6141 3577 l 6171 3587 l 6202 3596 l 6234 3606 l 6268 3615 l 6304 3624 l 6341 3634 l 6380 3643 l 6421 3652 l 6464 3662 l 6508 3672 l 6553 3681 l 6598 3691 l 6642 3700 l 6686 3709 l 6727 3717 l 6765 3724 l 6799 3731 l 6828 3737 l 6853 3741 l 6871 3745 l 6885 3747 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 5300 3187 m 5144 3029 l 5350 3112 l 5295 3130 l 5300 3187 l cp gs 0.00 setgray ef gr col-1 s /Times-Roman ff 360.00 scf sf 6825 3923 m gs 1 -1 sc (*) col-1 sh gr /Times-Bold ff 270.00 scf sf 5025 2400 m gs 1 -1 sc (1) col-1 sh gr /Times-Bold ff 270.00 scf sf 6225 2400 m gs 1 -1 sc (2) col-1 sh gr /Times-Bold ff 270.00 scf sf 7425 2400 m gs 1 -1 sc (3) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1088 1132 a FP(Figure)j(5.4.)40 b FQ(A)28 b(standard)f(sphere)g(\(with)h(4)f(holes\).)605 1354 y FP(Exer)n(cise)32 b FQ(5.2.2)p FP(.)40 b FQ(Sho)n(w)31 b(that)h(the)g(mo)n(v)n(es)e FJ(Z)q(;)14 b(B)t(;)g(F)44 b FQ(connect)32 b(the)g(parameterizations)456 1453 y(corresp)r(onding) 25 b(to)j(the)g(marking)e(graphs)g(sho)n(wn)h(in)h(Figures)f(5.5,)g (5.6)f(and)i(5.7)f(b)r(elo)n(w.)1230 2023 y @beginspecial 0 @llx 0 @lly 75 @urx 50 @ury 750 @rwi @setspecial %%BeginDocument: figures/zmove1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: zmove1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 14:26:31 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 75 50 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -22.0 121.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7090 m -1000 -1000 l 5868 -1000 l 5868 7090 l cp clip 0.01980 0.01980 sc 7.500 slw % Rotated Ellipse gs 4800 4050 tr -0.000 rot n 0 0 60 60 0 360 DrawEllipse -0.000 rot gs 0.00 setgray ef gr gs col-1 s gr gr % Rotated Ellipse gs 3600 4050 tr -0.000 rot n 0 0 60 60 0 360 DrawEllipse -0.000 rot gs 0.00 setgray ef gr gs col-1 s gr gr % Rotated Ellipse gs 2400 4050 tr -0.000 rot n 0 0 60 60 0 360 DrawEllipse -0.000 rot gs 0.00 setgray ef gr gs col-1 s gr gr % Rotated Ellipse gs 1200 4050 tr -0.000 rot n 0 0 60 60 0 360 DrawEllipse -0.000 rot gs 0.00 setgray ef gr gs col-1 s gr gr % Polyline 30.000 slw [15 45] 45 sd n 3000 5850 m 4800 4050 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 3017 5839 m 2400 4050 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 3435 4356 m 3582 4101 l 3549 4393 l 3671 4026 l 3557 3988 l cp clip n 3002 5851 m 3600 4050 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 3435 4356 m 3582 4101 l 3549 4393 l 3507 4329 l 3435 4356 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 3000 5850 m 1200 4050 l gs col-1 s gr [] 0 sd /Times-Roman ff 450.00 scf sf 2895 6090 m gs 1 -1 sc (*) col-1 sh gr /Symbol ff 420.00 scf sf 3525 3840 m gs 1 -1 sc (a) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 2091 1750 a FI(Z)2040 1815 y FL(\000)-42 b(\000)-18 b Fw( )2294 2023 y @beginspecial 0 @llx 0 @lly 75 @urx 50 @ury 750 @rwi @setspecial %%BeginDocument: figures/zmove2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: zmove2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 14:27:33 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 75 50 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -22.0 121.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7090 m -1000 -1000 l 5868 -1000 l 5868 7090 l cp clip 0.01980 0.01980 sc 7.500 slw % Rotated Ellipse gs 4800 4050 tr -0.000 rot n 0 0 60 60 0 360 DrawEllipse -0.000 rot gs 0.00 setgray ef gr gs col-1 s gr gr % Rotated Ellipse gs 3600 4050 tr -0.000 rot n 0 0 60 60 0 360 DrawEllipse -0.000 rot gs 0.00 setgray ef gr gs col-1 s gr gr % Rotated Ellipse gs 2400 4050 tr -0.000 rot n 0 0 60 60 0 360 DrawEllipse -0.000 rot gs 0.00 setgray ef gr gs col-1 s gr gr % Rotated Ellipse gs 1200 4050 tr -0.000 rot n 0 0 60 60 0 360 DrawEllipse -0.000 rot gs 0.00 setgray ef gr gs col-1 s gr gr % Polyline 30.000 slw [15 45] 45 sd n 3000 5850 m 4800 4050 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 2455 4393 m 2417 4101 l 2568 4354 l 2442 3988 l 2329 4027 l cp clip n 3017 5839 m 2400 4050 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2455 4393 m 2417 4101 l 2568 4354 l 2496 4328 l 2455 4393 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 3002 5851 m 3600 4050 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 3000 5850 m 1200 4050 l gs col-1 s gr [] 0 sd /Times-Roman ff 450.00 scf sf 2895 6090 m gs 1 -1 sc (*) col-1 sh gr /Symbol ff 420.00 scf sf 3525 3840 m gs 1 -1 sc (a) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 1322 2228 a FP(Figure)32 b(5.5.)40 b FQ(Z-mo)n(v)n(e)26 b(\(\\rotation"\).)1244 3376 y @beginspecial 0 @llx 0 @lly 93 @urx 107 @ury 930 @rwi @setspecial %%BeginDocument: figures/bmv1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: bmv1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Jun 2 12:46:23 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 93 107 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3600 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -51.0 172.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8956 m -1000 -1000 l 7622 -1000 l 7622 8956 l cp clip 0.02160 0.02160 sc % Arc 15.000 slw gs n 4534.8 6530.4 820.4 140.7 46.5 arcn gs col-1 s gr gr % Arc gs [90] 0 sd n 4534.8 7569.6 820.4 -140.7 -46.5 arc gs col-1 s gr gr [] 0 sd 7.500 slw % Ellipse n 3000 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr 15.000 slw % Ellipse n 3000 3900 600 300 0 360 DrawEllipse gs col-1 s gr 7.500 slw % Ellipse n 6000 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr 15.000 slw % Ellipse n 5997 3900 600 300 0 360 DrawEllipse gs col-1 s gr 7.500 slw % Ellipse n 4500 7350 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 4500 5850 m 4500 7350 l gs col-1 s gr [] 0 sd % Polyline 15.000 slw n 3600 3900 m 3600 3903 l 3600 3911 l 3600 3924 l 3601 3944 l 3602 3970 l 3603 4001 l 3604 4037 l 3605 4075 l 3607 4114 l 3609 4153 l 3611 4190 l 3613 4226 l 3616 4259 l 3619 4290 l 3622 4318 l 3625 4344 l 3629 4368 l 3634 4390 l 3639 4411 l 3644 4431 l 3650 4450 l 3657 4470 l 3665 4490 l 3674 4510 l 3684 4529 l 3695 4549 l 3707 4568 l 3719 4587 l 3733 4606 l 3748 4625 l 3764 4643 l 3780 4661 l 3798 4679 l 3815 4696 l 3834 4712 l 3852 4728 l 3871 4743 l 3890 4758 l 3910 4772 l 3930 4786 l 3950 4800 l 3967 4811 l 3985 4823 l 4004 4835 l 4024 4846 l 4044 4858 l 4065 4870 l 4087 4881 l 4110 4893 l 4133 4904 l 4157 4915 l 4182 4926 l 4207 4936 l 4232 4946 l 4258 4955 l 4283 4963 l 4308 4971 l 4334 4978 l 4358 4984 l 4383 4989 l 4407 4993 l 4431 4996 l 4454 4998 l 4477 5000 l 4500 5000 l 4523 5000 l 4546 4998 l 4569 4996 l 4593 4993 l 4617 4989 l 4642 4984 l 4666 4978 l 4692 4971 l 4717 4963 l 4742 4955 l 4768 4946 l 4793 4936 l 4818 4926 l 4843 4915 l 4867 4904 l 4890 4893 l 4913 4881 l 4935 4870 l 4956 4858 l 4976 4846 l 4996 4835 l 5015 4823 l 5033 4811 l 5050 4800 l 5070 4786 l 5090 4772 l 5110 4758 l 5129 4743 l 5148 4728 l 5166 4712 l 5185 4696 l 5202 4679 l 5220 4661 l 5236 4643 l 5252 4625 l 5267 4606 l 5281 4587 l 5293 4568 l 5305 4549 l 5316 4529 l 5326 4510 l 5335 4490 l 5343 4470 l 5350 4450 l 5356 4431 l 5361 4411 l 5366 4390 l 5371 4368 l 5375 4344 l 5378 4318 l 5381 4290 l 5384 4259 l 5387 4226 l 5389 4190 l 5391 4153 l 5393 4114 l 5395 4075 l 5396 4037 l 5397 4001 l 5398 3970 l 5399 3944 l 5400 3924 l 5400 3911 l 5400 3903 l 5400 3900 l gs col-1 s gr % Polyline n 6600 3900 m 6600 3902 l 6600 3908 l 6599 3917 l 6599 3933 l 6598 3953 l 6597 3980 l 6595 4012 l 6594 4049 l 6591 4090 l 6589 4133 l 6586 4178 l 6582 4224 l 6578 4270 l 6574 4315 l 6570 4359 l 6565 4402 l 6560 4442 l 6554 4481 l 6548 4519 l 6541 4555 l 6534 4590 l 6526 4623 l 6517 4657 l 6508 4689 l 6498 4722 l 6487 4755 l 6475 4788 l 6465 4815 l 6454 4843 l 6442 4871 l 6430 4900 l 6417 4929 l 6403 4959 l 6388 4989 l 6373 5020 l 6358 5052 l 6341 5084 l 6324 5116 l 6306 5149 l 6288 5182 l 6269 5216 l 6249 5249 l 6230 5283 l 6209 5316 l 6189 5350 l 6168 5383 l 6147 5415 l 6126 5447 l 6105 5479 l 6084 5510 l 6063 5540 l 6042 5570 l 6021 5599 l 6001 5627 l 5980 5654 l 5960 5680 l 5940 5706 l 5921 5730 l 5901 5754 l 5882 5777 l 5863 5800 l 5839 5827 l 5816 5853 l 5792 5878 l 5769 5903 l 5745 5928 l 5721 5952 l 5697 5976 l 5673 6000 l 5648 6023 l 5624 6047 l 5600 6070 l 5576 6093 l 5552 6116 l 5528 6138 l 5505 6160 l 5482 6181 l 5461 6203 l 5439 6223 l 5419 6244 l 5399 6263 l 5381 6283 l 5363 6302 l 5346 6321 l 5330 6339 l 5315 6358 l 5301 6376 l 5288 6394 l 5275 6413 l 5261 6434 l 5248 6456 l 5236 6479 l 5225 6504 l 5214 6529 l 5204 6556 l 5194 6585 l 5185 6616 l 5176 6649 l 5167 6685 l 5158 6723 l 5150 6762 l 5142 6803 l 5134 6844 l 5127 6884 l 5120 6922 l 5114 6957 l 5110 6987 l 5106 7011 l 5103 7029 l 5101 7040 l 5100 7047 l 5100 7050 l gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 6000 4200 m 6000 4203 l 6000 4209 l 5999 4219 l 5999 4235 l 5998 4257 l 5996 4284 l 5994 4315 l 5992 4350 l 5989 4387 l 5986 4424 l 5983 4461 l 5979 4498 l 5975 4533 l 5970 4566 l 5965 4598 l 5959 4627 l 5953 4655 l 5946 4681 l 5938 4706 l 5930 4730 l 5921 4754 l 5911 4777 l 5900 4800 l 5890 4820 l 5879 4839 l 5867 4859 l 5855 4880 l 5841 4900 l 5827 4921 l 5811 4942 l 5795 4964 l 5778 4985 l 5760 5007 l 5741 5029 l 5721 5052 l 5700 5074 l 5679 5097 l 5657 5119 l 5635 5141 l 5612 5163 l 5589 5184 l 5566 5205 l 5542 5226 l 5518 5246 l 5494 5266 l 5471 5285 l 5447 5304 l 5423 5322 l 5399 5340 l 5374 5358 l 5350 5375 l 5327 5391 l 5303 5407 l 5279 5423 l 5254 5439 l 5229 5455 l 5202 5471 l 5173 5488 l 5144 5506 l 5112 5524 l 5079 5543 l 5043 5563 l 5006 5583 l 4967 5605 l 4926 5627 l 4884 5650 l 4840 5673 l 4796 5696 l 4753 5719 l 4710 5741 l 4670 5762 l 4633 5782 l 4599 5799 l 4571 5814 l 4547 5826 l 4528 5835 l 4515 5842 l 4507 5847 l 4502 5849 l 4500 5850 l gs col-1 s gr [] 0 sd % Polyline 15.000 slw n 2400 3900 m 2400 3902 l 2400 3908 l 2401 3917 l 2401 3933 l 2402 3953 l 2403 3980 l 2405 4012 l 2406 4049 l 2409 4090 l 2411 4133 l 2414 4178 l 2418 4224 l 2422 4270 l 2426 4315 l 2430 4359 l 2435 4402 l 2440 4442 l 2446 4481 l 2452 4519 l 2459 4555 l 2466 4590 l 2474 4623 l 2483 4657 l 2492 4689 l 2502 4722 l 2513 4755 l 2525 4788 l 2535 4815 l 2546 4843 l 2558 4871 l 2570 4900 l 2583 4929 l 2597 4959 l 2612 4989 l 2627 5020 l 2642 5052 l 2659 5084 l 2676 5116 l 2694 5149 l 2712 5182 l 2731 5216 l 2751 5249 l 2770 5283 l 2791 5316 l 2811 5350 l 2832 5383 l 2853 5415 l 2874 5447 l 2895 5479 l 2916 5510 l 2937 5540 l 2958 5570 l 2979 5599 l 2999 5627 l 3020 5654 l 3040 5680 l 3060 5706 l 3079 5730 l 3099 5754 l 3118 5777 l 3138 5800 l 3161 5827 l 3184 5853 l 3208 5878 l 3231 5903 l 3255 5928 l 3279 5952 l 3303 5976 l 3327 6000 l 3352 6023 l 3376 6047 l 3400 6070 l 3424 6093 l 3448 6116 l 3472 6138 l 3495 6160 l 3518 6181 l 3539 6203 l 3561 6223 l 3581 6244 l 3601 6263 l 3619 6283 l 3637 6302 l 3654 6321 l 3670 6339 l 3685 6358 l 3699 6376 l 3712 6394 l 3725 6413 l 3739 6434 l 3752 6456 l 3764 6479 l 3775 6504 l 3786 6529 l 3796 6556 l 3806 6585 l 3815 6616 l 3824 6649 l 3833 6685 l 3842 6723 l 3850 6762 l 3858 6803 l 3866 6844 l 3873 6884 l 3880 6922 l 3886 6957 l 3890 6987 l 3894 7011 l 3897 7029 l 3899 7040 l 3900 7047 l 3900 7050 l gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd gs clippath 2950 4544 m 3001 4253 l 3070 4540 l 3059 4153 l 2939 4157 l cp clip n 3000 4200 m 3001 4235 l 3002 4257 l 3004 4284 l 3006 4315 l 3008 4350 l 3011 4387 l 3014 4424 l 3017 4461 l 3021 4498 l 3025 4533 l 3030 4566 l 3035 4598 l 3041 4627 l 3047 4655 l 3054 4681 l 3062 4706 l 3070 4730 l 3079 4754 l 3089 4777 l 3100 4800 l 3110 4820 l 3121 4839 l 3133 4859 l 3145 4880 l 3159 4900 l 3173 4921 l 3189 4942 l 3205 4964 l 3222 4985 l 3240 5007 l 3259 5029 l 3279 5052 l 3300 5074 l 3321 5097 l 3343 5119 l 3365 5141 l 3388 5163 l 3411 5184 l 3434 5205 l 3458 5226 l 3482 5246 l 3506 5266 l 3529 5285 l 3553 5304 l 3577 5322 l 3601 5340 l 3626 5358 l 3650 5375 l 3673 5391 l 3697 5407 l 3721 5423 l 3746 5439 l 3771 5455 l 3798 5471 l 3827 5488 l 3856 5506 l 3888 5524 l 3921 5543 l 3957 5563 l 3994 5583 l 4033 5605 l 4074 5627 l 4116 5650 l 4160 5673 l 4204 5696 l 4247 5719 l 4290 5741 l 4330 5762 l 4367 5782 l 4401 5799 l 4429 5814 l 4453 5826 l 4472 5835 l 4485 5842 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2950 4544 m 3001 4253 l 3070 4540 l 3008 4494 l 2950 4544 l cp gs 0.00 setgray ef gr col-1 s /Times-Roman ff 375.00 scf sf 4425 6075 m gs 1 -1 sc (*) col-1 sh gr /Symbol ff 360.00 scf sf 2925 3375 m gs 1 -1 sc (a) col-1 sh gr /Symbol ff 360.00 scf sf 5925 3375 m gs 1 -1 sc (b) col-1 sh gr /Symbol ff 360.00 scf sf 4425 7875 m gs 1 -1 sc (g) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 2206 2856 a FI(B)2256 2865 y FG(\013;\014)2203 2931 y FL(\000)-42 b(\000)-18 b Fw( )2457 3381 y @beginspecial 0 @llx 0 @lly 92 @urx 108 @ury 920 @rwi @setspecial %%BeginDocument: figures/bmv2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: bmv2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Mon Aug 10 20:09:24 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 92 108 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3600 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -8.0 128.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 6886 m -1000 -1000 l 5622 -1000 l 5622 6886 l cp clip 0.02160 0.02160 sc % Arc 15.000 slw gs n 2495.2 4460.4 820.4 39.3 133.5 arc gs col-1 s gr gr % Arc gs [90] 0 sd n 2495.2 5499.6 820.4 -39.3 -133.5 arcn gs col-1 s gr gr [] 0 sd % Ellipse n 3998 1830 600 300 0 360 DrawEllipse gs col-1 s gr 7.500 slw % Ellipse n 1030 2130 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr 15.000 slw % Ellipse n 1001 1830 600 300 0 360 DrawEllipse gs col-1 s gr 7.500 slw % Ellipse n 2530 5280 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4030 2130 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 2530 3780 m 2530 5355 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 3957 2469 m 4027 2183 l 4077 2474 l 4092 2087 l 3972 2083 l cp clip n 2005 2730 m 2008 2733 l 2015 2740 l 2026 2751 l 2042 2767 l 2061 2786 l 2082 2807 l 2103 2828 l 2123 2848 l 2142 2867 l 2160 2885 l 2176 2901 l 2190 2915 l 2204 2929 l 2217 2942 l 2230 2955 l 2241 2966 l 2253 2978 l 2265 2990 l 2278 3002 l 2290 3014 l 2304 3027 l 2317 3040 l 2331 3053 l 2346 3066 l 2361 3079 l 2376 3091 l 2390 3103 l 2405 3115 l 2420 3127 l 2435 3137 l 2450 3148 l 2465 3158 l 2480 3168 l 2496 3177 l 2512 3186 l 2529 3196 l 2546 3205 l 2565 3214 l 2585 3223 l 2605 3232 l 2626 3240 l 2648 3248 l 2670 3256 l 2692 3263 l 2714 3269 l 2736 3275 l 2758 3280 l 2779 3284 l 2801 3287 l 2822 3290 l 2843 3293 l 2862 3294 l 2881 3295 l 2901 3295 l 2921 3295 l 2943 3294 l 2965 3293 l 2987 3291 l 3011 3288 l 3034 3285 l 3058 3280 l 3083 3275 l 3107 3270 l 3131 3264 l 3155 3257 l 3179 3250 l 3202 3242 l 3225 3233 l 3248 3224 l 3270 3215 l 3293 3205 l 3313 3195 l 3334 3185 l 3355 3174 l 3376 3162 l 3398 3150 l 3421 3137 l 3444 3123 l 3467 3108 l 3490 3093 l 3514 3077 l 3537 3061 l 3560 3044 l 3583 3027 l 3605 3010 l 3627 2993 l 3648 2977 l 3668 2960 l 3687 2944 l 3705 2927 l 3722 2911 l 3739 2896 l 3755 2880 l 3772 2863 l 3788 2845 l 3804 2828 l 3820 2810 l 3835 2791 l 3850 2772 l 3865 2752 l 3879 2733 l 3892 2713 l 3905 2692 l 3918 2672 l 3929 2652 l 3940 2633 l 3950 2613 l 3959 2594 l 3967 2575 l 3974 2557 l 3981 2540 l 3987 2522 l 3993 2505 l 3998 2486 l 4003 2466 l 4007 2446 l 4011 2425 l 4014 2403 l 4017 2378 l 4019 2352 l 4022 2324 l 4024 2293 l 4025 2262 l 4027 2231 l 4028 2202 l 4029 2177 l 4029 2156 l 4030 2130 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 3957 2469 m 4027 2183 l 4077 2474 l 4019 2424 l 3957 2469 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 2530 3780 m 2527 3780 l 2521 3780 l 2511 3780 l 2495 3780 l 2473 3779 l 2446 3779 l 2414 3779 l 2379 3778 l 2342 3777 l 2304 3777 l 2266 3776 l 2229 3775 l 2194 3774 l 2160 3772 l 2128 3771 l 2098 3770 l 2069 3768 l 2042 3766 l 2016 3765 l 1991 3763 l 1966 3760 l 1942 3758 l 1918 3755 l 1893 3752 l 1868 3749 l 1843 3745 l 1818 3741 l 1792 3737 l 1765 3733 l 1738 3728 l 1711 3724 l 1683 3718 l 1655 3713 l 1627 3707 l 1599 3702 l 1572 3696 l 1545 3690 l 1518 3684 l 1493 3677 l 1468 3671 l 1443 3665 l 1420 3659 l 1398 3653 l 1377 3647 l 1356 3642 l 1336 3636 l 1318 3630 l 1293 3622 l 1270 3615 l 1247 3607 l 1224 3598 l 1200 3589 l 1176 3579 l 1150 3569 l 1124 3557 l 1097 3545 l 1069 3533 l 1042 3520 l 1016 3509 l 994 3499 l 977 3490 l 965 3485 l 958 3482 l 955 3480 l gs col-1 s gr [] 0 sd % Polyline [15 90] 90 sd n 955 3480 m 955 3479 l 953 3475 l 948 3465 l 941 3450 l 933 3432 l 924 3412 l 917 3394 l 910 3376 l 904 3360 l 899 3346 l 896 3332 l 893 3318 l 890 3305 l 888 3292 l 887 3278 l 885 3264 l 884 3248 l 884 3232 l 883 3216 l 884 3199 l 884 3183 l 885 3166 l 887 3150 l 888 3135 l 890 3120 l 893 3105 l 895 3090 l 898 3075 l 902 3060 l 905 3044 l 910 3027 l 914 3011 l 919 2994 l 924 2978 l 930 2962 l 935 2946 l 940 2932 l 945 2918 l 950 2905 l 955 2893 l 961 2878 l 967 2864 l 973 2850 l 980 2836 l 988 2822 l 996 2808 l 1005 2795 l 1014 2783 l 1023 2771 l 1033 2761 l 1044 2751 l 1055 2743 l 1065 2735 l 1076 2728 l 1088 2721 l 1102 2715 l 1116 2708 l 1131 2702 l 1148 2696 l 1165 2690 l 1182 2685 l 1199 2681 l 1216 2677 l 1233 2673 l 1250 2670 l 1268 2668 l 1283 2665 l 1298 2664 l 1315 2662 l 1331 2661 l 1349 2659 l 1367 2658 l 1385 2657 l 1403 2657 l 1421 2656 l 1439 2656 l 1456 2655 l 1473 2655 l 1488 2655 l 1503 2655 l 1517 2655 l 1530 2655 l 1544 2655 l 1559 2655 l 1573 2655 l 1587 2655 l 1601 2656 l 1616 2656 l 1630 2657 l 1644 2658 l 1659 2659 l 1673 2660 l 1687 2661 l 1701 2663 l 1716 2665 l 1730 2668 l 1743 2670 l 1757 2672 l 1772 2675 l 1789 2679 l 1808 2683 l 1829 2688 l 1853 2693 l 1879 2699 l 1905 2706 l 1932 2712 l 1957 2718 l 1977 2723 l 1992 2727 l 2001 2729 l 2004 2730 l 2005 2730 l gs col-1 s gr [] 0 sd % Polyline 15.000 slw n 3412 1830 m 3412 1833 l 3412 1841 l 3412 1854 l 3411 1874 l 3410 1900 l 3409 1931 l 3408 1967 l 3407 2005 l 3405 2044 l 3403 2083 l 3401 2120 l 3399 2156 l 3396 2189 l 3393 2220 l 3390 2248 l 3387 2274 l 3383 2298 l 3378 2320 l 3373 2341 l 3368 2361 l 3362 2380 l 3355 2400 l 3347 2420 l 3338 2440 l 3328 2459 l 3317 2479 l 3305 2498 l 3293 2517 l 3279 2536 l 3264 2555 l 3248 2573 l 3232 2591 l 3214 2609 l 3197 2626 l 3178 2642 l 3160 2658 l 3141 2673 l 3122 2688 l 3102 2702 l 3082 2716 l 3062 2730 l 3045 2741 l 3027 2753 l 3008 2765 l 2988 2776 l 2968 2788 l 2947 2800 l 2925 2811 l 2902 2823 l 2879 2834 l 2855 2845 l 2830 2856 l 2805 2866 l 2780 2876 l 2754 2885 l 2729 2893 l 2704 2901 l 2678 2908 l 2654 2914 l 2629 2919 l 2605 2923 l 2581 2926 l 2558 2928 l 2535 2930 l 2512 2930 l 2489 2930 l 2466 2928 l 2443 2926 l 2419 2923 l 2395 2919 l 2370 2914 l 2346 2908 l 2320 2901 l 2295 2893 l 2270 2885 l 2244 2876 l 2219 2866 l 2194 2856 l 2169 2845 l 2145 2834 l 2122 2823 l 2099 2811 l 2077 2800 l 2056 2788 l 2036 2776 l 2016 2765 l 1997 2753 l 1979 2741 l 1962 2730 l 1942 2716 l 1922 2702 l 1902 2688 l 1883 2673 l 1864 2658 l 1846 2642 l 1827 2626 l 1810 2609 l 1792 2591 l 1776 2573 l 1760 2555 l 1745 2536 l 1731 2517 l 1719 2498 l 1707 2479 l 1696 2459 l 1686 2440 l 1677 2420 l 1669 2400 l 1662 2380 l 1656 2361 l 1651 2341 l 1646 2320 l 1641 2298 l 1637 2274 l 1634 2248 l 1631 2220 l 1628 2189 l 1625 2156 l 1623 2120 l 1621 2083 l 1619 2044 l 1617 2005 l 1616 1967 l 1615 1931 l 1614 1900 l 1613 1874 l 1612 1854 l 1612 1841 l 1612 1833 l 1612 1830 l gs col-1 s gr % Polyline n 4600 1830 m 4600 1832 l 4600 1838 l 4599 1847 l 4599 1863 l 4598 1883 l 4597 1910 l 4595 1942 l 4594 1979 l 4591 2020 l 4589 2063 l 4586 2108 l 4582 2154 l 4578 2200 l 4574 2245 l 4570 2289 l 4565 2332 l 4560 2372 l 4554 2411 l 4548 2449 l 4541 2485 l 4534 2520 l 4526 2553 l 4517 2587 l 4508 2619 l 4498 2652 l 4487 2685 l 4475 2718 l 4465 2745 l 4454 2773 l 4442 2801 l 4430 2830 l 4417 2859 l 4403 2889 l 4388 2919 l 4373 2950 l 4358 2982 l 4341 3014 l 4324 3046 l 4306 3079 l 4288 3112 l 4269 3146 l 4249 3179 l 4230 3213 l 4209 3246 l 4189 3280 l 4168 3313 l 4147 3345 l 4126 3377 l 4105 3409 l 4084 3440 l 4063 3470 l 4042 3500 l 4021 3529 l 4001 3557 l 3980 3584 l 3960 3610 l 3940 3636 l 3921 3660 l 3901 3684 l 3882 3707 l 3863 3730 l 3839 3757 l 3816 3783 l 3792 3808 l 3769 3833 l 3745 3858 l 3721 3882 l 3697 3906 l 3673 3930 l 3648 3953 l 3624 3977 l 3600 4000 l 3576 4023 l 3552 4046 l 3528 4068 l 3505 4090 l 3482 4111 l 3461 4133 l 3439 4153 l 3419 4174 l 3399 4193 l 3381 4213 l 3363 4232 l 3346 4251 l 3330 4269 l 3315 4288 l 3301 4306 l 3288 4324 l 3275 4343 l 3261 4364 l 3248 4386 l 3236 4409 l 3225 4434 l 3214 4459 l 3204 4486 l 3194 4515 l 3185 4546 l 3176 4579 l 3167 4615 l 3158 4653 l 3150 4692 l 3142 4733 l 3134 4774 l 3127 4814 l 3120 4852 l 3114 4887 l 3110 4917 l 3106 4941 l 3103 4959 l 3101 4970 l 3100 4977 l 3100 4980 l gs col-1 s gr % Polyline n 430 1830 m 430 1832 l 430 1838 l 431 1847 l 431 1863 l 432 1883 l 433 1910 l 435 1942 l 436 1979 l 439 2020 l 441 2063 l 444 2108 l 448 2154 l 452 2200 l 456 2245 l 460 2289 l 465 2332 l 470 2372 l 476 2411 l 482 2449 l 489 2485 l 496 2520 l 504 2553 l 513 2587 l 522 2619 l 532 2652 l 543 2685 l 555 2718 l 565 2745 l 576 2773 l 588 2801 l 600 2830 l 613 2859 l 627 2889 l 642 2919 l 657 2950 l 672 2982 l 689 3014 l 706 3046 l 724 3079 l 742 3112 l 761 3146 l 781 3179 l 800 3213 l 821 3246 l 841 3280 l 862 3313 l 883 3345 l 904 3377 l 925 3409 l 946 3440 l 967 3470 l 988 3500 l 1009 3529 l 1029 3557 l 1050 3584 l 1070 3610 l 1090 3636 l 1109 3660 l 1129 3684 l 1148 3707 l 1168 3730 l 1191 3757 l 1214 3783 l 1238 3808 l 1261 3833 l 1285 3858 l 1309 3882 l 1333 3906 l 1357 3930 l 1382 3953 l 1406 3977 l 1430 4000 l 1454 4023 l 1478 4046 l 1502 4068 l 1525 4090 l 1548 4111 l 1569 4133 l 1591 4153 l 1611 4174 l 1631 4193 l 1649 4213 l 1667 4232 l 1684 4251 l 1700 4269 l 1715 4288 l 1729 4306 l 1742 4324 l 1755 4343 l 1769 4364 l 1782 4386 l 1794 4409 l 1805 4434 l 1816 4459 l 1826 4486 l 1836 4515 l 1845 4546 l 1854 4579 l 1863 4615 l 1872 4653 l 1880 4692 l 1888 4733 l 1896 4774 l 1903 4814 l 1910 4852 l 1916 4887 l 1920 4917 l 1924 4941 l 1927 4959 l 1929 4970 l 1930 4977 l 1930 4980 l gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 1060 2130 m 1060 2133 l 1060 2139 l 1061 2149 l 1061 2165 l 1062 2187 l 1064 2214 l 1066 2245 l 1068 2280 l 1071 2317 l 1074 2354 l 1077 2391 l 1081 2428 l 1085 2463 l 1090 2496 l 1095 2528 l 1101 2557 l 1107 2585 l 1114 2611 l 1122 2636 l 1130 2660 l 1139 2684 l 1149 2707 l 1160 2730 l 1170 2750 l 1181 2769 l 1193 2789 l 1205 2810 l 1219 2830 l 1233 2851 l 1249 2872 l 1265 2894 l 1282 2915 l 1300 2937 l 1319 2959 l 1339 2982 l 1360 3004 l 1381 3027 l 1403 3049 l 1425 3071 l 1448 3093 l 1471 3114 l 1494 3135 l 1518 3156 l 1542 3176 l 1566 3196 l 1589 3215 l 1613 3234 l 1637 3252 l 1661 3270 l 1686 3288 l 1710 3305 l 1733 3321 l 1757 3337 l 1781 3353 l 1806 3369 l 1831 3385 l 1858 3401 l 1887 3418 l 1916 3436 l 1948 3454 l 1981 3473 l 2017 3493 l 2054 3513 l 2093 3535 l 2134 3557 l 2176 3580 l 2220 3603 l 2264 3626 l 2307 3649 l 2350 3671 l 2390 3692 l 2427 3712 l 2461 3729 l 2489 3744 l 2513 3756 l 2532 3765 l 2545 3772 l 2553 3777 l 2558 3779 l 2560 3780 l gs col-1 s gr [] 0 sd /Symbol ff 360.00 scf sf 920 1305 m gs 1 -1 sc (a) col-1 sh gr /Symbol ff 360.00 scf sf 3995 1305 m gs 1 -1 sc (b) col-1 sh gr /Symbol ff 360.00 scf sf 2420 5805 m gs 1 -1 sc (g) col-1 sh gr /Times-Roman ff 375.00 scf sf 2475 3975 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1313 3586 a FP(Figure)32 b(5.6.)40 b FQ(B-mo)n(v)n(e)26 b(\(\\braiding"\).)1202 4463 y @beginspecial 0 @llx 0 @lly 110 @urx 75 @ury 1100 @rwi @setspecial %%BeginDocument: figures/fmove1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: fmove1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Jun 2 12:39:21 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 110 75 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -46.0 156.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8867 m -1000 -1000 l 8868 -1000 l 8868 8867 l cp clip 0.01980 0.01980 sc 7.500 slw % Ellipse n 2400 6000 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2400 4800 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2400 7200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7800 7800 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7800 6600 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7800 5400 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7800 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 5100 6000 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 4200 6000 m 2400 4800 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 7516 4399 m 7761 4238 l 7601 4484 l 7874 4211 l 7789 4126 l cp clip n 6000 6000 m 7800 4200 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 7516 4399 m 7761 4238 l 7601 4484 l 7592 4408 l 7516 4399 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 6000 6000 m 7800 7800 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 2400 6000 m 4125 6000 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 6011 6017 m 7800 5400 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 5999 6002 m 7800 6600 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 2400 7200 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 5160 6014 m 5970 6014 l gs col0 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 4717 5939 m 5005 5999 l 4717 6059 l 5077 6059 l 5077 5939 l cp clip n 4200 6000 m 5032 5999 l gs col-1 s gr gr [] 0 sd % arrowhead 7.500 slw n 4717 5939 m 5005 5999 l 4717 6059 l 4765 5999 l 4717 5939 l cp gs 0.00 setgray ef gr col-1 s /Times-Roman ff 450.00 scf sf 4095 6225 m gs 1 -1 sc (*) col-1 sh gr /Times-Roman ff 450.00 scf sf 5895 6225 m gs 1 -1 sc (*) col-1 sh gr /Times-Italic ff 420.00 scf sf 5025 5700 m gs 1 -1 sc (c) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 2343 4084 a FI(F)2385 4092 y FG(c)2303 4150 y FL(\000)-42 b(\000)-18 b Fw( )2557 4463 y @beginspecial 0 @llx 0 @lly 75 @urx 75 @ury 750 @rwi @setspecial %%BeginDocument: figures/fmove2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: fmove2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Jun 2 12:40:37 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 75 75 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -81.0 156.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8867 m -1000 -1000 l 8868 -1000 l 8868 8867 l cp clip 0.01980 0.01980 sc 7.500 slw % Ellipse n 7800 7800 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7800 6600 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7800 5400 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7800 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4200 4800 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4185 6000 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4200 7200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 6000 6000 m 7800 7800 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 6011 6017 m 7800 5400 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 5999 6002 m 7800 6600 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 5977 6000 m 4177 4800 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 5988 6000 m 4188 7200 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 5925 6000 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 7516 4399 m 7761 4238 l 7601 4484 l 7874 4211 l 7789 4126 l cp clip n 6000 6000 m 7800 4200 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 7516 4399 m 7761 4238 l 7601 4484 l 7592 4408 l 7516 4399 l cp gs 0.00 setgray ef gr col-1 s /Times-Roman ff 450.00 scf sf 5895 6225 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1039 4668 a FP(Figure)32 b(5.7.)41 b FQ(F-mo)n(v)n(e)26 b(\(\\fusion")h(or)g(\\cut)g(remo)n(v)-5 b(al"\).)605 4913 y(Next,)38 b(one)d(often)h(needs)g(comp)r(ositions)f(of)g(the)h (form)g FJ(Z)2480 4883 y FI(a)2520 4913 y FJ(F)2573 4925 y FI(c)2607 4913 y FQ(\()p FJ(Z)2702 4883 y FI(m)2696 4934 y(i)2789 4913 y FL(t)24 b FJ(Z)2931 4883 y FI(n)2925 4934 y(j)2976 4913 y FQ(\),)38 b(where)d FJ(c)h FQ(is)456 5016 y(a)h(cut)h(separating)e(comp)r(onen)n(ts)i(\006)1628 5028 y FI(i)1693 5016 y FQ(and)g(\006)1925 5028 y FI(j)1998 5016 y FQ(\(compare)f(with)h(the)g(de\014nition)h(of)e(the)i(F-)456 5116 y(mo)n(v)n(e\).)34 b(W)-7 b(e)25 b(will)f(call)g(an)n(y)g(suc)n(h) f(comp)r(osition)h(a)g FO(gener)l(alize)l(d)k(F-move)p FQ(;)e(for)d(brevit)n(y)-7 b(,)24 b(w)n(e)g(will)456 5216 y(frequen)n(tly)g(denote)g(it)h(just)g(b)n(y)g FJ(F)1516 5228 y FI(c)1550 5216 y FQ(.)36 b(The)25 b(Rotation)f(axiom)f(form)n (ulated)h(b)r(elo)n(w)g(implies)h(that)p eop %%Page: 101 9 101 104 bop 1599 226 a FM(5.2.)29 b(THE)g(LEGO)g(GAME)1021 b(101)456 425 y FQ(suc)n(h)24 b(a)f(comp)r(osition)h(is)g(uniquely)h (determined)f(b)n(y)g(the)h(original)d(parameterization)h FJ(M)33 b FQ(and)456 525 y(b)n(y)d(the)h(c)n(hoice)f(of)h(the)g (distinguished)g(edge)f(for)h(the)g(resulting)f(parameterization)f FJ(F)3233 537 y FI(c)3267 525 y FQ(\()p FJ(M)9 b FQ(\).)456 624 y(Moreo)n(v)n(er,)18 b(the)i(Symmetry)g(of)f(F)h(axiom)f(along)f (with)i(the)g(comm)n(utativit)n(y)f(of)h(disjoin)n(t)f(union,)456 724 y(also)34 b(form)n(ulated)h(b)r(elo)n(w,)j(imply)e(that)g(if)g(w)n (e)g(switc)n(h)f(the)h(roles)f(of)h(\006)2752 736 y FM(1)2825 724 y FQ(and)f(\006)3054 736 y FM(2)3092 724 y FQ(,)j(then)e(w)n(e)456 824 y(get)41 b(the)g(same)g(generalized)f(F-mo)n(v)n(e.)76 b(Th)n(us,)44 b(the)e(generalized)e(F-mo)n(v)n(e)g(is)h(completely)456 923 y(determined)24 b(b)n(y)g(the)h(marking)e(graph)g(of)i FJ(M)33 b FQ(and)24 b(b)n(y)g(the)h(c)n(hoice)e(of)i(the)g (distinguished)f(edge)456 1023 y(for)j(the)h(resulting)f(marking)f (graph)h(of)g FJ(F)1776 1035 y FI(c)1810 1023 y FQ(\()p FJ(M)9 b FQ(\).)605 1123 y(Finally)-7 b(,)25 b(let)g FJ(M)32 b FL(2)23 b FJ(M)9 b FQ(\(\006\))25 b(and)g(let)g(\006)1784 1135 y FI(i)1836 1123 y FQ(b)r(e)g(one)f(of)h(the)g(comp)r(onen)n(ts)f (of)g(\006.)36 b(As)25 b(discussed)456 1222 y(b)r(efore,)d(the)h (parameterization)c FJ( )1550 1234 y FI(i)1600 1222 y FQ(de\014nes)j(an)f(order)g(on)g(the)h(set)g(of)g(b)r(oundary)f(comp)r (onen)n(ts)456 1322 y(of)31 b(\006)614 1334 y FI(i)642 1322 y FQ(.)49 b(Let)31 b(us)h(assume)f(that)h(w)n(e)f(ha)n(v)n(e)f(a)i (presen)n(tation)e(of)i FJ(\031)2470 1334 y FM(0)2507 1322 y FQ(\()p FJ(@)5 b FQ(\006)2648 1334 y FI(i)2676 1322 y FQ(\))32 b(as)f(a)g(disjoin)n(t)g(union,)456 1421 y FJ(\031)503 1433 y FM(0)540 1421 y FQ(\()p FJ(@)5 b FQ(\006)681 1433 y FI(i)709 1421 y FQ(\))29 b(=)f FJ(I)899 1433 y FM(1)958 1421 y FL(t)21 b FJ(I)1070 1433 y FM(2)1128 1421 y FL(t)g FJ(I)1240 1433 y FM(3)1299 1421 y FL(t)g FJ(I)1411 1433 y FM(4)1448 1421 y FQ(,)32 b(where)f(the)g(order)f(is)h (giv)n(en)f(b)n(y)h FJ(I)2576 1433 y FM(1)2642 1421 y FJ(<)d(I)2771 1433 y FM(2)2838 1421 y FJ(<)g(I)2967 1433 y FM(3)3034 1421 y FJ(<)g(I)3163 1433 y FM(4)3232 1421 y FQ(\(some)456 1521 y(of)i(the)g FJ(I)734 1533 y FI(k)806 1521 y FQ(ma)n(y)f(b)r(e)i(empt)n(y\).)45 b(Then)30 b(w)n(e)g(de\014ne) g(the)h FO(gener)l(alize)l(d)i(br)l(aiding)h(move)j FJ(B)3193 1533 y FI(I)3222 1541 y FF(2)3255 1533 y FI(;I)3304 1541 y FF(3)3371 1521 y FQ(to)456 1621 y(b)r(e)27 b(the)h(pro)r(duct)f(of)g (simple)g(mo)n(v)n(es)f(sho)n(wn)h(in)g(Figure)g(5.8)f(b)r(elo)n(w)h (\(note)g(that)h(w)n(e)f(are)f(using)456 1720 y(generalized)c(F-mo)n(v) n(es,)h(see)h(ab)r(o)n(v)n(e\).)35 b(It)24 b(is)g(easy)f(to)h(sho)n(w)f (that)h(this)g(\014gure)f(uniquely)h(de\014nes)456 1820 y(the)k(cuts)f FJ(c)810 1832 y FM(1)847 1820 y FJ(;)14 b(c)920 1832 y FM(2)958 1820 y FJ(;)g(c)1031 1832 y FM(3)1095 1820 y FQ(and)28 b(th)n(us,)f(the)h(generalized)f(braiding)f(mo)n(v)n (e)h FJ(B)t FQ(.)747 2524 y @beginspecial 0 @llx 0 @lly 102 @urx 54 @ury 1020 @rwi @setspecial %%BeginDocument: figures/genbraid1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: genbraid1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 15:32:40 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 102 54 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2700 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -25.0 101.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7225 m -1000 -1000 l 8815 -1000 l 8815 7225 l cp clip 0.01620 0.01620 sc /Times-Italic ff 420.00 scf sf 1830 3240 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 1950 3360 m gs 1 -1 sc (1) col-1 sh gr /Times-Italic ff 420.00 scf sf 7500 3270 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 7620 3390 m gs 1 -1 sc (4) col-1 sh gr /Times-Italic ff 420.00 scf sf 3472 3323 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 3592 3443 m gs 1 -1 sc (2) col-1 sh gr /Times-Italic ff 420.00 scf sf 5625 3307 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 5760 3427 m gs 1 -1 sc (3) col-1 sh gr 7.500 slw % Ellipse n 1800 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2160 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3912 3904 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 6105 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 5387 3885 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7215 3915 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7605 3915 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 5715 3877 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3441 3902 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 4200 6000 m 3900 3900 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 5700 3907 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 6120 3915 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 5385 3900 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 2018 4170 m 1840 3935 l 2097 4080 l 1806 3825 l 1727 3916 l cp clip n 4200 6000 m 1800 3900 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2018 4170 m 1840 3935 l 2097 4080 l 2021 4094 l 2018 4170 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 4200 6000 m 7605 3930 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 2175 3915 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4230 6000 m 7125 3960 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4193 5929 m 3420 3892 l gs col-1 s gr [] 0 sd % Polyline 15.000 slw n 1595 3764 m 1595 3763 l 1598 3758 l 1603 3748 l 1611 3734 l 1621 3718 l 1631 3704 l 1641 3693 l 1652 3684 l 1663 3676 l 1676 3671 l 1689 3667 l 1703 3663 l 1718 3660 l 1735 3658 l 1753 3655 l 1771 3653 l 1790 3651 l 1808 3649 l 1825 3647 l 1841 3645 l 1855 3642 l 1868 3640 l 1886 3635 l 1901 3629 l 1915 3623 l 1927 3616 l 1937 3610 l 1946 3606 l 1953 3603 l 1960 3602 l 1966 3603 l 1972 3606 l 1980 3610 l 1988 3616 l 1998 3623 l 2010 3629 l 2023 3635 l 2037 3640 l 2048 3642 l 2060 3645 l 2074 3647 l 2088 3649 l 2104 3651 l 2120 3653 l 2137 3655 l 2153 3658 l 2168 3661 l 2183 3664 l 2196 3668 l 2208 3672 l 2220 3677 l 2230 3683 l 2241 3690 l 2252 3700 l 2263 3710 l 2275 3723 l 2287 3737 l 2298 3750 l 2307 3761 l 2312 3768 l 2315 3771 l 2315 3772 l gs col0 s gr % Polyline n 7073 3802 m 7073 3801 l 7076 3796 l 7081 3786 l 7089 3772 l 7099 3756 l 7109 3742 l 7119 3731 l 7130 3722 l 7141 3714 l 7154 3709 l 7167 3705 l 7181 3701 l 7196 3698 l 7213 3696 l 7231 3693 l 7249 3691 l 7268 3689 l 7286 3687 l 7303 3685 l 7319 3683 l 7333 3680 l 7346 3678 l 7364 3673 l 7379 3667 l 7393 3661 l 7405 3654 l 7415 3648 l 7424 3644 l 7431 3641 l 7438 3640 l 7444 3641 l 7450 3644 l 7458 3648 l 7466 3654 l 7476 3661 l 7488 3667 l 7501 3673 l 7515 3678 l 7526 3680 l 7538 3683 l 7552 3685 l 7566 3687 l 7582 3689 l 7598 3691 l 7615 3693 l 7631 3696 l 7646 3699 l 7661 3702 l 7674 3706 l 7686 3710 l 7698 3715 l 7708 3721 l 7719 3728 l 7730 3738 l 7741 3748 l 7753 3761 l 7765 3775 l 7776 3788 l 7785 3799 l 7790 3806 l 7793 3809 l 7793 3810 l gs col0 s gr % Polyline n 5274 3760 m 5274 3759 l 5277 3756 l 5284 3749 l 5295 3737 l 5309 3723 l 5323 3709 l 5338 3696 l 5353 3684 l 5367 3675 l 5380 3667 l 5395 3661 l 5411 3657 l 5425 3653 l 5441 3650 l 5458 3648 l 5476 3646 l 5496 3644 l 5516 3643 l 5536 3642 l 5556 3641 l 5576 3640 l 5595 3639 l 5613 3637 l 5629 3636 l 5644 3635 l 5657 3633 l 5674 3630 l 5689 3626 l 5702 3622 l 5715 3617 l 5725 3612 l 5735 3607 l 5742 3603 l 5749 3601 l 5755 3599 l 5760 3598 l 5764 3599 l 5770 3601 l 5776 3604 l 5783 3608 l 5791 3612 l 5802 3617 l 5813 3622 l 5827 3627 l 5842 3632 l 5860 3636 l 5872 3638 l 5885 3639 l 5900 3641 l 5915 3643 l 5932 3644 l 5950 3646 l 5968 3647 l 5987 3649 l 6006 3651 l 6024 3653 l 6042 3655 l 6059 3657 l 6075 3659 l 6090 3662 l 6103 3665 l 6116 3668 l 6133 3674 l 6148 3682 l 6162 3692 l 6175 3704 l 6187 3719 l 6199 3736 l 6209 3751 l 6216 3762 l 6219 3767 l 6219 3768 l gs col0 s gr % Polyline n 3300 3772 m 3300 3771 l 3303 3766 l 3308 3756 l 3316 3742 l 3326 3726 l 3336 3712 l 3346 3701 l 3357 3692 l 3368 3684 l 3381 3679 l 3394 3675 l 3408 3671 l 3423 3668 l 3440 3666 l 3458 3663 l 3476 3661 l 3495 3659 l 3513 3657 l 3530 3655 l 3546 3653 l 3560 3650 l 3573 3648 l 3591 3643 l 3606 3637 l 3620 3631 l 3632 3624 l 3642 3618 l 3651 3614 l 3658 3611 l 3665 3610 l 3671 3611 l 3677 3614 l 3685 3618 l 3693 3624 l 3703 3631 l 3715 3637 l 3728 3643 l 3742 3648 l 3753 3650 l 3765 3653 l 3779 3655 l 3793 3657 l 3809 3659 l 3825 3661 l 3842 3663 l 3858 3666 l 3873 3669 l 3888 3672 l 3901 3676 l 3913 3680 l 3925 3685 l 3935 3691 l 3946 3698 l 3957 3708 l 3968 3718 l 3980 3731 l 3992 3745 l 4003 3758 l 4012 3769 l 4017 3776 l 4020 3779 l 4020 3780 l gs col0 s gr /Times-Roman ff 450.00 scf sf 4095 6225 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1698 2212 a FI(F)1749 2187 y Fx(\000)p FF(1)1740 2229 y FG(c)1767 2241 y FF(1)1827 2212 y FI(F)1878 2187 y Fx(\000)p FF(1)1869 2229 y FG(c)1896 2241 y FF(2)1955 2212 y FI(F)2006 2187 y Fx(\000)p FF(1)1997 2229 y FG(c)2024 2241 y FF(3)1815 2299 y FL(\000)-42 b(\000)-18 b Fw( )2226 2566 y @beginspecial 0 @llx 0 @lly 102 @urx 64 @ury 1020 @rwi @setspecial %%BeginDocument: figures/genbraid2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: genbraid2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 15:40:46 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 102 64 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2700 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -25.0 111.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7802 m -1000 -1000 l 8815 -1000 l 8815 7802 l cp clip 0.01620 0.01620 sc /Times-Italic ff 420.00 scf sf 1830 3240 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 1950 3360 m gs 1 -1 sc (1) col-1 sh gr /Times-Italic ff 420.00 scf sf 7500 3270 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 7620 3390 m gs 1 -1 sc (4) col-1 sh gr /Times-Italic ff 420.00 scf sf 3472 3323 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 3592 3443 m gs 1 -1 sc (2) col-1 sh gr /Times-Italic ff 420.00 scf sf 5625 3307 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 5760 3427 m gs 1 -1 sc (3) col-1 sh gr 7.500 slw % Ellipse n 1800 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2160 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3912 3904 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 6105 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 5387 3885 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7215 3915 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7605 3915 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 5715 3877 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3441 3902 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4222 6270 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3945 5325 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4683 5329 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 3840 4837 m 3900 3900 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 5055 4852 m 5700 3907 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 5070 4845 m 6120 3915 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6600 m 2175 3915 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 3486 4233 m 3439 3942 l 3598 4190 l 3460 3829 l 3348 3871 l cp clip n 3787 4852 m 3420 3892 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 3486 4233 m 3439 3942 l 3598 4190 l 3525 4167 l 3486 4233 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd gs clippath 1982 4195 m 1835 3940 l 2072 4116 l 1815 3827 l 1725 3906 l cp clip n 4200 6600 m 1800 3900 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 1982 4195 m 1835 3940 l 2072 4116 l 1995 4120 l 1982 4195 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 4230 6600 m 7125 3960 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6600 m 7605 3930 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 5219 4205 m 5367 3951 l 5333 4243 l 5456 3876 l 5342 3838 l cp clip n 5062 4860 m 5385 3900 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 5219 4205 m 5367 3951 l 5333 4243 l 5291 4179 l 5219 4205 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 4212 6547 m 4207 5917 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 4045 5693 m 3988 5404 l 4156 5646 l 4005 5290 l 3894 5337 l cp clip n 4215 5940 m 3967 5355 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 4045 5693 m 3988 5404 l 4156 5646 l 4082 5626 l 4045 5693 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 3937 5325 m 3810 4845 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4225 5906 m 5040 4882 l gs col-1 s gr [] 0 sd % Polyline 15.000 slw n 1595 3764 m 1595 3763 l 1598 3758 l 1603 3748 l 1611 3734 l 1621 3718 l 1631 3704 l 1641 3693 l 1652 3684 l 1663 3676 l 1676 3671 l 1689 3667 l 1703 3663 l 1718 3660 l 1735 3658 l 1753 3655 l 1771 3653 l 1790 3651 l 1808 3649 l 1825 3647 l 1841 3645 l 1855 3642 l 1868 3640 l 1886 3635 l 1901 3629 l 1915 3623 l 1927 3616 l 1937 3610 l 1946 3606 l 1953 3603 l 1960 3602 l 1966 3603 l 1972 3606 l 1980 3610 l 1988 3616 l 1998 3623 l 2010 3629 l 2023 3635 l 2037 3640 l 2048 3642 l 2060 3645 l 2074 3647 l 2088 3649 l 2104 3651 l 2120 3653 l 2137 3655 l 2153 3658 l 2168 3661 l 2183 3664 l 2196 3668 l 2208 3672 l 2220 3677 l 2230 3683 l 2241 3690 l 2252 3700 l 2263 3710 l 2275 3723 l 2287 3737 l 2298 3750 l 2307 3761 l 2312 3768 l 2315 3771 l 2315 3772 l gs col0 s gr % Polyline n 7073 3802 m 7073 3801 l 7076 3796 l 7081 3786 l 7089 3772 l 7099 3756 l 7109 3742 l 7119 3731 l 7130 3722 l 7141 3714 l 7154 3709 l 7167 3705 l 7181 3701 l 7196 3698 l 7213 3696 l 7231 3693 l 7249 3691 l 7268 3689 l 7286 3687 l 7303 3685 l 7319 3683 l 7333 3680 l 7346 3678 l 7364 3673 l 7379 3667 l 7393 3661 l 7405 3654 l 7415 3648 l 7424 3644 l 7431 3641 l 7438 3640 l 7444 3641 l 7450 3644 l 7458 3648 l 7466 3654 l 7476 3661 l 7488 3667 l 7501 3673 l 7515 3678 l 7526 3680 l 7538 3683 l 7552 3685 l 7566 3687 l 7582 3689 l 7598 3691 l 7615 3693 l 7631 3696 l 7646 3699 l 7661 3702 l 7674 3706 l 7686 3710 l 7698 3715 l 7708 3721 l 7719 3728 l 7730 3738 l 7741 3748 l 7753 3761 l 7765 3775 l 7776 3788 l 7785 3799 l 7790 3806 l 7793 3809 l 7793 3810 l gs col0 s gr % Polyline n 5274 3760 m 5274 3759 l 5277 3756 l 5284 3749 l 5295 3737 l 5309 3723 l 5323 3709 l 5338 3696 l 5353 3684 l 5367 3675 l 5380 3667 l 5395 3661 l 5411 3657 l 5425 3653 l 5441 3650 l 5458 3648 l 5476 3646 l 5496 3644 l 5516 3643 l 5536 3642 l 5556 3641 l 5576 3640 l 5595 3639 l 5613 3637 l 5629 3636 l 5644 3635 l 5657 3633 l 5674 3630 l 5689 3626 l 5702 3622 l 5715 3617 l 5725 3612 l 5735 3607 l 5742 3603 l 5749 3601 l 5755 3599 l 5760 3598 l 5764 3599 l 5770 3601 l 5776 3604 l 5783 3608 l 5791 3612 l 5802 3617 l 5813 3622 l 5827 3627 l 5842 3632 l 5860 3636 l 5872 3638 l 5885 3639 l 5900 3641 l 5915 3643 l 5932 3644 l 5950 3646 l 5968 3647 l 5987 3649 l 6006 3651 l 6024 3653 l 6042 3655 l 6059 3657 l 6075 3659 l 6090 3662 l 6103 3665 l 6116 3668 l 6133 3674 l 6148 3682 l 6162 3692 l 6175 3704 l 6187 3719 l 6199 3736 l 6209 3751 l 6216 3762 l 6219 3767 l 6219 3768 l gs col0 s gr % Polyline n 3300 3772 m 3300 3771 l 3303 3766 l 3308 3756 l 3316 3742 l 3326 3726 l 3336 3712 l 3346 3701 l 3357 3692 l 3368 3684 l 3381 3679 l 3394 3675 l 3408 3671 l 3423 3668 l 3440 3666 l 3458 3663 l 3476 3661 l 3495 3659 l 3513 3657 l 3530 3655 l 3546 3653 l 3560 3650 l 3573 3648 l 3591 3643 l 3606 3637 l 3620 3631 l 3632 3624 l 3642 3618 l 3651 3614 l 3658 3611 l 3665 3610 l 3671 3611 l 3677 3614 l 3685 3618 l 3693 3624 l 3703 3631 l 3715 3637 l 3728 3643 l 3742 3648 l 3753 3650 l 3765 3653 l 3779 3655 l 3793 3657 l 3809 3659 l 3825 3661 l 3842 3663 l 3858 3666 l 3873 3669 l 3888 3672 l 3901 3676 l 3913 3680 l 3925 3685 l 3935 3691 l 3946 3698 l 3957 3708 l 3968 3718 l 3980 3731 l 3992 3745 l 4003 3758 l 4012 3769 l 4017 3776 l 4020 3779 l 4020 3780 l gs col0 s gr /Times-Roman ff 450.00 scf sf 4102 6802 m gs 1 -1 sc (*) col-1 sh gr /Times-Roman ff 450.00 scf sf 3712 5085 m gs 1 -1 sc (*) col-1 sh gr /Times-Roman ff 450.00 scf sf 4957 5077 m gs 1 -1 sc (*) col-1 sh gr /Times-Roman ff 450.00 scf sf 4102 6142 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 3178 2220 a FI(B)3228 2228 y FG(c)3255 2240 y FF(1)3287 2228 y FG(;c)3333 2240 y FF(2)3198 2299 y FL(\000)-42 b(\000)-18 b Fw( )779 2832 y FI(B)829 2840 y FG(c)856 2852 y FF(1)888 2840 y FG(;c)934 2852 y FF(2)799 2910 y FL(\000)-42 b(\000)-18 b Fw( )1095 3177 y @beginspecial 0 @llx 0 @lly 102 @urx 64 @ury 1020 @rwi @setspecial %%BeginDocument: figures/genbraid3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: genbraid3.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 15:43:33 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 102 64 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2700 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -25.0 111.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7802 m -1000 -1000 l 8815 -1000 l 8815 7802 l cp clip 0.01620 0.01620 sc /Times-Italic ff 420.00 scf sf 1830 3240 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 1950 3360 m gs 1 -1 sc (1) col-1 sh gr /Times-Italic ff 420.00 scf sf 7500 3270 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 7620 3390 m gs 1 -1 sc (4) col-1 sh gr /Times-Italic ff 420.00 scf sf 3629 3315 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 3764 3435 m gs 1 -1 sc (3) col-1 sh gr /Times-Italic ff 420.00 scf sf 5368 3323 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 5488 3443 m gs 1 -1 sc (2) col-1 sh gr 7.500 slw % Ellipse n 1800 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2160 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7215 3915 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7605 3915 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4222 6270 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3945 5325 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4683 5329 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4109 3908 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3391 3893 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3719 3885 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 5808 3904 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 5337 3902 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 4200 6600 m 2175 3915 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 1982 4195 m 1835 3940 l 2072 4116 l 1815 3827 l 1725 3906 l cp clip n 4200 6600 m 1800 3900 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 1982 4195 m 1835 3940 l 2072 4116 l 1995 4120 l 1982 4195 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 4230 6600 m 7125 3960 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6600 m 7605 3930 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4212 6547 m 4207 5917 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 4045 5693 m 3988 5404 l 4156 5646 l 4005 5290 l 3894 5337 l cp clip n 4215 5940 m 3967 5355 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 4045 5693 m 3988 5404 l 4156 5646 l 4082 5626 l 4045 5693 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 3937 5325 m 3810 4845 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4225 5906 m 5040 4882 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 3810 4807 m 3704 3915 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 3810 4845 m 4124 3923 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 3476 4244 m 3411 3957 l 3585 4195 l 3425 3842 l 3316 3892 l cp clip n 3817 4852 m 3389 3908 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 3476 4244 m 3411 3957 l 3585 4195 l 3510 4176 l 3476 4244 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 5070 4867 m 5796 3900 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 5172 4208 m 5302 3944 l 5289 4238 l 5385 3863 l 5269 3833 l cp clip n 5070 4845 m 5316 3892 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 5172 4208 m 5302 3944 l 5289 4238 l 5243 4177 l 5172 4208 l cp gs 0.00 setgray ef gr col-1 s % Polyline n 1595 3764 m 1595 3763 l 1598 3758 l 1603 3748 l 1611 3734 l 1621 3718 l 1631 3704 l 1641 3693 l 1652 3684 l 1663 3676 l 1676 3671 l 1689 3667 l 1703 3663 l 1718 3660 l 1735 3658 l 1753 3655 l 1771 3653 l 1790 3651 l 1808 3649 l 1825 3647 l 1841 3645 l 1855 3642 l 1868 3640 l 1886 3635 l 1901 3629 l 1915 3623 l 1927 3616 l 1937 3610 l 1946 3606 l 1953 3603 l 1960 3602 l 1966 3603 l 1972 3606 l 1980 3610 l 1988 3616 l 1998 3623 l 2010 3629 l 2023 3635 l 2037 3640 l 2048 3642 l 2060 3645 l 2074 3647 l 2088 3649 l 2104 3651 l 2120 3653 l 2137 3655 l 2153 3658 l 2168 3661 l 2183 3664 l 2196 3668 l 2208 3672 l 2220 3677 l 2230 3683 l 2241 3690 l 2252 3700 l 2263 3710 l 2275 3723 l 2287 3737 l 2298 3750 l 2307 3761 l 2312 3768 l 2315 3771 l 2315 3772 l gs col0 s gr % Polyline n 7073 3802 m 7073 3801 l 7076 3796 l 7081 3786 l 7089 3772 l 7099 3756 l 7109 3742 l 7119 3731 l 7130 3722 l 7141 3714 l 7154 3709 l 7167 3705 l 7181 3701 l 7196 3698 l 7213 3696 l 7231 3693 l 7249 3691 l 7268 3689 l 7286 3687 l 7303 3685 l 7319 3683 l 7333 3680 l 7346 3678 l 7364 3673 l 7379 3667 l 7393 3661 l 7405 3654 l 7415 3648 l 7424 3644 l 7431 3641 l 7438 3640 l 7444 3641 l 7450 3644 l 7458 3648 l 7466 3654 l 7476 3661 l 7488 3667 l 7501 3673 l 7515 3678 l 7526 3680 l 7538 3683 l 7552 3685 l 7566 3687 l 7582 3689 l 7598 3691 l 7615 3693 l 7631 3696 l 7646 3699 l 7661 3702 l 7674 3706 l 7686 3710 l 7698 3715 l 7708 3721 l 7719 3728 l 7730 3738 l 7741 3748 l 7753 3761 l 7765 3775 l 7776 3788 l 7785 3799 l 7790 3806 l 7793 3809 l 7793 3810 l gs col0 s gr % Polyline n 3278 3768 m 3278 3767 l 3281 3764 l 3288 3757 l 3299 3745 l 3313 3731 l 3327 3717 l 3342 3704 l 3357 3692 l 3371 3683 l 3384 3675 l 3399 3669 l 3415 3665 l 3429 3661 l 3445 3658 l 3462 3656 l 3480 3654 l 3500 3652 l 3520 3651 l 3540 3650 l 3560 3649 l 3580 3648 l 3599 3647 l 3617 3645 l 3633 3644 l 3648 3643 l 3661 3641 l 3678 3638 l 3693 3634 l 3706 3630 l 3719 3625 l 3729 3620 l 3739 3615 l 3746 3611 l 3753 3609 l 3759 3607 l 3764 3606 l 3768 3607 l 3774 3609 l 3780 3612 l 3787 3616 l 3795 3620 l 3806 3625 l 3817 3630 l 3831 3635 l 3846 3640 l 3864 3644 l 3876 3646 l 3889 3647 l 3904 3649 l 3919 3651 l 3936 3652 l 3954 3654 l 3972 3655 l 3991 3657 l 4010 3659 l 4028 3661 l 4046 3663 l 4063 3665 l 4079 3667 l 4094 3670 l 4107 3673 l 4120 3676 l 4137 3682 l 4152 3690 l 4166 3700 l 4179 3712 l 4191 3727 l 4203 3744 l 4213 3759 l 4220 3770 l 4223 3775 l 4223 3776 l gs col0 s gr % Polyline n 5196 3772 m 5196 3771 l 5199 3766 l 5204 3756 l 5212 3742 l 5222 3726 l 5232 3712 l 5242 3701 l 5253 3692 l 5264 3684 l 5277 3679 l 5290 3675 l 5304 3671 l 5319 3668 l 5336 3666 l 5354 3663 l 5372 3661 l 5391 3659 l 5409 3657 l 5426 3655 l 5442 3653 l 5456 3650 l 5469 3648 l 5487 3643 l 5502 3637 l 5516 3631 l 5528 3624 l 5538 3618 l 5547 3614 l 5554 3611 l 5561 3610 l 5567 3611 l 5573 3614 l 5581 3618 l 5589 3624 l 5599 3631 l 5611 3637 l 5624 3643 l 5638 3648 l 5649 3650 l 5661 3653 l 5675 3655 l 5689 3657 l 5705 3659 l 5721 3661 l 5738 3663 l 5754 3666 l 5769 3669 l 5784 3672 l 5797 3676 l 5809 3680 l 5821 3685 l 5831 3691 l 5842 3698 l 5853 3708 l 5864 3718 l 5876 3731 l 5888 3745 l 5899 3758 l 5908 3769 l 5913 3776 l 5916 3779 l 5916 3780 l gs col0 s gr /Times-Roman ff 450.00 scf sf 4102 6802 m gs 1 -1 sc (*) col-1 sh gr /Times-Roman ff 450.00 scf sf 3712 5085 m gs 1 -1 sc (*) col-1 sh gr /Times-Roman ff 450.00 scf sf 4957 5077 m gs 1 -1 sc (*) col-1 sh gr /Times-Roman ff 450.00 scf sf 4102 6142 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 2047 2832 a FI(F)2089 2840 y FG(c)2116 2852 y FF(1)2152 2832 y FI(F)2194 2840 y FG(c)2221 2852 y FF(2)2258 2832 y FI(F)2300 2840 y FG(c)2327 2852 y FF(3)2129 2910 y FL(\000)-42 b(\000)-18 b Fw( )2507 3135 y @beginspecial 0 @llx 0 @lly 102 @urx 54 @ury 1020 @rwi @setspecial %%BeginDocument: figures/genbraid4.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: genbraid4.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 15:45:38 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 102 54 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2700 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -25.0 101.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7225 m -1000 -1000 l 8815 -1000 l 8815 7225 l cp clip 0.01620 0.01620 sc /Times-Italic ff 420.00 scf sf 1830 3240 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 1950 3360 m gs 1 -1 sc (1) col-1 sh gr /Times-Italic ff 420.00 scf sf 7500 3270 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 7620 3390 m gs 1 -1 sc (4) col-1 sh gr /Times-Italic ff 420.00 scf sf 5588 3323 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 5708 3443 m gs 1 -1 sc (2) col-1 sh gr 7.500 slw % Ellipse n 6028 3904 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 5557 3902 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 15.000 slw n 5416 3772 m 5416 3771 l 5419 3766 l 5424 3756 l 5432 3742 l 5442 3726 l 5452 3712 l 5462 3701 l 5473 3692 l 5484 3684 l 5497 3679 l 5510 3675 l 5524 3671 l 5539 3668 l 5556 3666 l 5574 3663 l 5592 3661 l 5611 3659 l 5629 3657 l 5646 3655 l 5662 3653 l 5676 3650 l 5689 3648 l 5707 3643 l 5722 3637 l 5736 3631 l 5748 3624 l 5758 3618 l 5767 3614 l 5774 3611 l 5781 3610 l 5787 3611 l 5793 3614 l 5801 3618 l 5809 3624 l 5819 3631 l 5831 3637 l 5844 3643 l 5858 3648 l 5869 3650 l 5881 3653 l 5895 3655 l 5909 3657 l 5925 3659 l 5941 3661 l 5958 3663 l 5974 3666 l 5989 3669 l 6004 3672 l 6017 3676 l 6029 3680 l 6041 3685 l 6051 3691 l 6062 3698 l 6073 3708 l 6084 3718 l 6096 3731 l 6108 3745 l 6119 3758 l 6128 3769 l 6133 3776 l 6136 3779 l 6136 3780 l gs col0 s gr /Times-Italic ff 420.00 scf sf 3584 3307 m gs 1 -1 sc (I) col-1 sh gr /Times-Roman ff 270.00 scf sf 3719 3427 m gs 1 -1 sc (3) col-1 sh gr 7.500 slw % Ellipse n 4064 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3346 3885 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3674 3877 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 15.000 slw n 3233 3760 m 3233 3759 l 3236 3756 l 3243 3749 l 3254 3737 l 3268 3723 l 3282 3709 l 3297 3696 l 3312 3684 l 3326 3675 l 3339 3667 l 3354 3661 l 3370 3657 l 3384 3653 l 3400 3650 l 3417 3648 l 3435 3646 l 3455 3644 l 3475 3643 l 3495 3642 l 3515 3641 l 3535 3640 l 3554 3639 l 3572 3637 l 3588 3636 l 3603 3635 l 3616 3633 l 3633 3630 l 3648 3626 l 3661 3622 l 3674 3617 l 3684 3612 l 3694 3607 l 3701 3603 l 3708 3601 l 3714 3599 l 3719 3598 l 3723 3599 l 3729 3601 l 3735 3604 l 3742 3608 l 3750 3612 l 3761 3617 l 3772 3622 l 3786 3627 l 3801 3632 l 3819 3636 l 3831 3638 l 3844 3639 l 3859 3641 l 3874 3643 l 3891 3644 l 3909 3646 l 3927 3647 l 3946 3649 l 3965 3651 l 3983 3653 l 4001 3655 l 4018 3657 l 4034 3659 l 4049 3662 l 4062 3665 l 4075 3668 l 4092 3674 l 4107 3682 l 4121 3692 l 4134 3704 l 4146 3719 l 4158 3736 l 4168 3751 l 4175 3762 l 4178 3767 l 4178 3768 l gs col0 s gr 7.500 slw % Ellipse n 1800 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2160 3900 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7215 3915 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7605 3915 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 4200 6000 m 3675 3892 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 5535 3915 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 6022 3915 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 4080 3960 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 2018 4170 m 1840 3935 l 2097 4080 l 1806 3825 l 1727 3916 l cp clip n 4200 6000 m 1800 3900 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2018 4170 m 1840 3935 l 2097 4080 l 2021 4094 l 2018 4170 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd n 4200 6000 m 7605 3930 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 2175 3915 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4230 6000 m 7125 3960 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4193 5929 m 3352 3907 l gs col-1 s gr [] 0 sd % Polyline 15.000 slw n 1595 3764 m 1595 3763 l 1598 3758 l 1603 3748 l 1611 3734 l 1621 3718 l 1631 3704 l 1641 3693 l 1652 3684 l 1663 3676 l 1676 3671 l 1689 3667 l 1703 3663 l 1718 3660 l 1735 3658 l 1753 3655 l 1771 3653 l 1790 3651 l 1808 3649 l 1825 3647 l 1841 3645 l 1855 3642 l 1868 3640 l 1886 3635 l 1901 3629 l 1915 3623 l 1927 3616 l 1937 3610 l 1946 3606 l 1953 3603 l 1960 3602 l 1966 3603 l 1972 3606 l 1980 3610 l 1988 3616 l 1998 3623 l 2010 3629 l 2023 3635 l 2037 3640 l 2048 3642 l 2060 3645 l 2074 3647 l 2088 3649 l 2104 3651 l 2120 3653 l 2137 3655 l 2153 3658 l 2168 3661 l 2183 3664 l 2196 3668 l 2208 3672 l 2220 3677 l 2230 3683 l 2241 3690 l 2252 3700 l 2263 3710 l 2275 3723 l 2287 3737 l 2298 3750 l 2307 3761 l 2312 3768 l 2315 3771 l 2315 3772 l gs col0 s gr % Polyline n 7073 3802 m 7073 3801 l 7076 3796 l 7081 3786 l 7089 3772 l 7099 3756 l 7109 3742 l 7119 3731 l 7130 3722 l 7141 3714 l 7154 3709 l 7167 3705 l 7181 3701 l 7196 3698 l 7213 3696 l 7231 3693 l 7249 3691 l 7268 3689 l 7286 3687 l 7303 3685 l 7319 3683 l 7333 3680 l 7346 3678 l 7364 3673 l 7379 3667 l 7393 3661 l 7405 3654 l 7415 3648 l 7424 3644 l 7431 3641 l 7438 3640 l 7444 3641 l 7450 3644 l 7458 3648 l 7466 3654 l 7476 3661 l 7488 3667 l 7501 3673 l 7515 3678 l 7526 3680 l 7538 3683 l 7552 3685 l 7566 3687 l 7582 3689 l 7598 3691 l 7615 3693 l 7631 3696 l 7646 3699 l 7661 3702 l 7674 3706 l 7686 3710 l 7698 3715 l 7708 3721 l 7719 3728 l 7730 3738 l 7741 3748 l 7753 3761 l 7765 3775 l 7776 3788 l 7785 3799 l 7790 3806 l 7793 3809 l 7793 3810 l gs col0 s gr /Times-Roman ff 450.00 scf sf 4095 6225 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1204 3377 a FP(Figure)32 b(5.8.)40 b FQ(Generalized)27 b(braiding)g(mo)n(v)n(e.)605 3630 y(No)n(w)g(let)h(us)g(imp)r(ose)f (some)g(relations)g(among)f(these)i(mo)n(v)n(es:)612 3766 y FK(MF1:)41 b(Rotation)31 b(axiom:)40 b FQ(If)28 b(\006)1740 3778 y FI(i)1795 3766 y FQ(is)f(a)h(comp)r(onen)n(t)f(with) h FJ(n)g FQ(holes,)f(then)h FJ(Z)3122 3736 y FI(n)3116 3787 y(i)3190 3766 y FQ(=)22 b(id.)612 3865 y FK(MF2:)41 b(Symmetry)30 b(of)i FJ(F)12 b FK(:)41 b FQ(If)36 b FJ(c;)14 b FQ(\006)1810 3877 y FI(i)1838 3865 y FJ(;)g FQ(\006)1935 3877 y FI(j)2006 3865 y FQ(are)35 b(as)g(in)i(the)f(de\014nition)h(of)f (the)h(F-mo)n(v)n(e,)711 3970 y(then)28 b FJ(Z)963 3940 y FI(k)q FE(\000)p FM(1)1089 3970 y FJ(F)1142 3982 y FI(c)1199 3970 y FQ(=)23 b FJ(F)1340 3982 y FI(c)1374 3970 y FQ(\()p FJ(Z)1469 3935 y FE(\000)p FM(1)1463 3993 y FI(i)1576 3970 y FL(t)c FJ(Z)1707 3982 y FI(j)1742 3970 y FQ(\).)612 4070 y FK(MF3:)41 b(Asso)s(ciativit)m(y)31 b(of)h FJ(F)12 b FK(:)41 b FQ(If)f(\006)f(is)g(a)g(connected)g(surface) f(of)h(gen)n(us)g(zero,)i(and)711 4170 y FJ(M)46 b FQ(=)37 b(\()p FJ(C)q(;)14 b(m)p FQ(\))39 b FL(2)f FJ(M)9 b FQ(\(\006\))37 b(is)f(a)g(parameterization)e(with)j(t)n(w)n(o)e(cuts,)k FJ(C)44 b FQ(=)37 b FL(f)p FJ(c)3233 4182 y FM(1)3270 4170 y FJ(;)14 b(c)3343 4182 y FM(2)3380 4170 y FL(g)p FQ(,)711 4269 y(then)1501 4441 y FJ(F)1554 4453 y FI(c)1584 4461 y FF(1)1621 4441 y FJ(F)1674 4453 y FI(c)1704 4461 y FF(2)1740 4441 y FQ(\()p FJ(M)9 b FQ(\))24 b(=)e FJ(F)2058 4453 y FI(c)2088 4461 y FF(2)2125 4441 y FJ(F)2178 4453 y FI(c)2208 4461 y FF(1)2245 4441 y FQ(\()p FJ(M)9 b FQ(\))-1943 b(\(5.2.4\))711 4618 y(\(here)28 b FJ(F)39 b FQ(denotes)27 b(generalized)g(F-mo)n(v)n(es\).)612 4717 y FK(MF4:)41 b(Comm)m(utativit)m(y)30 b(of)i(disjoin)m(t)f(union:) 40 b FQ(If)29 b FJ(E)2441 4729 y FM(1)2479 4717 y FJ(;)14 b(E)2577 4729 y FM(2)2643 4717 y FQ(are)28 b(simple)i(mo)n(v)n(es)d (that)711 4817 y(in)n(v)n(olv)n(e)f(non-in)n(tersecting)g(sets)i(of)f (comp)r(onen)n(ts,)g(then)i FJ(E)2585 4829 y FM(1)2622 4817 y FJ(E)2683 4829 y FM(2)2744 4817 y FQ(=)22 b FJ(E)2892 4829 y FM(2)2930 4817 y FJ(E)2991 4829 y FM(1)3028 4817 y FQ(.)612 4917 y FK(MF5:)41 b(Cylinder)31 b(axiom:)40 b FQ(Let)34 b FJ(S)1797 4929 y FM(0)p FI(;)p FM(2)1921 4917 y FQ(b)r(e)h(a)e(cylinder)h(with)h(b)r(oundary)e(comp)r(onen)n(ts) 711 5016 y FJ(\013)764 5028 y FM(0)801 5016 y FJ(;)14 b(\013)891 5028 y FM(1)961 5016 y FQ(and)32 b(with)g(the)h(standard)e (parameterization)f FJ(M)2546 5028 y FM(0)2613 5016 y FQ(=)g(\()p FL(;)p FJ(;)14 b FQ(id\).)51 b(Let)32 b(\006)g(b)r(e)h(an) 711 5116 y(extended)d(surface,)f FJ(M)35 b FL(2)27 b FJ(M)9 b FQ(\(\006\))30 b(b)r(e)f(a)h(parameterization,)e(and)h FJ(\013)h FQ(b)r(e)g(a)f(b)r(oundary)711 5216 y(comp)r(onen)n(t)34 b(of)g(\006.)57 b(Then,)36 b(for)e(ev)n(ery)f(mo)n(v)n(e)g FJ(E)14 b FQ(:)30 b FJ(M)42 b Fw( )35 b FJ(M)2671 5185 y FE(0)2728 5216 y FQ(w)n(e)f(require)f(that)h(the)p eop %%Page: 102 10 102 105 bop 456 226 a FM(102)1010 b(5.)29 b(MODULAR)g(FUNCTOR)711 425 y FQ(follo)n(wing)e(square)f(b)r(e)i(comm)n(utativ)n(e:)1220 596 y FJ(M)f FL(t)1383 608 y FI(\013;\013)1489 616 y FF(1)1544 596 y FJ(M)1625 608 y FM(0)1737 536 y FI(E)s FE(t)1834 544 y FG(\013;\013)1929 556 y FF(1)1965 536 y FM(id)1708 596 y FL(\000)-28 b(\000)-19 b(\000)g(\000)g(\000)g(\000) -29 b(!)47 b FJ(M)2185 566 y FE(0)2226 596 y FL(t)2281 608 y FI(\013;\013)2387 616 y FF(1)2443 596 y FJ(M)2524 608 y FM(0)1329 757 y FI(F)1371 765 y FG(\013)1413 667 y Fy(?)1413 716 y(?)1413 766 y(y)2300 667 y(?)2300 716 y(?)2300 766 y(y)2355 757 y FI(F)2397 765 y FG(\013)1396 928 y FJ(M)226 b FL(\000)-23 b(\000)k(\000)g(\000)g(\000)g(\000)c(!) 1852 989 y FI(E)2271 928 y FJ(M)2361 898 y FE(0)2644 763 y FJ(;)-2211 b FQ(\(5.2.5\))711 1100 y(see)27 b(Figure)g(5.9)g(b)r (elo)n(w.)985 1963 y @beginspecial 0 @llx 0 @lly 61 @urx 84 @ury 610 @rwi @setspecial %%BeginDocument: figures/cylax1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: cylax1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Aug 13 17:13:43 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 61 84 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3600 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -44.0 135.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7225 m -1000 -1000 l 5817 -1000 l 5817 7225 l cp clip 0.02160 0.02160 sc % Polyline 15.000 slw n 2535 5805 m 2535 6030 l 2760 6030 l 2760 5805 l gs col-1 s gr /Symbol ff 270.00 scf sf 2835 6180 m gs 1 -1 sc (a) col-1 sh gr /Symbol ff 270.00 scf sf 3030 6180 m gs 1 -1 sc (,a) col-1 sh gr /Times-Italic ff 420.00 scf sf 3510 6030 m gs 1 -1 sc (S) col-1 sh gr /Times-Roman ff 225.00 scf sf 3735 6105 m gs 1 -1 sc (0,2) col-1 sh gr /Symbol ff 420.00 scf sf 2085 6030 m gs 1 -1 sc (S) col-1 sh gr /Times-Roman ff 180.00 scf sf 3300 6225 m gs 1 -1 sc (1) col-1 sh gr % Arc gs n 3000.0 3450.0 750.0 143.1 36.9 arcn gs col-1 s gr gr % Arc gs [90] 0 sd n 3000.0 5025.0 1275.0 -118.1 -61.9 arc gs col-1 s gr gr [] 0 sd % Arc gs n 3000.0 2250.0 750.0 143.1 36.9 arcn gs col-1 s gr gr % Arc gs n 3000.0 3150.0 750.0 -143.1 -36.9 arc gs col-1 s gr gr 7.500 slw % Ellipse n 3000 3000 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 3000 4185 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd gs clippath 2940 3342 m 3000 3054 l 3060 3342 l 3060 2955 l 2940 2955 l cp clip n 3000 3000 m 3000 4170 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2940 3342 m 3000 3054 l 3060 3342 l 3000 3294 l 2940 3342 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd gs clippath 2947 4566 m 3007 4278 l 3067 4566 l 3067 4179 l 2947 4179 l cp clip n 3007 4224 m 3007 5387 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 2947 4566 m 3007 4278 l 3067 4566 l 3007 4518 l 2947 4566 l cp gs 0.00 setgray ef gr col0 s % Polyline n 3600 2700 m 3600 2702 l 3600 2707 l 3600 2716 l 3600 2730 l 3600 2749 l 3600 2775 l 3600 2807 l 3600 2844 l 3600 2887 l 3600 2934 l 3600 2985 l 3600 3039 l 3600 3094 l 3600 3151 l 3600 3207 l 3600 3263 l 3600 3317 l 3600 3369 l 3600 3419 l 3600 3467 l 3600 3513 l 3600 3556 l 3600 3596 l 3600 3634 l 3600 3670 l 3600 3704 l 3600 3737 l 3600 3767 l 3600 3796 l 3600 3823 l 3600 3850 l 3600 3875 l 3600 3900 l 3600 3931 l 3600 3961 l 3600 3991 l 3600 4020 l 3600 4048 l 3601 4076 l 3601 4104 l 3602 4132 l 3602 4159 l 3603 4186 l 3604 4212 l 3605 4239 l 3607 4265 l 3609 4290 l 3611 4316 l 3613 4340 l 3615 4365 l 3618 4389 l 3621 4413 l 3624 4436 l 3628 4459 l 3632 4482 l 3636 4505 l 3640 4528 l 3645 4551 l 3650 4575 l 3655 4597 l 3661 4620 l 3667 4644 l 3673 4669 l 3680 4696 l 3688 4723 l 3696 4753 l 3705 4785 l 3715 4818 l 3726 4854 l 3738 4893 l 3751 4933 l 3764 4976 l 3778 5021 l 3792 5066 l 3807 5113 l 3822 5159 l 3836 5203 l 3850 5245 l 3862 5283 l 3873 5316 l 3882 5344 l 3889 5366 l 3894 5382 l 3897 5392 l 3899 5397 l 3900 5400 l gs col-1 s gr % Polyline n 2400 2700 m 2400 2702 l 2400 2707 l 2400 2716 l 2400 2730 l 2400 2749 l 2400 2775 l 2400 2807 l 2400 2844 l 2400 2887 l 2400 2934 l 2400 2985 l 2400 3039 l 2400 3094 l 2400 3151 l 2400 3207 l 2400 3263 l 2400 3317 l 2400 3369 l 2400 3419 l 2400 3467 l 2400 3513 l 2400 3556 l 2400 3596 l 2400 3634 l 2400 3670 l 2400 3704 l 2400 3737 l 2400 3767 l 2400 3796 l 2400 3823 l 2400 3850 l 2400 3875 l 2400 3900 l 2400 3931 l 2400 3961 l 2400 3991 l 2400 4020 l 2400 4048 l 2399 4076 l 2399 4104 l 2398 4132 l 2398 4159 l 2397 4186 l 2396 4212 l 2395 4239 l 2393 4265 l 2391 4290 l 2389 4316 l 2387 4340 l 2385 4365 l 2382 4389 l 2379 4413 l 2376 4436 l 2372 4459 l 2368 4482 l 2364 4505 l 2360 4528 l 2355 4551 l 2350 4575 l 2345 4597 l 2339 4620 l 2333 4644 l 2327 4669 l 2320 4696 l 2312 4723 l 2304 4753 l 2295 4785 l 2285 4818 l 2274 4854 l 2262 4893 l 2249 4933 l 2236 4976 l 2222 5021 l 2208 5066 l 2193 5113 l 2178 5159 l 2164 5203 l 2150 5245 l 2138 5283 l 2127 5316 l 2118 5344 l 2111 5366 l 2106 5382 l 2103 5392 l 2101 5397 l 2100 5400 l gs col-1 s gr /Symbol ff 360.00 scf sf 3900 3975 m gs 1 -1 sc (a) col-1 sh gr /Symbol ff 360.00 scf sf 3900 2775 m gs 1 -1 sc (a) col-1 sh gr /Times-Roman ff 225.00 scf sf 4155 2850 m gs 1 -1 sc (0) col-1 sh gr /Symbol ff 360.00 scf sf 4200 3975 m gs 1 -1 sc (= a) col-1 sh gr /Times-Roman ff 225.00 scf sf 4710 4035 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 375.00 scf sf 2910 5595 m gs 1 -1 sc (*) col-1 sh gr /Times-Roman ff 375.00 scf sf 2910 3802 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1628 1565 a FI(F)1670 1573 y FG(\013)1600 1613 y FL(\000)-36 b(\000)f(!)1846 1963 y @beginspecial 0 @llx 0 @lly 49 @urx 84 @ury 490 @rwi @setspecial %%BeginDocument: figures/cylax2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: cylax2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Aug 13 17:13:20 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 49 84 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3600 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -44.0 135.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7240 m -1000 -1000 l 5262 -1000 l 5262 7240 l cp clip 0.02160 0.02160 sc % Polyline 15.000 slw n 2565 5820 m 2565 6045 l 2790 6045 l 2790 5820 l gs col-1 s gr /Symbol ff 270.00 scf sf 2865 6195 m gs 1 -1 sc (a) col-1 sh gr /Symbol ff 270.00 scf sf 3060 6195 m gs 1 -1 sc (,a) col-1 sh gr /Times-Italic ff 420.00 scf sf 3540 6045 m gs 1 -1 sc (S) col-1 sh gr /Times-Roman ff 225.00 scf sf 3765 6120 m gs 1 -1 sc (0,2) col-1 sh gr /Symbol ff 420.00 scf sf 2115 6045 m gs 1 -1 sc (S) col-1 sh gr /Times-Roman ff 180.00 scf sf 3330 6240 m gs 1 -1 sc (1) col-1 sh gr % Arc gs n 3000.0 2250.0 750.0 143.1 36.9 arcn gs col-1 s gr gr % Arc gs n 3000.0 3150.0 750.0 -143.1 -36.9 arc gs col-1 s gr gr 7.500 slw % Ellipse n 3000 3000 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd gs clippath 2947 3379 m 3007 3091 l 3067 3379 l 3067 2992 l 2947 2992 l cp clip n 3007 3037 m 3007 5387 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 2947 3379 m 3007 3091 l 3067 3379 l 3007 3331 l 2947 3379 l cp gs 0.00 setgray ef gr col0 s % Polyline n 3600 2700 m 3600 2702 l 3600 2707 l 3600 2716 l 3600 2730 l 3600 2749 l 3600 2775 l 3600 2807 l 3600 2844 l 3600 2887 l 3600 2934 l 3600 2985 l 3600 3039 l 3600 3094 l 3600 3151 l 3600 3207 l 3600 3263 l 3600 3317 l 3600 3369 l 3600 3419 l 3600 3467 l 3600 3513 l 3600 3556 l 3600 3596 l 3600 3634 l 3600 3670 l 3600 3704 l 3600 3737 l 3600 3767 l 3600 3796 l 3600 3823 l 3600 3850 l 3600 3875 l 3600 3900 l 3600 3931 l 3600 3961 l 3600 3991 l 3600 4020 l 3600 4048 l 3601 4076 l 3601 4104 l 3602 4132 l 3602 4159 l 3603 4186 l 3604 4212 l 3605 4239 l 3607 4265 l 3609 4290 l 3611 4316 l 3613 4340 l 3615 4365 l 3618 4389 l 3621 4413 l 3624 4436 l 3628 4459 l 3632 4482 l 3636 4505 l 3640 4528 l 3645 4551 l 3650 4575 l 3655 4597 l 3661 4620 l 3667 4644 l 3673 4669 l 3680 4696 l 3688 4723 l 3696 4753 l 3705 4785 l 3715 4818 l 3726 4854 l 3738 4893 l 3751 4933 l 3764 4976 l 3778 5021 l 3792 5066 l 3807 5113 l 3822 5159 l 3836 5203 l 3850 5245 l 3862 5283 l 3873 5316 l 3882 5344 l 3889 5366 l 3894 5382 l 3897 5392 l 3899 5397 l 3900 5400 l gs col-1 s gr % Polyline n 2400 2700 m 2400 2702 l 2400 2707 l 2400 2716 l 2400 2730 l 2400 2749 l 2400 2775 l 2400 2807 l 2400 2844 l 2400 2887 l 2400 2934 l 2400 2985 l 2400 3039 l 2400 3094 l 2400 3151 l 2400 3207 l 2400 3263 l 2400 3317 l 2400 3369 l 2400 3419 l 2400 3467 l 2400 3513 l 2400 3556 l 2400 3596 l 2400 3634 l 2400 3670 l 2400 3704 l 2400 3737 l 2400 3767 l 2400 3796 l 2400 3823 l 2400 3850 l 2400 3875 l 2400 3900 l 2400 3931 l 2400 3961 l 2400 3991 l 2400 4020 l 2400 4048 l 2399 4076 l 2399 4104 l 2398 4132 l 2398 4159 l 2397 4186 l 2396 4212 l 2395 4239 l 2393 4265 l 2391 4290 l 2389 4316 l 2387 4340 l 2385 4365 l 2382 4389 l 2379 4413 l 2376 4436 l 2372 4459 l 2368 4482 l 2364 4505 l 2360 4528 l 2355 4551 l 2350 4575 l 2345 4597 l 2339 4620 l 2333 4644 l 2327 4669 l 2320 4696 l 2312 4723 l 2304 4753 l 2295 4785 l 2285 4818 l 2274 4854 l 2262 4893 l 2249 4933 l 2236 4976 l 2222 5021 l 2208 5066 l 2193 5113 l 2178 5159 l 2164 5203 l 2150 5245 l 2138 5283 l 2127 5316 l 2118 5344 l 2111 5366 l 2106 5382 l 2103 5392 l 2101 5397 l 2100 5400 l gs col-1 s gr /Times-Roman ff 225.00 scf sf 4155 2850 m gs 1 -1 sc (0) col-1 sh gr /Times-Roman ff 375.00 scf sf 2910 5595 m gs 1 -1 sc (*) col-1 sh gr /Symbol ff 360.00 scf sf 3900 2775 m gs 1 -1 sc (a) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 2361 1613 a(')2532 1933 y @beginspecial 0 @llx 0 @lly 46 @urx 77 @ury 460 @rwi @setspecial %%BeginDocument: figures/cylax3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: cylax3.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Mon Jun 7 10:14:48 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 46 77 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3600 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -44.0 130.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7000 m -1000 -1000 l 5146 -1000 l 5146 7000 l cp clip 0.02160 0.02160 sc % Arc 15.000 slw gs n 3000.0 4350.0 750.0 -143.1 -36.9 arc gs col-1 s gr gr 7.500 slw % Ellipse n 3000 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd gs clippath 2955 4470 m 3000 4254 l 3045 4470 l 3045 4155 l 2955 4155 l cp clip n 3000 4200 m 3000 5400 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2955 4470 m 3000 4254 l 3045 4470 l 3000 4434 l 2955 4470 l cp gs 0.00 setgray ef gr col-1 s % Polyline 0.000 slw n 2400 2475 m 2400 3900 l % Arc 15.000 slw gs n 3000.0 3450.0 750.0 143.1 36.9 arcn gs col-1 s gr gr % Polyline n 3600 3900 m 3600 3903 l 3600 3909 l 3600 3920 l 3601 3936 l 3601 3958 l 3602 3986 l 3603 4018 l 3604 4054 l 3605 4092 l 3607 4131 l 3609 4170 l 3611 4209 l 3613 4246 l 3615 4281 l 3618 4315 l 3620 4348 l 3624 4378 l 3627 4408 l 3631 4437 l 3635 4465 l 3639 4493 l 3645 4522 l 3650 4550 l 3655 4575 l 3661 4600 l 3667 4626 l 3673 4653 l 3680 4681 l 3688 4710 l 3696 4741 l 3705 4774 l 3715 4809 l 3726 4846 l 3738 4886 l 3751 4927 l 3764 4971 l 3778 5016 l 3792 5063 l 3807 5110 l 3822 5156 l 3836 5201 l 3850 5244 l 3862 5282 l 3873 5316 l 3882 5344 l 3889 5366 l 3894 5381 l 3897 5392 l 3899 5397 l 3900 5400 l gs col-1 s gr /Symbol ff 420.00 scf sf 2925 6000 m gs 1 -1 sc (S) col-1 sh gr % Polyline 30.000 slw n 2400 3900 m 2400 3903 l 2400 3910 l 2400 3923 l 2400 3942 l 2400 3965 l 2400 3993 l 2400 4024 l 2400 4056 l 2400 4088 l 2400 4118 l 2400 4146 l 2400 4172 l 2400 4196 l 2400 4218 l 2400 4237 l 2400 4255 l 2400 4271 l 2400 4286 l 2400 4300 l 2400 4315 l 2400 4329 l 2400 4344 l 2399 4358 l 2399 4372 l 2398 4387 l 2397 4403 l 2395 4419 l 2393 4435 l 2391 4453 l 2387 4471 l 2384 4490 l 2380 4510 l 2375 4531 l 2370 4552 l 2364 4575 l 2357 4599 l 2350 4625 l 2345 4643 l 2339 4661 l 2333 4681 l 2327 4702 l 2320 4725 l 2312 4750 l 2304 4777 l 2295 4806 l 2285 4837 l 2274 4871 l 2262 4907 l 2249 4946 l 2236 4986 l 2222 5029 l 2208 5074 l 2193 5118 l 2178 5163 l 2164 5207 l 2150 5248 l 2138 5285 l 2127 5318 l 2118 5345 l 2111 5366 l 2106 5382 l 2103 5392 l 2101 5398 l 2100 5400 l gs col-1 s gr /Symbol ff 360.00 scf sf 3900 3975 m gs 1 -1 sc (a) col-1 sh gr /Times-Roman ff 375.00 scf sf 2925 5595 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1398 2163 a FP(Figure)32 b(5.9.)40 b FQ(Cylinder)27 b(Axiom.)612 2366 y FK(MF6:)41 b(Braiding)31 b(axiom:)40 b FQ(Let)34 b(\006)1805 2378 y FI(i)1867 2366 y FQ(b)r(e)g(a)g (connected)g(comp)r(onen)n(t)g(of)g(\006)23 b FL(n)f FJ(C)41 b FQ(whic)n(h)711 2468 y(has)26 b(4)g(holes.)36 b(Denote)27 b(the)g(b)r(oundary)f(comp)r(onen)n(ts)g FJ( )2478 2432 y FE(\000)p FM(1)2475 2491 y FI(i)2567 2468 y FQ(\()p FK(1)p FQ(\))p FJ(;)14 b(:)g(:)g(:)g(;)g( )2921 2432 y FE(\000)p FM(1)2918 2491 y FI(i)3010 2468 y FQ(\()p FK(4)p FQ(\))27 b(of)g(\006)3303 2480 y FI(i)3357 2468 y FQ(b)n(y)711 2567 y FJ(\013;)14 b(:)g(:)g(:)g(;)g(\016)s FQ(,)28 b(resp)r(ectiv)n(ely)-7 b(.)36 b(Then:)1602 2704 y FJ(B)1665 2716 y FI(\013;\014)s(\015)1834 2704 y FQ(=)23 b FJ(B)1985 2716 y FI(\013;\015)2090 2704 y FJ(B)2153 2716 y FI(\013;\014)2261 2704 y FJ(;)-1828 b FQ(\(5.2.6\))1602 2834 y FJ(B)1665 2846 y FI(\013\014)s(;\015)1834 2834 y FQ(=)23 b FJ(B)1985 2846 y FI(\013;\015)2090 2834 y FJ(B)2153 2846 y FI(\014)s(;\015)2256 2834 y FJ(:)-1823 b FQ(\(5.2.7\))711 2976 y(F)-7 b(or)33 b(an)g(illustration)f(of)h(Eq.)g (\(5.2.6\))o(,)i(see)e(Figure)g(5.10.)52 b(Note)33 b(that)h(all)f (braidings)711 3075 y(in)n(v)n(olv)n(ed)26 b(are)h(generalized)f (braidings)h(as)f(de\014ned)i(ab)r(o)n(v)n(e.)612 3175 y FK(MF7:)41 b(Dehn)32 b(t)m(wist)f(axiom:)40 b FQ(Let)25 b(\006)1895 3187 y FI(i)1947 3175 y FQ(b)r(e)f(a)g(connected)h(comp)r (onen)n(t)f(of)g(\006)12 b FL(n)g FJ(C)31 b FQ(whic)n(h)711 3277 y(has)c(2)g(holes:)37 b FJ(\013)23 b FQ(=)g FJ( )1390 3241 y FE(\000)p FM(1)1387 3300 y FI(i)1479 3277 y FQ(\()p FK(1)p FQ(\))p FJ(;)14 b(\014)28 b FQ(=)22 b FJ( )1847 3241 y FE(\000)p FM(1)1844 3300 y FI(i)1936 3277 y FQ(\()p FK(2)p FQ(\).)38 b(Then)1640 3414 y FJ(Z)1697 3426 y FI(i)1724 3414 y FJ(B)1787 3426 y FI(\013;\014)1918 3414 y FQ(=)22 b FJ(B)2068 3426 y FI(\014)s(;\013)2176 3414 y FJ(Z)2233 3426 y FI(i)456 3414 y FQ(\(5.2.8\))711 3556 y(\(as)g(b)r(efore,)h FJ(B)k FQ(denotes)22 b(the)g(generalized)f (braidings\).)35 b(This)22 b(axiom)f(is)i(equiv)-5 b(alen)n(t)22 b(to)711 3655 y(the)29 b(iden)n(tit)n(y)g FJ(T)1212 3667 y FI(\013)1284 3655 y FQ(=)c FJ(T)1423 3667 y FI(\014)1467 3655 y FQ(,)k(where)g FJ(T)1810 3667 y FI(\013)1885 3655 y FQ(is)g(the)g(Dehn)h(t)n(wist)f(de\014ned)g(in)g(Example)f(5.2.4)711 3755 y(b)r(elo)n(w)f(\(see)h(Figure)f(5.11\).)605 3906 y FP(Theorem)32 b FQ(5.2.3)p FP(.)40 b FO(L)l(et)26 b FQ(\006)g FO(b)l(e)g(an)h(extende)l(d)f(surfac)l(e)h(of)g(genus)f(zer)l (o.)38 b(Denote)26 b(by)h FL(M)p FQ(\(\006\))456 4005 y FO(the)i(2-c)l(omplex)h(with)g(a)f(set)g(of)h(vertic)l(es)g FJ(M)9 b FQ(\(\006\))p FO(,)29 b(e)l(dges)h(given)g(by)g(the)f(B-,)h (Z-,)f(and)h(F-moves)637 4990 y @beginspecial 0 @llx 0 @lly 75 @urx 83 @ury 750 @rwi @setspecial %%BeginDocument: figures/trax1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: trax1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Jun 2 14:18:39 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 75 83 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -46.0 153.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8725 m -1000 -1000 l 7094 -1000 l 7094 8725 l cp clip 0.01980 0.01980 sc 7.500 slw % Ellipse n 4200 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 6000 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2400 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4200 7200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 4200 6000 m 6000 4200 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 4200 7200 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 4200 m 4200 5925 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 2599 4484 m 2438 4238 l 2684 4399 l 2411 4126 l 2326 4211 l cp clip n 4200 6000 m 2400 4200 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2599 4484 m 2438 4238 l 2684 4399 l 2608 4408 l 2599 4484 l cp gs 0.00 setgray ef gr col-1 s /Times-Roman ff 450.00 scf sf 4095 6225 m gs 1 -1 sc (*) col-1 sh gr /Symbol ff 360.00 scf sf 5925 3825 m gs 1 -1 sc (g) col-1 sh gr /Symbol ff 360.00 scf sf 2325 3825 m gs 1 -1 sc (a) col-1 sh gr /Symbol ff 360.00 scf sf 4125 7725 m gs 1 -1 sc (d) col-1 sh gr /Symbol ff 360.00 scf sf 4125 3900 m gs 1 -1 sc (b) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1449 4569 a FI(B)1499 4578 y FG(\013;\014)1446 4644 y FL(\000)-42 b(\000)-18 b Fw( )1700 4990 y @beginspecial 0 @llx 0 @lly 77 @urx 83 @ury 770 @rwi @setspecial %%BeginDocument: figures/trax2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: trax2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 14:29:20 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 77 83 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -44.0 153.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8725 m -1000 -1000 l 7094 -1000 l 7094 8725 l cp clip 0.01980 0.01980 sc 7.500 slw % Ellipse n 4200 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 6000 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2400 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4200 7200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 4200 6000 m 6000 4200 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 4200 7200 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 4200 m 4200 5925 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 2599 4484 m 2438 4238 l 2684 4399 l 2411 4126 l 2326 4211 l cp clip n 4200 6000 m 2400 4200 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2599 4484 m 2438 4238 l 2684 4399 l 2608 4408 l 2599 4484 l cp gs 0.00 setgray ef gr col-1 s /Times-Roman ff 450.00 scf sf 4095 6225 m gs 1 -1 sc (*) col-1 sh gr /Symbol ff 360.00 scf sf 5925 3825 m gs 1 -1 sc (g) col-1 sh gr /Symbol ff 360.00 scf sf 4125 7725 m gs 1 -1 sc (d) col-1 sh gr /Symbol ff 360.00 scf sf 2250 3900 m gs 1 -1 sc (b) col-1 sh gr /Symbol ff 360.00 scf sf 4065 3825 m gs 1 -1 sc (a) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 2529 4570 a FI(B)2579 4578 y FG(\013;\015)2526 4644 y FL(\000)-42 b(\000)-18 b Fw( )2780 4990 y @beginspecial 0 @llx 0 @lly 78 @urx 83 @ury 780 @rwi @setspecial %%BeginDocument: figures/trax3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: trax3.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 14:29:56 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 78 83 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -44.0 153.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8725 m -1000 -1000 l 7156 -1000 l 7156 8725 l cp clip 0.01980 0.01980 sc 7.500 slw % Ellipse n 4200 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 6000 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2400 4200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4200 7200 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 4200 6000 m 6000 4200 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 6000 m 4200 7200 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 4200 4200 m 4200 5925 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 2599 4484 m 2438 4238 l 2684 4399 l 2411 4126 l 2326 4211 l cp clip n 4200 6000 m 2400 4200 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2599 4484 m 2438 4238 l 2684 4399 l 2608 4408 l 2599 4484 l cp gs 0.00 setgray ef gr col-1 s /Times-Roman ff 450.00 scf sf 4095 6225 m gs 1 -1 sc (*) col-1 sh gr /Symbol ff 360.00 scf sf 4125 7725 m gs 1 -1 sc (d) col-1 sh gr /Symbol ff 360.00 scf sf 2250 3900 m gs 1 -1 sc (b) col-1 sh gr /Symbol ff 360.00 scf sf 4110 3825 m gs 1 -1 sc (g) col-1 sh gr /Symbol ff 360.00 scf sf 5910 3825 m gs 1 -1 sc (a) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1253 5195 a FP(Figure)32 b(5.10.)40 b FQ(Braiding)27 b(axiom)g(\(5.2.6\))o(.)p eop %%Page: 103 11 103 106 bop 1599 226 a FM(5.2.)29 b(THE)g(LEGO)g(GAME)1021 b(103)456 425 y FO(de\014ne)l(d)31 b(ab)l(ove,)i(and)f(2-c)l(el)t(ls)g (given)g(by)f(r)l(elations)39 b FQ(MF1{MF7)p FO(.)j(Then)32 b FL(M)p FQ(\(\006\))f FO(is)h(c)l(onne)l(cte)l(d)456 525 y(and)e(simply-c)l(onne)l(cte)l(d.)605 674 y FQ(As)40 b(men)n(tioned)f(ab)r(o)n(v)n(e,)i(this)f(theorem)f(w)n(as)f(\014rst)h (pro)n(v)n(ed)f(\(in)i(a)f(di\013eren)n(t)h(form\))f(in)456 774 y([)p FK(MS1)o FQ(];)28 b(our)f(exp)r(osition)g(follo)n(ws)f([)p FK(BK)p FQ(].)605 930 y FP(Example)31 b FQ(5.2.4)p FP(.)40 b FQ(Let)27 b(\006)f(b)r(e)h(an)g(extended)g(surface,)f FJ( )12 b FQ(:)28 b(\006)2579 883 y FE(\030)2551 930 y FL(\000)-40 b(!)23 b FJ(S)2733 942 y FM(0)p FI(;n)2858 930 y FQ(b)r(e)k(a)f(homeomor-)456 1030 y(phism,)32 b(and)e(let)h FJ(\013)g FQ(b)r(e)h(one)e(of)h(the)g(b)r(oundary)f(comp)r(onen)n(ts.) 46 b(Then)31 b(one)f(can)h(connect)f(the)456 1129 y(parameterization)18 b(\()p FL(;)p FJ(;)c( )s FQ(\))21 b(with)h(\()p FL(;)p FJ(;)14 b(t)1635 1141 y FI(\013)1686 1129 y FL(\016)5 b FJ( )s FQ(\),)22 b(where)e FJ(t)2130 1141 y FI(\013)2201 1129 y FL(2)j FQ(\000\()p FJ(S)2414 1141 y FM(0)p FI(;n)2512 1129 y FQ(\))e(is)g(the)g(Dehn)h(t)n(wist)e(around)456 1229 y FJ(\013)28 b FQ(\(see)f(Figure)g(5.1\),)g(b)n(y)h(the)g(follo)n (wing)e(sequence)h(of)h(mo)n(v)n(es:)1628 1365 y FJ(T)1677 1377 y FI(\013)1747 1365 y FQ(=)22 b FJ(F)1887 1377 y FI(c)1922 1365 y FJ(B)1985 1377 y FI(\013;c)2081 1365 y FJ(F)2146 1330 y FE(\000)p FM(1)2134 1385 y FI(c)2235 1365 y FJ(;)456 1504 y FQ(where)27 b FJ(c)g FQ(is)h(a)f(small)g(closed) g(curv)n(e)g(around)f(the)i(hole)g FJ(\013)g FQ(\(see)f(Figure)g (5.11\).)726 2209 y @beginspecial 0 @llx 0 @lly 76 @urx 53 @ury 760 @rwi @setspecial %%BeginDocument: figures/dehntw0.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: dehntw0.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Mon Jun 7 10:10:08 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 76 53 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3600 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -64.0 130.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7001 m -1000 -1000 l 7466 -1000 l 7466 7001 l cp clip 0.02160 0.02160 sc % Arc 15.000 slw gs n 6987.5 4800.0 912.5 -138.9 138.9 arcn gs col-1 s gr gr % Arc gs [90] 0 sd n 2175.0 4800.0 1275.0 -28.1 28.1 arc gs col-1 s gr gr [] 0 sd % Arc gs n 5175.0 4800.0 1275.0 -28.1 28.1 arc gs col-1 s gr gr 7.500 slw % Ellipse n 3075 4800 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 6075 4800 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Arc 15.000 slw gs n 3987.5 4800.0 912.5 -138.9 138.9 arcn gs col-1 s gr gr % Polyline n 3300 5400 m 6300 5400 l gs col-1 s gr /Symbol ff 360.00 scf sf 6150 5850 m gs 1 -1 sc (b) col-1 sh gr % Polyline n 3300 4200 m 6300 4200 l gs col-1 s gr % Polyline 0.000 slw n 3000 3600 m 3000 6000 l % Polyline 30.000 slw [15 45] 45 sd gs clippath 3345 4845 m 3129 4800 l 3345 4755 l 3030 4755 l 3030 4845 l cp clip n 3075 4800 m 6000 4800 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 3345 4845 m 3129 4800 l 3345 4755 l 3309 4800 l 3345 4845 l cp gs 0.00 setgray ef gr col-1 s /Times-Roman ff 375.00 scf sf 4710 4995 m gs 1 -1 sc (*) col-1 sh gr /Symbol ff 360.00 scf sf 3150 5850 m gs 1 -1 sc (a) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1579 1922 a FI(T)1618 1930 y FG(\013)1543 1988 y FL(\000)-42 b(\000)-18 b Fw( )1797 2209 y @beginspecial 0 @llx 0 @lly 76 @urx 53 @ury 760 @rwi @setspecial %%BeginDocument: figures/dehntw1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: dehntw1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Mon Jun 7 10:09:23 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 76 53 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3600 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -64.0 130.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7001 m -1000 -1000 l 7466 -1000 l 7466 7001 l cp clip 0.02160 0.02160 sc % Arc 15.000 slw gs n 6987.5 4800.0 912.5 -138.9 138.9 arcn gs col-1 s gr gr % Arc gs [90] 0 sd n 2175.0 4800.0 1275.0 -28.1 28.1 arc gs col-1 s gr gr [] 0 sd % Arc gs n 5175.0 4800.0 1275.0 -28.1 28.1 arc gs col-1 s gr gr 7.500 slw % Ellipse n 3075 4800 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 6075 4800 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 15.000 slw n 3300 5400 m 6300 5400 l gs col-1 s gr % Polyline n 3300 4200 m 6300 4200 l gs col-1 s gr % Arc gs n 3987.5 4800.0 912.5 -138.9 138.9 arcn gs col-1 s gr gr % Polyline 30.000 slw [15 45] 45 sd n 4800 4800 m 6000 4800 l gs col-1 s gr [] 0 sd /Symbol ff 360.00 scf sf 6150 5850 m gs 1 -1 sc (b) col-1 sh gr % Polyline 0.000 slw n 3000 3600 m 3000 6000 l % Polyline 30.000 slw [15 45] 45 sd n 4800 4800 m 4799 4798 l 4796 4793 l 4790 4784 l 4783 4772 l 4773 4756 l 4762 4738 l 4749 4718 l 4735 4696 l 4722 4676 l 4709 4656 l 4696 4637 l 4684 4620 l 4673 4604 l 4661 4589 l 4650 4575 l 4638 4561 l 4625 4547 l 4612 4532 l 4599 4518 l 4585 4503 l 4570 4489 l 4556 4474 l 4541 4459 l 4526 4444 l 4511 4430 l 4497 4415 l 4482 4401 l 4468 4388 l 4453 4375 l 4439 4362 l 4425 4350 l 4411 4339 l 4396 4327 l 4380 4316 l 4363 4304 l 4344 4291 l 4324 4278 l 4304 4265 l 4283 4251 l 4262 4238 l 4244 4227 l 4228 4217 l 4216 4210 l 4207 4204 l 4202 4201 l 4200 4200 l gs col-1 s gr [] 0 sd % Polyline [15 90] 90 sd n 4200 4200 m 4198 4199 l 4193 4196 l 4186 4193 l 4176 4189 l 4166 4186 l 4156 4185 l 4146 4186 l 4136 4191 l 4125 4200 l 4118 4208 l 4110 4217 l 4101 4228 l 4092 4241 l 4082 4254 l 4071 4268 l 4061 4283 l 4050 4298 l 4039 4314 l 4029 4330 l 4018 4346 l 4008 4361 l 3999 4377 l 3990 4393 l 3982 4409 l 3975 4425 l 3968 4442 l 3962 4459 l 3956 4476 l 3951 4494 l 3947 4511 l 3942 4529 l 3938 4547 l 3934 4564 l 3930 4583 l 3926 4601 l 3922 4620 l 3918 4639 l 3914 4659 l 3909 4680 l 3905 4702 l 3900 4725 l 3896 4744 l 3893 4764 l 3889 4785 l 3885 4807 l 3882 4830 l 3879 4854 l 3875 4878 l 3872 4903 l 3869 4928 l 3866 4954 l 3863 4979 l 3860 5004 l 3856 5029 l 3853 5053 l 3849 5076 l 3845 5098 l 3840 5119 l 3836 5139 l 3830 5158 l 3825 5175 l 3818 5195 l 3809 5215 l 3800 5233 l 3789 5252 l 3776 5271 l 3763 5290 l 3748 5310 l 3734 5329 l 3719 5347 l 3706 5363 l 3695 5376 l 3686 5387 l 3680 5394 l 3677 5398 l 3675 5400 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 3328 4963 m 3148 4833 l 3364 4880 l 3052 4741 l 3016 4823 l cp clip n 3675 5400 m 3672 5398 l 3667 5393 l 3658 5386 l 3647 5376 l 3636 5366 l 3626 5356 l 3616 5346 l 3608 5336 l 3600 5325 l 3594 5315 l 3588 5304 l 3582 5293 l 3577 5281 l 3571 5269 l 3566 5257 l 3561 5244 l 3555 5231 l 3549 5218 l 3542 5204 l 3534 5190 l 3525 5175 l 3518 5163 l 3510 5150 l 3502 5137 l 3494 5123 l 3486 5108 l 3477 5093 l 3469 5078 l 3461 5063 l 3452 5047 l 3443 5032 l 3433 5017 l 3423 5002 l 3412 4988 l 3401 4975 l 3388 4962 l 3375 4950 l 3362 4940 l 3347 4930 l 3331 4920 l 3313 4909 l 3292 4898 l 3269 4887 l 3244 4875 l 3219 4863 l 3192 4851 l 3167 4840 l 3143 4829 l 3122 4820 l 3104 4813 l 3075 4800 l gs col-1 s gr gr [] 0 sd % arrowhead n 3328 4963 m 3148 4833 l 3364 4880 l 3313 4907 l 3328 4963 l cp gs 0.00 setgray ef gr col-1 s /Times-Roman ff 375.00 scf sf 4710 4995 m gs 1 -1 sc (*) col-1 sh gr /Symbol ff 360.00 scf sf 3150 5850 m gs 1 -1 sc (a) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 2536 1988 a FQ(=)2707 2209 y @beginspecial 0 @llx 0 @lly 76 @urx 53 @ury 760 @rwi @setspecial %%BeginDocument: figures/dehntw2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: dehntw2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Mon Jun 7 10:08:22 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 76 53 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3600 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -64.0 130.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7001 m -1000 -1000 l 7466 -1000 l 7466 7001 l cp clip 0.02160 0.02160 sc % Arc 15.000 slw gs n 6987.5 4800.0 912.5 -138.9 138.9 arcn gs col-1 s gr gr % Arc gs [90] 0 sd n 2175.0 4800.0 1275.0 -28.1 28.1 arc gs col-1 s gr gr [] 0 sd % Arc gs n 5175.0 4800.0 1275.0 -28.1 28.1 arc gs col-1 s gr gr 7.500 slw % Ellipse n 3075 4800 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 6075 4800 60 60 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 15.000 slw n 3300 5400 m 6300 5400 l gs col-1 s gr % Polyline n 3300 4200 m 6300 4200 l gs col-1 s gr % Arc gs n 3987.5 4800.0 912.5 -138.9 138.9 arcn gs col-1 s gr gr % Polyline 0.000 slw n 3000 3600 m 3000 6000 l /Symbol ff 360.00 scf sf 6150 5850 m gs 1 -1 sc (b) col-1 sh gr % Polyline 30.000 slw [15 45] 45 sd gs clippath 3345 4845 m 3129 4800 l 3345 4755 l 3030 4755 l 3030 4845 l cp clip n 3075 4800 m 4800 4800 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 3345 4845 m 3129 4800 l 3345 4755 l 3309 4800 l 3345 4845 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 90] 90 sd n 5775 4200 m 5773 4199 l 5768 4196 l 5761 4193 l 5751 4189 l 5741 4186 l 5731 4185 l 5721 4186 l 5711 4191 l 5700 4200 l 5693 4208 l 5685 4217 l 5676 4228 l 5667 4241 l 5657 4254 l 5646 4268 l 5636 4283 l 5625 4298 l 5614 4314 l 5604 4330 l 5593 4346 l 5583 4361 l 5574 4377 l 5565 4393 l 5557 4409 l 5550 4425 l 5543 4442 l 5537 4459 l 5531 4476 l 5526 4494 l 5522 4511 l 5517 4529 l 5513 4547 l 5509 4564 l 5505 4583 l 5501 4601 l 5497 4620 l 5493 4639 l 5489 4659 l 5484 4680 l 5480 4702 l 5475 4725 l 5471 4744 l 5468 4764 l 5464 4785 l 5460 4807 l 5457 4830 l 5454 4854 l 5450 4878 l 5447 4903 l 5444 4928 l 5441 4954 l 5438 4979 l 5435 5004 l 5431 5029 l 5428 5053 l 5424 5076 l 5420 5098 l 5415 5119 l 5411 5139 l 5405 5158 l 5400 5175 l 5393 5195 l 5384 5215 l 5375 5233 l 5364 5252 l 5351 5271 l 5338 5290 l 5323 5310 l 5309 5329 l 5294 5347 l 5281 5363 l 5270 5376 l 5261 5387 l 5255 5394 l 5252 5398 l 5250 5400 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 6075 4800 m 6074 4797 l 6072 4790 l 6068 4778 l 6062 4761 l 6055 4741 l 6047 4717 l 6039 4693 l 6032 4670 l 6024 4647 l 6017 4627 l 6011 4608 l 6005 4591 l 6000 4575 l 5995 4559 l 5990 4543 l 5985 4526 l 5981 4510 l 5977 4493 l 5973 4476 l 5970 4459 l 5966 4442 l 5961 4426 l 5956 4409 l 5951 4393 l 5943 4378 l 5935 4364 l 5925 4350 l 5915 4339 l 5903 4327 l 5889 4316 l 5873 4304 l 5855 4291 l 5834 4278 l 5812 4265 l 5790 4251 l 5768 4238 l 5748 4227 l 5731 4217 l 5717 4210 l 5708 4204 l 5703 4201 l 5700 4200 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 5250 5400 m 5248 5398 l 5245 5393 l 5240 5384 l 5231 5372 l 5221 5356 l 5209 5338 l 5195 5318 l 5181 5296 l 5167 5276 l 5154 5256 l 5141 5237 l 5130 5220 l 5119 5204 l 5109 5189 l 5100 5175 l 5091 5161 l 5081 5147 l 5072 5132 l 5063 5118 l 5053 5103 l 5044 5089 l 5034 5074 l 5025 5059 l 5016 5044 l 5006 5030 l 4997 5015 l 4988 5001 l 4978 4988 l 4969 4975 l 4959 4962 l 4950 4950 l 4939 4937 l 4928 4924 l 4915 4911 l 4902 4897 l 4887 4882 l 4871 4867 l 4855 4851 l 4840 4837 l 4826 4824 l 4815 4814 l 4807 4806 l 4802 4802 l 4800 4800 l gs col-1 s gr [] 0 sd /Times-Roman ff 375.00 scf sf 4710 4995 m gs 1 -1 sc (*) col-1 sh gr /Symbol ff 360.00 scf sf 3150 5850 m gs 1 -1 sc (a) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1269 2414 a FP(Figure)32 b(5.11.)40 b FQ(Dehn)29 b(t)n(wist)e(\()p FJ(T)2324 2426 y FI(\013)2395 2414 y FQ(=)22 b FJ(T)2531 2426 y FI(\014)2575 2414 y FQ(\).)605 2665 y FP(Exer)n(cise)32 b FQ(5.2.5)p FP(.)40 b FQ(Let)19 b FJ(S)1432 2677 y FM(0)p FI(;)p FM(3)1540 2665 y FQ(b)r(e)h(the)f (standard)f(sphere)g(with)h(3)g(holes,)h(with)f(the)h(marking)456 2765 y(as)30 b(sho)n(wn)g(in)i(the)f(left)h(hand)f(side)g(of)g(Figure)f (5.6.)47 b(Deduce)31 b(from)g(the)g(axioms)f(MF1{MF7)456 2865 y(the)e(follo)n(wing)e(relation)h(in)h FL(M)p FQ(\()p FJ(S)1534 2877 y FM(0)p FI(;)p FM(3)1624 2865 y FQ(\):)1572 2999 y FJ(T)1621 3011 y FI(\015)1687 2999 y FQ(=)22 b FJ(B)1837 3011 y FI(\014)s(;\013)1945 2999 y FJ(B)2008 3011 y FI(\013;\014)2115 2999 y FJ(T)2164 3011 y FI(\013)2211 2999 y FJ(T)2260 3011 y FI(\014)2305 2999 y FJ(:)-1872 b FQ(\(5.2.9\))456 3134 y FO(Hint)8 b FQ(:)36 b(this)28 b(is)f(analogous)f(to)h(Step)h(7)f(in)h(the)g(pro)r(of)f(of)h(Theorem)e (5.3.8.)605 3283 y(No)n(w,)h(let)h(us)f(consider)f(extended)i(surfaces) e(of)h(p)r(ositiv)n(e)g(gen)n(us.)36 b(In)27 b(this)h(case,)e(w)n(e)h (need)456 3383 y(to)g(add)h(to)f(the)h(complex)f FL(M)p FQ(\(\006\))h(one)f(more)g(simple)h(mo)n(v)n(e)e(and)i(sev)n(eral)e (more)g(relations.)612 3500 y FK(S-mo)m(v)m(e:)40 b FQ(Let)32 b FJ(S)1185 3512 y FM(1)p FI(;)p FM(1)1308 3500 y FQ(b)r(e)g(a)h (\\standard")d(torus)i(with)h(one)f(b)r(oundary)f(comp)r(onen)n(t)i (and)711 3599 y(one)h(cut,)j(and)e(with)g(the)g(parameterization)e FJ(M)43 b FQ(corresp)r(onding)33 b(to)i(the)g(graph)e(in)711 3699 y(the)27 b(left)g(hand)g(side)f(of)h(Figure)f(5.12.)35 b(Then)27 b(w)n(e)f(add)g(the)h(edge)f FJ(S)14 b FQ(:)28 b FJ(M)j Fw( )23 b FJ(M)3182 3669 y FE(0)3232 3699 y FQ(where)711 3799 y(the)28 b(parameterization)e FJ(M)1586 3769 y FE(0)1636 3799 y FQ(corresp)r(onds)g(to)h(the)h(graph)f(sho)n (wn)g(in)h(the)g(righ)n(t)f(hand)711 3898 y(side)h(of)f(Figure)g(5.12.) 861 3998 y(More)d(generally)-7 b(,)25 b(let)g(\006)1618 4010 y FI(a)1684 3998 y FQ(b)r(e)h(a)f(comp)r(onen)n(t)g(of)g(an)g (extended)h(surface)e(and)i FJ( )i FQ(b)r(e)711 4100 y(a)33 b(homeomorphism)f FJ( )12 b FQ(:)30 b(\006)1594 4112 y FI(a)1695 4053 y FE(\030)1666 4100 y FL(\000)-39 b(!)32 b FJ(S)1858 4112 y FM(1)p FI(;)p FM(1)1948 4100 y FQ(.)54 b(Then)33 b(w)n(e)g(add)g(the)h(mo)n(v)n(e)e FJ(S)14 b FQ(:)30 b FJ( )3086 4070 y FE(\000)p FM(1)3175 4100 y FQ(\()p FJ(M)9 b FQ(\))32 b Fw( )711 4200 y FJ( )768 4170 y FE(\000)p FM(1)857 4200 y FQ(\()p FJ(M)979 4170 y FE(0)1002 4200 y FQ(\).)605 4349 y FP(Remark)g FQ(5.2.6)p FP(.)39 b FQ(If)24 b(\006)e(is)h(a)f(surface)f(of)i(gen)n(us)f(one)g (with)h(one)f(hole,)i(w)n(e)e(can)g(iden)n(tify)h(the)456 4449 y(set)j(of)h(all)f(parameterizations)f(with)i(one)f(cut)i(on)e (\006)h(with)g(the)g(set)g(of)g(all)f(homeomorphisms)456 4551 y FJ( )12 b FQ(:)30 b(\006)699 4504 y FE(\030)670 4551 y FL(\000)-39 b(!)35 b FJ(S)865 4563 y FM(1)p FI(;)p FM(1)955 4551 y FQ(.)59 b(Then)35 b(the)h(S-mo)n(v)n(e)d(connects)i (the)g(marking)f FJ( )k FQ(with)d FJ(s)24 b FL(\016)e FJ( )s FQ(,)37 b(where)e FJ(s)g FL(2)456 4650 y FQ(\000\()p FJ(S)591 4662 y FM(1)p FI(;)p FM(1)681 4650 y FQ(\))28 b(is)f(as)g(in)h(Example)f(5.1.11\(i\).)605 4800 y(No)n(w,)33 b(let)g(us)g(form)n(ulate)e(the)i(new)g(relations.)50 b(In)33 b(addition)f(to)h(relations)e(MF1{MF7,)456 4899 y(let)d(us)f(also)g(imp)r(ose)g(the)h(follo)n(wing)f(ones:)612 5016 y FK(MF8:)41 b(Relations)30 b(for)i FJ(g)26 b FQ(=)c(1)p FJ(;)14 b(n)23 b FQ(=)f(1)p FK(:)41 b FQ(Let)25 b(\006)f(b)r(e)h(a)g (mark)n(ed)e(torus)h(with)h(one)g(hole)f FJ(\013)p FQ(,)711 5116 y(isomorphic)30 b(to)i(the)g(one)f(sho)n(wn)g(in)h(the)f(left)i (hand)e(side)h(of)f(Figure)g(5.13.)47 b(F)-7 b(or)31 b(an)n(y)711 5216 y(parameterization)23 b FJ(M)32 b FQ(=)23 b(\()p FL(f)p FJ(c)p FL(g)p FJ(;)14 b( )s FQ(\))25 b(with)h(one)f(cut,) h(w)n(e)f(let)h FJ(T)36 b FQ(act)25 b(on)g FJ(M)34 b FQ(as)25 b(the)h(edge)p eop %%Page: 104 12 104 107 bop 456 226 a FM(104)1010 b(5.)29 b(MODULAR)g(FUNCTOR)1218 1244 y @beginspecial 0 @llx 0 @lly 75 @urx 102 @ury 750 @rwi @setspecial %%BeginDocument: figures/smove1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: smv1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 11:00:13 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 75 102 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -57.0 162.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 9175 m -1000 -1000 l 7663 -1000 l 7663 9175 l cp clip 0.01980 0.01980 sc /Times-Italic ff 390.00 scf sf 6375 4575 m gs 1 -1 sc (c) col-1 sh gr /Times-Roman ff 270.00 scf sf 6525 4680 m gs 1 -1 sc (1) col-1 sh gr % Arc 15.000 slw gs n 5700.0 4290.0 664.2 25.4 154.6 arc gs col-1 s gr gr % Arc gs [90] 0 sd n 5700.0 5025.0 750.0 -36.9 -143.1 arcn gs col-1 s gr gr [] 0 sd % Ellipse n 4575 7500 600 300 0 360 DrawEllipse gs col-1 s gr % Ellipse n 5775 4935 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4613 4948 562 750 0 360 DrawEllipse gs col-1 s gr % Ellipse n 4605 7215 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd gs clippath 4680 6858 m 4620 7146 l 4560 6858 l 4560 7245 l 4680 7245 l cp clip n 4620 6675 m 4620 7200 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 4680 6858 m 4620 7146 l 4560 6858 l 4620 6906 l 4680 6858 l cp gs 0.00 setgray ef gr col-1 s % Polyline n 5175 7500 m 5175 7497 l 5175 7490 l 5176 7478 l 5177 7461 l 5178 7439 l 5179 7415 l 5181 7388 l 5184 7361 l 5186 7334 l 5189 7308 l 5193 7284 l 5196 7260 l 5201 7238 l 5206 7216 l 5211 7194 l 5218 7173 l 5225 7150 l 5230 7134 l 5236 7117 l 5243 7100 l 5250 7082 l 5257 7064 l 5266 7044 l 5274 7024 l 5284 7003 l 5294 6981 l 5305 6958 l 5316 6935 l 5328 6911 l 5341 6886 l 5354 6861 l 5367 6836 l 5381 6810 l 5396 6784 l 5410 6758 l 5425 6732 l 5441 6706 l 5456 6680 l 5472 6654 l 5488 6628 l 5504 6602 l 5521 6576 l 5538 6550 l 5552 6528 l 5566 6506 l 5581 6484 l 5596 6461 l 5612 6437 l 5628 6413 l 5645 6388 l 5662 6362 l 5680 6335 l 5698 6308 l 5716 6280 l 5735 6251 l 5754 6222 l 5773 6191 l 5792 6161 l 5811 6129 l 5830 6097 l 5849 6065 l 5868 6033 l 5886 6000 l 5904 5967 l 5922 5934 l 5940 5901 l 5957 5868 l 5973 5834 l 5989 5801 l 6005 5768 l 6020 5735 l 6034 5701 l 6048 5668 l 6062 5634 l 6075 5600 l 6086 5569 l 6097 5538 l 6108 5506 l 6119 5473 l 6129 5440 l 6139 5406 l 6148 5371 l 6157 5336 l 6166 5299 l 6175 5262 l 6183 5224 l 6191 5186 l 6198 5146 l 6205 5107 l 6211 5066 l 6217 5025 l 6222 4984 l 6226 4943 l 6230 4902 l 6233 4860 l 6236 4819 l 6237 4778 l 6238 4737 l 6239 4696 l 6238 4656 l 6237 4616 l 6236 4577 l 6233 4539 l 6230 4501 l 6226 4463 l 6221 4426 l 6216 4390 l 6210 4355 l 6203 4319 l 6196 4284 l 6188 4250 l 6179 4216 l 6169 4182 l 6158 4147 l 6146 4113 l 6134 4079 l 6121 4045 l 6106 4010 l 6091 3976 l 6074 3941 l 6056 3906 l 6038 3872 l 6018 3837 l 5997 3803 l 5975 3768 l 5952 3734 l 5929 3701 l 5904 3667 l 5878 3635 l 5852 3603 l 5825 3571 l 5797 3541 l 5768 3511 l 5739 3482 l 5709 3454 l 5679 3427 l 5649 3401 l 5618 3376 l 5587 3353 l 5555 3330 l 5523 3308 l 5491 3288 l 5459 3268 l 5426 3250 l 5393 3232 l 5359 3216 l 5325 3200 l 5292 3186 l 5259 3172 l 5224 3160 l 5189 3148 l 5154 3136 l 5117 3126 l 5080 3116 l 5041 3106 l 5002 3098 l 4962 3090 l 4921 3083 l 4880 3077 l 4838 3071 l 4795 3066 l 4751 3062 l 4708 3059 l 4664 3057 l 4619 3056 l 4575 3055 l 4531 3056 l 4486 3057 l 4442 3059 l 4399 3062 l 4355 3066 l 4312 3071 l 4270 3077 l 4229 3083 l 4188 3090 l 4148 3098 l 4109 3106 l 4070 3116 l 4033 3126 l 3996 3136 l 3961 3148 l 3926 3160 l 3891 3172 l 3858 3186 l 3825 3200 l 3791 3216 l 3757 3232 l 3724 3250 l 3691 3268 l 3659 3288 l 3627 3308 l 3595 3330 l 3563 3353 l 3532 3376 l 3501 3401 l 3471 3427 l 3441 3454 l 3411 3482 l 3382 3511 l 3353 3541 l 3325 3571 l 3298 3603 l 3272 3635 l 3246 3667 l 3221 3701 l 3198 3734 l 3175 3768 l 3153 3803 l 3132 3837 l 3112 3872 l 3094 3906 l 3076 3941 l 3059 3976 l 3044 4010 l 3029 4045 l 3016 4079 l 3004 4113 l 2992 4147 l 2981 4182 l 2971 4216 l 2963 4250 l 2954 4284 l 2947 4319 l 2940 4355 l 2934 4390 l 2929 4426 l 2924 4463 l 2920 4501 l 2917 4539 l 2914 4577 l 2913 4616 l 2912 4656 l 2911 4696 l 2912 4737 l 2913 4778 l 2914 4819 l 2917 4860 l 2920 4902 l 2924 4943 l 2928 4984 l 2933 5025 l 2939 5066 l 2945 5107 l 2952 5146 l 2959 5186 l 2967 5224 l 2975 5262 l 2984 5299 l 2993 5336 l 3002 5371 l 3011 5406 l 3021 5440 l 3031 5473 l 3042 5506 l 3053 5538 l 3064 5569 l 3075 5600 l 3088 5634 l 3102 5668 l 3116 5701 l 3130 5735 l 3145 5768 l 3161 5801 l 3177 5834 l 3193 5868 l 3210 5901 l 3228 5934 l 3246 5967 l 3264 6000 l 3282 6033 l 3301 6065 l 3320 6097 l 3339 6129 l 3358 6161 l 3377 6191 l 3396 6222 l 3415 6251 l 3434 6280 l 3452 6308 l 3470 6335 l 3488 6362 l 3505 6388 l 3522 6413 l 3538 6437 l 3554 6461 l 3569 6484 l 3584 6506 l 3598 6528 l 3613 6550 l 3629 6576 l 3646 6602 l 3662 6628 l 3678 6654 l 3694 6680 l 3709 6706 l 3725 6732 l 3740 6758 l 3754 6784 l 3769 6810 l 3783 6836 l 3796 6861 l 3809 6886 l 3822 6911 l 3834 6935 l 3845 6958 l 3856 6981 l 3866 7003 l 3876 7024 l 3884 7044 l 3893 7064 l 3900 7082 l 3907 7100 l 3914 7117 l 3920 7134 l 3925 7150 l 3932 7173 l 3939 7194 l 3944 7216 l 3949 7238 l 3954 7260 l 3957 7284 l 3961 7308 l 3964 7334 l 3966 7361 l 3969 7388 l 3971 7415 l 3972 7439 l 3973 7461 l 3974 7478 l 3975 7490 l 3975 7497 l 3975 7500 l gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 4650 6675 m 4648 6673 l 4645 6670 l 4639 6663 l 4629 6653 l 4615 6639 l 4597 6621 l 4575 6599 l 4550 6574 l 4522 6545 l 4491 6514 l 4459 6482 l 4426 6448 l 4393 6414 l 4360 6381 l 4328 6348 l 4297 6316 l 4267 6285 l 4239 6256 l 4212 6228 l 4186 6201 l 4162 6176 l 4139 6151 l 4117 6128 l 4096 6105 l 4076 6084 l 4056 6062 l 4037 6041 l 4018 6021 l 4000 6000 l 3980 5978 l 3961 5956 l 3941 5933 l 3922 5910 l 3902 5887 l 3883 5863 l 3863 5838 l 3843 5813 l 3824 5788 l 3804 5762 l 3785 5735 l 3766 5708 l 3747 5680 l 3728 5652 l 3710 5624 l 3692 5595 l 3676 5567 l 3659 5538 l 3644 5509 l 3629 5480 l 3615 5451 l 3601 5423 l 3589 5394 l 3577 5365 l 3566 5337 l 3556 5308 l 3546 5279 l 3538 5250 l 3530 5222 l 3522 5194 l 3516 5165 l 3509 5135 l 3504 5105 l 3498 5074 l 3493 5042 l 3489 5009 l 3485 4975 l 3482 4941 l 3479 4907 l 3477 4871 l 3475 4836 l 3475 4800 l 3474 4764 l 3475 4728 l 3475 4693 l 3477 4657 l 3479 4623 l 3482 4588 l 3485 4555 l 3489 4522 l 3493 4490 l 3498 4458 l 3504 4428 l 3509 4398 l 3516 4369 l 3522 4341 l 3530 4314 l 3538 4288 l 3546 4261 l 3555 4236 l 3564 4210 l 3574 4185 l 3585 4160 l 3597 4135 l 3610 4111 l 3623 4087 l 3637 4063 l 3652 4039 l 3668 4015 l 3685 3992 l 3703 3970 l 3721 3947 l 3740 3926 l 3760 3905 l 3781 3885 l 3802 3866 l 3823 3847 l 3846 3829 l 3868 3813 l 3891 3797 l 3914 3782 l 3938 3768 l 3962 3754 l 3986 3742 l 4011 3730 l 4036 3720 l 4061 3709 l 4088 3700 l 4114 3691 l 4142 3683 l 4170 3675 l 4199 3668 l 4229 3661 l 4260 3655 l 4292 3649 l 4325 3644 l 4359 3639 l 4394 3635 l 4429 3631 l 4464 3628 l 4500 3626 l 4537 3624 l 4573 3623 l 4610 3622 l 4646 3622 l 4682 3622 l 4717 3623 l 4752 3624 l 4786 3626 l 4819 3629 l 4851 3631 l 4883 3635 l 4913 3638 l 4942 3642 l 4971 3647 l 4998 3652 l 5024 3657 l 5050 3663 l 5081 3670 l 5111 3678 l 5140 3687 l 5169 3696 l 5197 3707 l 5225 3718 l 5251 3730 l 5278 3742 l 5303 3756 l 5328 3770 l 5353 3784 l 5376 3800 l 5398 3815 l 5419 3832 l 5439 3848 l 5459 3865 l 5477 3881 l 5493 3898 l 5509 3915 l 5524 3932 l 5538 3949 l 5551 3966 l 5563 3983 l 5575 4000 l 5587 4019 l 5599 4038 l 5610 4058 l 5622 4079 l 5632 4101 l 5643 4123 l 5653 4146 l 5663 4170 l 5672 4195 l 5681 4220 l 5690 4246 l 5698 4272 l 5705 4299 l 5712 4326 l 5719 4353 l 5724 4379 l 5730 4406 l 5735 4432 l 5739 4459 l 5743 4485 l 5747 4511 l 5750 4538 l 5753 4560 l 5755 4583 l 5757 4607 l 5759 4631 l 5761 4656 l 5762 4682 l 5763 4708 l 5764 4736 l 5764 4764 l 5764 4792 l 5763 4821 l 5763 4850 l 5761 4880 l 5759 4910 l 5757 4940 l 5754 4970 l 5751 5000 l 5747 5029 l 5743 5058 l 5738 5087 l 5733 5115 l 5727 5143 l 5721 5170 l 5715 5197 l 5708 5224 l 5700 5250 l 5692 5275 l 5684 5299 l 5675 5324 l 5666 5350 l 5656 5375 l 5645 5401 l 5634 5428 l 5621 5455 l 5608 5482 l 5595 5510 l 5581 5538 l 5566 5566 l 5550 5595 l 5534 5623 l 5518 5652 l 5501 5680 l 5484 5708 l 5467 5736 l 5449 5763 l 5431 5790 l 5414 5816 l 5396 5842 l 5378 5867 l 5360 5892 l 5342 5917 l 5324 5940 l 5306 5964 l 5288 5988 l 5270 6009 l 5253 6031 l 5234 6053 l 5216 6075 l 5196 6098 l 5176 6121 l 5155 6145 l 5133 6170 l 5109 6196 l 5084 6223 l 5057 6252 l 5030 6282 l 5000 6313 l 4969 6345 l 4938 6379 l 4905 6413 l 4872 6447 l 4840 6481 l 4808 6513 l 4778 6545 l 4750 6573 l 4724 6599 l 4703 6621 l 4685 6639 l 4671 6653 l 4661 6663 l 4655 6670 l 4652 6673 l 4650 6675 l cp gs col-1 s gr [] 0 sd /Symbol ff 390.00 scf sf 4425 8175 m gs 1 -1 sc (a) col-1 sh gr /Times-Roman ff 450.00 scf sf 4545 6870 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 2082 754 a FI(S)2028 819 y FL(\000)-42 b(\000)-18 b Fw( )2281 1252 y @beginspecial 0 @llx 0 @lly 68 @urx 104 @ury 680 @rwi @setspecial %%BeginDocument: figures/smove2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: smv2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 11:02:43 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 68 104 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -6.0 114.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 6731 m -1000 -1000 l 4712 -1000 l 4712 6731 l cp clip 0.01980 0.01980 sc /Times-Italic ff 390.00 scf sf 1230 1230 m gs 1 -1 sc (c) col-1 sh gr /Times-Roman ff 270.00 scf sf 1395 1335 m gs 1 -1 sc (2) col-1 sh gr 15.000 slw % Ellipse n 2022 4981 600 300 0 360 DrawEllipse gs col-1 s gr % Ellipse n 1989 2431 562 750 0 360 DrawEllipse gs col-1 s gr % Ellipse n 2026 2468 1050 1237 0 360 DrawEllipse gs col-1 s gr % Ellipse n 1976 4656 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2101 3706 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd gs clippath 2041 4339 m 1981 4627 l 1921 4339 l 1921 4726 l 2041 4726 l cp clip n 1981 4156 m 1981 4681 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2041 4339 m 1981 4627 l 1921 4339 l 1981 4387 l 2041 4339 l cp gs 0.00 setgray ef gr col-1 s % Polyline n 2626 4981 m 2626 4978 l 2626 4971 l 2627 4959 l 2628 4942 l 2629 4920 l 2630 4896 l 2632 4869 l 2635 4842 l 2637 4815 l 2640 4789 l 2644 4765 l 2647 4741 l 2652 4719 l 2657 4697 l 2662 4675 l 2669 4654 l 2676 4631 l 2681 4615 l 2687 4598 l 2694 4581 l 2701 4563 l 2708 4545 l 2717 4525 l 2725 4505 l 2735 4484 l 2745 4462 l 2756 4439 l 2767 4416 l 2779 4392 l 2792 4367 l 2805 4342 l 2818 4317 l 2832 4291 l 2847 4265 l 2861 4239 l 2876 4213 l 2892 4187 l 2907 4161 l 2923 4135 l 2939 4109 l 2955 4083 l 2972 4057 l 2989 4031 l 3003 4009 l 3017 3987 l 3032 3965 l 3047 3942 l 3063 3918 l 3079 3894 l 3096 3869 l 3113 3843 l 3131 3816 l 3149 3789 l 3167 3761 l 3186 3732 l 3205 3703 l 3224 3672 l 3243 3642 l 3262 3610 l 3281 3578 l 3300 3546 l 3319 3514 l 3337 3481 l 3355 3448 l 3373 3415 l 3391 3382 l 3408 3349 l 3424 3315 l 3440 3282 l 3456 3249 l 3471 3216 l 3485 3182 l 3499 3149 l 3513 3115 l 3526 3081 l 3537 3050 l 3548 3019 l 3559 2987 l 3570 2954 l 3580 2921 l 3590 2887 l 3599 2852 l 3608 2817 l 3617 2780 l 3626 2743 l 3634 2705 l 3642 2667 l 3649 2627 l 3656 2588 l 3662 2547 l 3668 2506 l 3673 2465 l 3677 2424 l 3681 2383 l 3684 2341 l 3687 2300 l 3688 2259 l 3689 2218 l 3690 2177 l 3689 2137 l 3688 2097 l 3687 2058 l 3684 2020 l 3681 1982 l 3677 1944 l 3672 1907 l 3667 1871 l 3661 1836 l 3654 1800 l 3647 1765 l 3639 1731 l 3630 1697 l 3620 1663 l 3609 1628 l 3597 1594 l 3585 1560 l 3572 1526 l 3557 1491 l 3542 1457 l 3525 1422 l 3507 1387 l 3489 1353 l 3469 1318 l 3448 1284 l 3426 1249 l 3403 1215 l 3380 1182 l 3355 1148 l 3329 1116 l 3303 1084 l 3276 1052 l 3248 1022 l 3219 992 l 3190 963 l 3160 935 l 3130 908 l 3100 882 l 3069 857 l 3038 834 l 3006 811 l 2974 789 l 2942 769 l 2910 749 l 2877 731 l 2844 713 l 2810 697 l 2776 681 l 2743 667 l 2710 653 l 2675 641 l 2640 629 l 2605 617 l 2568 607 l 2531 597 l 2492 587 l 2453 579 l 2413 571 l 2372 564 l 2331 558 l 2289 552 l 2246 547 l 2202 543 l 2159 540 l 2115 538 l 2070 537 l 2026 536 l 1982 537 l 1937 538 l 1893 540 l 1850 543 l 1806 547 l 1763 552 l 1721 558 l 1680 564 l 1639 571 l 1599 579 l 1560 587 l 1521 597 l 1484 607 l 1447 617 l 1412 629 l 1377 641 l 1342 653 l 1309 667 l 1276 681 l 1242 697 l 1208 713 l 1175 731 l 1142 749 l 1110 769 l 1078 789 l 1046 811 l 1014 834 l 983 857 l 952 882 l 922 908 l 892 935 l 862 963 l 833 992 l 804 1022 l 776 1052 l 749 1084 l 723 1116 l 697 1148 l 672 1182 l 649 1215 l 626 1249 l 604 1284 l 583 1318 l 563 1353 l 545 1387 l 527 1422 l 510 1457 l 495 1491 l 480 1526 l 467 1560 l 455 1594 l 443 1628 l 432 1663 l 422 1697 l 414 1731 l 405 1765 l 398 1800 l 391 1836 l 385 1871 l 380 1907 l 375 1944 l 371 1982 l 368 2020 l 365 2058 l 364 2097 l 363 2137 l 362 2177 l 363 2218 l 364 2259 l 365 2300 l 368 2341 l 371 2383 l 375 2424 l 379 2465 l 384 2506 l 390 2547 l 396 2588 l 403 2627 l 410 2667 l 418 2705 l 426 2743 l 435 2780 l 444 2817 l 453 2852 l 462 2887 l 472 2921 l 482 2954 l 493 2987 l 504 3019 l 515 3050 l 526 3081 l 539 3115 l 553 3149 l 567 3182 l 581 3216 l 596 3249 l 612 3282 l 628 3315 l 644 3349 l 661 3382 l 679 3415 l 697 3448 l 715 3481 l 733 3514 l 752 3546 l 771 3578 l 790 3610 l 809 3642 l 828 3672 l 847 3703 l 866 3732 l 885 3761 l 903 3789 l 921 3816 l 939 3843 l 956 3869 l 973 3894 l 989 3918 l 1005 3942 l 1020 3965 l 1035 3987 l 1049 4009 l 1064 4031 l 1080 4057 l 1097 4083 l 1113 4109 l 1129 4135 l 1145 4161 l 1160 4187 l 1176 4213 l 1191 4239 l 1205 4265 l 1220 4291 l 1234 4317 l 1247 4342 l 1260 4367 l 1273 4392 l 1285 4416 l 1296 4439 l 1307 4462 l 1317 4484 l 1327 4505 l 1335 4525 l 1344 4545 l 1351 4563 l 1358 4581 l 1365 4598 l 1371 4615 l 1376 4631 l 1383 4654 l 1390 4675 l 1395 4697 l 1400 4719 l 1405 4741 l 1408 4765 l 1412 4789 l 1415 4815 l 1417 4842 l 1420 4869 l 1422 4896 l 1423 4920 l 1424 4942 l 1425 4959 l 1426 4971 l 1426 4978 l 1426 4981 l gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 2476 2731 m 2476 2732 l 2475 2735 l 2473 2744 l 2469 2760 l 2463 2781 l 2456 2806 l 2449 2834 l 2441 2862 l 2434 2889 l 2426 2914 l 2420 2937 l 2413 2958 l 2407 2978 l 2401 2996 l 2395 3014 l 2389 3031 l 2383 3046 l 2377 3062 l 2370 3078 l 2363 3094 l 2356 3111 l 2349 3128 l 2341 3145 l 2333 3163 l 2324 3181 l 2316 3199 l 2307 3217 l 2299 3234 l 2291 3251 l 2282 3268 l 2274 3284 l 2266 3300 l 2259 3316 l 2251 3331 l 2243 3346 l 2236 3362 l 2228 3378 l 2220 3394 l 2211 3411 l 2203 3428 l 2195 3446 l 2186 3464 l 2178 3483 l 2169 3501 l 2161 3520 l 2153 3538 l 2146 3556 l 2139 3574 l 2132 3592 l 2125 3609 l 2119 3626 l 2114 3644 l 2108 3661 l 2102 3679 l 2097 3697 l 2092 3716 l 2086 3735 l 2081 3755 l 2076 3775 l 2072 3795 l 2067 3815 l 2063 3835 l 2059 3854 l 2055 3873 l 2051 3891 l 2048 3909 l 2045 3925 l 2043 3940 l 2041 3955 l 2039 3969 l 2036 3988 l 2034 4006 l 2032 4025 l 2030 4043 l 2029 4063 l 2028 4084 l 2027 4105 l 2027 4125 l 2026 4141 l 2026 4151 l 2026 4155 l 2026 4156 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 3526 3181 m 3525 3183 l 3522 3186 l 3517 3192 l 3511 3200 l 3502 3210 l 3491 3225 l 3476 3244 l 3468 3254 l 3459 3265 l 3449 3277 l 3438 3291 l 3426 3305 l 3414 3321 l 3400 3338 l 3386 3356 l 3371 3374 l 3356 3392 l 3340 3411 l 3325 3429 l 3310 3448 l 3295 3466 l 3280 3483 l 3266 3499 l 3252 3515 l 3239 3531 l 3225 3546 l 3212 3561 l 3198 3576 l 3185 3591 l 3171 3605 l 3156 3620 l 3142 3635 l 3127 3649 l 3112 3663 l 3097 3677 l 3081 3691 l 3066 3703 l 3051 3716 l 3036 3727 l 3021 3738 l 3006 3749 l 2991 3759 l 2976 3769 l 2962 3777 l 2948 3785 l 2932 3794 l 2917 3803 l 2900 3811 l 2882 3820 l 2864 3829 l 2844 3838 l 2824 3847 l 2803 3856 l 2782 3865 l 2760 3874 l 2737 3883 l 2715 3892 l 2692 3901 l 2669 3909 l 2646 3918 l 2623 3927 l 2600 3935 l 2576 3944 l 2556 3951 l 2535 3958 l 2513 3966 l 2490 3974 l 2465 3982 l 2439 3991 l 2411 4001 l 2381 4011 l 2348 4022 l 2313 4034 l 2276 4047 l 2237 4060 l 2196 4074 l 2156 4087 l 2116 4101 l 2078 4113 l 2044 4125 l 2014 4135 l 1990 4143 l 1972 4149 l 1960 4153 l 1954 4155 l 1951 4156 l gs col-1 s gr [] 0 sd % Polyline [15 90] 90 sd n 2476 2806 m 2478 2803 l 2483 2796 l 2491 2785 l 2501 2769 l 2514 2751 l 2529 2731 l 2544 2710 l 2558 2691 l 2571 2672 l 2584 2656 l 2596 2641 l 2607 2628 l 2617 2616 l 2628 2604 l 2639 2594 l 2649 2583 l 2661 2572 l 2673 2562 l 2685 2551 l 2699 2541 l 2713 2531 l 2727 2521 l 2742 2511 l 2757 2502 l 2773 2493 l 2788 2485 l 2803 2478 l 2819 2472 l 2834 2466 l 2849 2461 l 2864 2456 l 2879 2452 l 2894 2448 l 2911 2445 l 2928 2443 l 2945 2440 l 2964 2438 l 2982 2437 l 3001 2436 l 3020 2436 l 3038 2436 l 3057 2436 l 3074 2437 l 3091 2438 l 3108 2440 l 3123 2441 l 3139 2444 l 3156 2446 l 3173 2449 l 3190 2453 l 3207 2457 l 3225 2462 l 3243 2468 l 3260 2474 l 3277 2480 l 3294 2488 l 3309 2496 l 3324 2504 l 3338 2512 l 3351 2521 l 3364 2531 l 3376 2541 l 3388 2552 l 3400 2564 l 3411 2577 l 3423 2591 l 3435 2605 l 3446 2620 l 3456 2635 l 3466 2650 l 3475 2665 l 3483 2679 l 3490 2693 l 3496 2706 l 3501 2719 l 3506 2733 l 3511 2747 l 3515 2761 l 3518 2775 l 3521 2789 l 3523 2803 l 3524 2816 l 3525 2828 l 3526 2840 l 3526 2850 l 3526 2860 l 3526 2869 l 3526 2879 l 3526 2889 l 3526 2899 l 3526 2909 l 3526 2920 l 3526 2932 l 3526 2943 l 3526 2955 l 3526 2968 l 3526 2981 l 3526 2991 l 3526 3002 l 3526 3015 l 3526 3030 l 3526 3047 l 3526 3066 l 3526 3087 l 3526 3110 l 3526 3132 l 3526 3152 l 3526 3167 l 3526 3176 l 3526 3180 l 3526 3181 l gs col-1 s gr [] 0 sd /Symbol ff 390.00 scf sf 1921 5731 m gs 1 -1 sc (a) col-1 sh gr /Times-Roman ff 450.00 scf sf 1891 4373 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1534 1452 a FP(Figure)32 b(5.12.)40 b FQ(S-mo)n(v)n(e.)711 1668 y(Dehn)28 b(t)n(wist)f FJ(T)1185 1680 y FI(c)1245 1668 y FQ(around)f FJ(c)h FQ(\(see)g(Example)g(5.2.4\).)35 b(Then)28 b(w)n(e)e(imp)r(ose)h(the)h(follo)n(wing)711 1768 y(relations:)1720 1907 y FJ(S)1776 1873 y FM(2)1836 1907 y FQ(=)23 b FJ(Z)1987 1873 y FE(\000)p FM(1)2076 1907 y FJ(B)2139 1919 y FI(\013;c)2232 1927 y FF(1)2268 1907 y FJ(;)-1835 b FQ(\(5.2.10\))1596 2046 y(\()p FJ(S)5 b(T)12 b FQ(\))1777 2012 y FM(3)1836 2046 y FQ(=)23 b FJ(S)1980 2012 y FM(2)2017 2046 y FJ(:)-1584 b FQ(\(5.2.11\))711 2191 y(The)20 b(left)h(hand)e(side)h(of)g(relation)f(\(5.2.10\))g(is)g (sho)n(wn)g(in)i(Figure)e(5.13.)33 b(An)20 b(illustration)711 2290 y(of)34 b(\(5.2.11\))27 b(can)g(b)r(e)h(found)g(in)g([)p FK(BK)o FQ(,)g(App)r(endix)h(A].)724 3419 y @beginspecial 0 @llx 0 @lly 75 @urx 102 @ury 750 @rwi @setspecial %%BeginDocument: figures/smove1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: smv1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 11:00:13 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 75 102 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -57.0 162.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 9175 m -1000 -1000 l 7663 -1000 l 7663 9175 l cp clip 0.01980 0.01980 sc /Times-Italic ff 390.00 scf sf 6375 4575 m gs 1 -1 sc (c) col-1 sh gr /Times-Roman ff 270.00 scf sf 6525 4680 m gs 1 -1 sc (1) col-1 sh gr % Arc 15.000 slw gs n 5700.0 4290.0 664.2 25.4 154.6 arc gs col-1 s gr gr % Arc gs [90] 0 sd n 5700.0 5025.0 750.0 -36.9 -143.1 arcn gs col-1 s gr gr [] 0 sd % Ellipse n 4575 7500 600 300 0 360 DrawEllipse gs col-1 s gr % Ellipse n 5775 4935 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 4613 4948 562 750 0 360 DrawEllipse gs col-1 s gr % Ellipse n 4605 7215 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd gs clippath 4680 6858 m 4620 7146 l 4560 6858 l 4560 7245 l 4680 7245 l cp clip n 4620 6675 m 4620 7200 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 4680 6858 m 4620 7146 l 4560 6858 l 4620 6906 l 4680 6858 l cp gs 0.00 setgray ef gr col-1 s % Polyline n 5175 7500 m 5175 7497 l 5175 7490 l 5176 7478 l 5177 7461 l 5178 7439 l 5179 7415 l 5181 7388 l 5184 7361 l 5186 7334 l 5189 7308 l 5193 7284 l 5196 7260 l 5201 7238 l 5206 7216 l 5211 7194 l 5218 7173 l 5225 7150 l 5230 7134 l 5236 7117 l 5243 7100 l 5250 7082 l 5257 7064 l 5266 7044 l 5274 7024 l 5284 7003 l 5294 6981 l 5305 6958 l 5316 6935 l 5328 6911 l 5341 6886 l 5354 6861 l 5367 6836 l 5381 6810 l 5396 6784 l 5410 6758 l 5425 6732 l 5441 6706 l 5456 6680 l 5472 6654 l 5488 6628 l 5504 6602 l 5521 6576 l 5538 6550 l 5552 6528 l 5566 6506 l 5581 6484 l 5596 6461 l 5612 6437 l 5628 6413 l 5645 6388 l 5662 6362 l 5680 6335 l 5698 6308 l 5716 6280 l 5735 6251 l 5754 6222 l 5773 6191 l 5792 6161 l 5811 6129 l 5830 6097 l 5849 6065 l 5868 6033 l 5886 6000 l 5904 5967 l 5922 5934 l 5940 5901 l 5957 5868 l 5973 5834 l 5989 5801 l 6005 5768 l 6020 5735 l 6034 5701 l 6048 5668 l 6062 5634 l 6075 5600 l 6086 5569 l 6097 5538 l 6108 5506 l 6119 5473 l 6129 5440 l 6139 5406 l 6148 5371 l 6157 5336 l 6166 5299 l 6175 5262 l 6183 5224 l 6191 5186 l 6198 5146 l 6205 5107 l 6211 5066 l 6217 5025 l 6222 4984 l 6226 4943 l 6230 4902 l 6233 4860 l 6236 4819 l 6237 4778 l 6238 4737 l 6239 4696 l 6238 4656 l 6237 4616 l 6236 4577 l 6233 4539 l 6230 4501 l 6226 4463 l 6221 4426 l 6216 4390 l 6210 4355 l 6203 4319 l 6196 4284 l 6188 4250 l 6179 4216 l 6169 4182 l 6158 4147 l 6146 4113 l 6134 4079 l 6121 4045 l 6106 4010 l 6091 3976 l 6074 3941 l 6056 3906 l 6038 3872 l 6018 3837 l 5997 3803 l 5975 3768 l 5952 3734 l 5929 3701 l 5904 3667 l 5878 3635 l 5852 3603 l 5825 3571 l 5797 3541 l 5768 3511 l 5739 3482 l 5709 3454 l 5679 3427 l 5649 3401 l 5618 3376 l 5587 3353 l 5555 3330 l 5523 3308 l 5491 3288 l 5459 3268 l 5426 3250 l 5393 3232 l 5359 3216 l 5325 3200 l 5292 3186 l 5259 3172 l 5224 3160 l 5189 3148 l 5154 3136 l 5117 3126 l 5080 3116 l 5041 3106 l 5002 3098 l 4962 3090 l 4921 3083 l 4880 3077 l 4838 3071 l 4795 3066 l 4751 3062 l 4708 3059 l 4664 3057 l 4619 3056 l 4575 3055 l 4531 3056 l 4486 3057 l 4442 3059 l 4399 3062 l 4355 3066 l 4312 3071 l 4270 3077 l 4229 3083 l 4188 3090 l 4148 3098 l 4109 3106 l 4070 3116 l 4033 3126 l 3996 3136 l 3961 3148 l 3926 3160 l 3891 3172 l 3858 3186 l 3825 3200 l 3791 3216 l 3757 3232 l 3724 3250 l 3691 3268 l 3659 3288 l 3627 3308 l 3595 3330 l 3563 3353 l 3532 3376 l 3501 3401 l 3471 3427 l 3441 3454 l 3411 3482 l 3382 3511 l 3353 3541 l 3325 3571 l 3298 3603 l 3272 3635 l 3246 3667 l 3221 3701 l 3198 3734 l 3175 3768 l 3153 3803 l 3132 3837 l 3112 3872 l 3094 3906 l 3076 3941 l 3059 3976 l 3044 4010 l 3029 4045 l 3016 4079 l 3004 4113 l 2992 4147 l 2981 4182 l 2971 4216 l 2963 4250 l 2954 4284 l 2947 4319 l 2940 4355 l 2934 4390 l 2929 4426 l 2924 4463 l 2920 4501 l 2917 4539 l 2914 4577 l 2913 4616 l 2912 4656 l 2911 4696 l 2912 4737 l 2913 4778 l 2914 4819 l 2917 4860 l 2920 4902 l 2924 4943 l 2928 4984 l 2933 5025 l 2939 5066 l 2945 5107 l 2952 5146 l 2959 5186 l 2967 5224 l 2975 5262 l 2984 5299 l 2993 5336 l 3002 5371 l 3011 5406 l 3021 5440 l 3031 5473 l 3042 5506 l 3053 5538 l 3064 5569 l 3075 5600 l 3088 5634 l 3102 5668 l 3116 5701 l 3130 5735 l 3145 5768 l 3161 5801 l 3177 5834 l 3193 5868 l 3210 5901 l 3228 5934 l 3246 5967 l 3264 6000 l 3282 6033 l 3301 6065 l 3320 6097 l 3339 6129 l 3358 6161 l 3377 6191 l 3396 6222 l 3415 6251 l 3434 6280 l 3452 6308 l 3470 6335 l 3488 6362 l 3505 6388 l 3522 6413 l 3538 6437 l 3554 6461 l 3569 6484 l 3584 6506 l 3598 6528 l 3613 6550 l 3629 6576 l 3646 6602 l 3662 6628 l 3678 6654 l 3694 6680 l 3709 6706 l 3725 6732 l 3740 6758 l 3754 6784 l 3769 6810 l 3783 6836 l 3796 6861 l 3809 6886 l 3822 6911 l 3834 6935 l 3845 6958 l 3856 6981 l 3866 7003 l 3876 7024 l 3884 7044 l 3893 7064 l 3900 7082 l 3907 7100 l 3914 7117 l 3920 7134 l 3925 7150 l 3932 7173 l 3939 7194 l 3944 7216 l 3949 7238 l 3954 7260 l 3957 7284 l 3961 7308 l 3964 7334 l 3966 7361 l 3969 7388 l 3971 7415 l 3972 7439 l 3973 7461 l 3974 7478 l 3975 7490 l 3975 7497 l 3975 7500 l gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 4650 6675 m 4648 6673 l 4645 6670 l 4639 6663 l 4629 6653 l 4615 6639 l 4597 6621 l 4575 6599 l 4550 6574 l 4522 6545 l 4491 6514 l 4459 6482 l 4426 6448 l 4393 6414 l 4360 6381 l 4328 6348 l 4297 6316 l 4267 6285 l 4239 6256 l 4212 6228 l 4186 6201 l 4162 6176 l 4139 6151 l 4117 6128 l 4096 6105 l 4076 6084 l 4056 6062 l 4037 6041 l 4018 6021 l 4000 6000 l 3980 5978 l 3961 5956 l 3941 5933 l 3922 5910 l 3902 5887 l 3883 5863 l 3863 5838 l 3843 5813 l 3824 5788 l 3804 5762 l 3785 5735 l 3766 5708 l 3747 5680 l 3728 5652 l 3710 5624 l 3692 5595 l 3676 5567 l 3659 5538 l 3644 5509 l 3629 5480 l 3615 5451 l 3601 5423 l 3589 5394 l 3577 5365 l 3566 5337 l 3556 5308 l 3546 5279 l 3538 5250 l 3530 5222 l 3522 5194 l 3516 5165 l 3509 5135 l 3504 5105 l 3498 5074 l 3493 5042 l 3489 5009 l 3485 4975 l 3482 4941 l 3479 4907 l 3477 4871 l 3475 4836 l 3475 4800 l 3474 4764 l 3475 4728 l 3475 4693 l 3477 4657 l 3479 4623 l 3482 4588 l 3485 4555 l 3489 4522 l 3493 4490 l 3498 4458 l 3504 4428 l 3509 4398 l 3516 4369 l 3522 4341 l 3530 4314 l 3538 4288 l 3546 4261 l 3555 4236 l 3564 4210 l 3574 4185 l 3585 4160 l 3597 4135 l 3610 4111 l 3623 4087 l 3637 4063 l 3652 4039 l 3668 4015 l 3685 3992 l 3703 3970 l 3721 3947 l 3740 3926 l 3760 3905 l 3781 3885 l 3802 3866 l 3823 3847 l 3846 3829 l 3868 3813 l 3891 3797 l 3914 3782 l 3938 3768 l 3962 3754 l 3986 3742 l 4011 3730 l 4036 3720 l 4061 3709 l 4088 3700 l 4114 3691 l 4142 3683 l 4170 3675 l 4199 3668 l 4229 3661 l 4260 3655 l 4292 3649 l 4325 3644 l 4359 3639 l 4394 3635 l 4429 3631 l 4464 3628 l 4500 3626 l 4537 3624 l 4573 3623 l 4610 3622 l 4646 3622 l 4682 3622 l 4717 3623 l 4752 3624 l 4786 3626 l 4819 3629 l 4851 3631 l 4883 3635 l 4913 3638 l 4942 3642 l 4971 3647 l 4998 3652 l 5024 3657 l 5050 3663 l 5081 3670 l 5111 3678 l 5140 3687 l 5169 3696 l 5197 3707 l 5225 3718 l 5251 3730 l 5278 3742 l 5303 3756 l 5328 3770 l 5353 3784 l 5376 3800 l 5398 3815 l 5419 3832 l 5439 3848 l 5459 3865 l 5477 3881 l 5493 3898 l 5509 3915 l 5524 3932 l 5538 3949 l 5551 3966 l 5563 3983 l 5575 4000 l 5587 4019 l 5599 4038 l 5610 4058 l 5622 4079 l 5632 4101 l 5643 4123 l 5653 4146 l 5663 4170 l 5672 4195 l 5681 4220 l 5690 4246 l 5698 4272 l 5705 4299 l 5712 4326 l 5719 4353 l 5724 4379 l 5730 4406 l 5735 4432 l 5739 4459 l 5743 4485 l 5747 4511 l 5750 4538 l 5753 4560 l 5755 4583 l 5757 4607 l 5759 4631 l 5761 4656 l 5762 4682 l 5763 4708 l 5764 4736 l 5764 4764 l 5764 4792 l 5763 4821 l 5763 4850 l 5761 4880 l 5759 4910 l 5757 4940 l 5754 4970 l 5751 5000 l 5747 5029 l 5743 5058 l 5738 5087 l 5733 5115 l 5727 5143 l 5721 5170 l 5715 5197 l 5708 5224 l 5700 5250 l 5692 5275 l 5684 5299 l 5675 5324 l 5666 5350 l 5656 5375 l 5645 5401 l 5634 5428 l 5621 5455 l 5608 5482 l 5595 5510 l 5581 5538 l 5566 5566 l 5550 5595 l 5534 5623 l 5518 5652 l 5501 5680 l 5484 5708 l 5467 5736 l 5449 5763 l 5431 5790 l 5414 5816 l 5396 5842 l 5378 5867 l 5360 5892 l 5342 5917 l 5324 5940 l 5306 5964 l 5288 5988 l 5270 6009 l 5253 6031 l 5234 6053 l 5216 6075 l 5196 6098 l 5176 6121 l 5155 6145 l 5133 6170 l 5109 6196 l 5084 6223 l 5057 6252 l 5030 6282 l 5000 6313 l 4969 6345 l 4938 6379 l 4905 6413 l 4872 6447 l 4840 6481 l 4808 6513 l 4778 6545 l 4750 6573 l 4724 6599 l 4703 6621 l 4685 6639 l 4671 6653 l 4661 6663 l 4655 6670 l 4652 6673 l 4650 6675 l cp gs col-1 s gr [] 0 sd /Symbol ff 390.00 scf sf 4425 8175 m gs 1 -1 sc (a) col-1 sh gr /Times-Roman ff 450.00 scf sf 4545 6870 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1587 2929 a FI(S)1533 2994 y FL(\000)-42 b(\000)-18 b Fw( )1746 3427 y @beginspecial 0 @llx 0 @lly 68 @urx 104 @ury 680 @rwi @setspecial %%BeginDocument: figures/smove2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: smv2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 11:02:43 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 68 104 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -6.0 114.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 6731 m -1000 -1000 l 4712 -1000 l 4712 6731 l cp clip 0.01980 0.01980 sc /Times-Italic ff 390.00 scf sf 1230 1230 m gs 1 -1 sc (c) col-1 sh gr /Times-Roman ff 270.00 scf sf 1395 1335 m gs 1 -1 sc (2) col-1 sh gr 15.000 slw % Ellipse n 2022 4981 600 300 0 360 DrawEllipse gs col-1 s gr % Ellipse n 1989 2431 562 750 0 360 DrawEllipse gs col-1 s gr % Ellipse n 2026 2468 1050 1237 0 360 DrawEllipse gs col-1 s gr % Ellipse n 1976 4656 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2101 3706 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd gs clippath 2041 4339 m 1981 4627 l 1921 4339 l 1921 4726 l 2041 4726 l cp clip n 1981 4156 m 1981 4681 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2041 4339 m 1981 4627 l 1921 4339 l 1981 4387 l 2041 4339 l cp gs 0.00 setgray ef gr col-1 s % Polyline n 2626 4981 m 2626 4978 l 2626 4971 l 2627 4959 l 2628 4942 l 2629 4920 l 2630 4896 l 2632 4869 l 2635 4842 l 2637 4815 l 2640 4789 l 2644 4765 l 2647 4741 l 2652 4719 l 2657 4697 l 2662 4675 l 2669 4654 l 2676 4631 l 2681 4615 l 2687 4598 l 2694 4581 l 2701 4563 l 2708 4545 l 2717 4525 l 2725 4505 l 2735 4484 l 2745 4462 l 2756 4439 l 2767 4416 l 2779 4392 l 2792 4367 l 2805 4342 l 2818 4317 l 2832 4291 l 2847 4265 l 2861 4239 l 2876 4213 l 2892 4187 l 2907 4161 l 2923 4135 l 2939 4109 l 2955 4083 l 2972 4057 l 2989 4031 l 3003 4009 l 3017 3987 l 3032 3965 l 3047 3942 l 3063 3918 l 3079 3894 l 3096 3869 l 3113 3843 l 3131 3816 l 3149 3789 l 3167 3761 l 3186 3732 l 3205 3703 l 3224 3672 l 3243 3642 l 3262 3610 l 3281 3578 l 3300 3546 l 3319 3514 l 3337 3481 l 3355 3448 l 3373 3415 l 3391 3382 l 3408 3349 l 3424 3315 l 3440 3282 l 3456 3249 l 3471 3216 l 3485 3182 l 3499 3149 l 3513 3115 l 3526 3081 l 3537 3050 l 3548 3019 l 3559 2987 l 3570 2954 l 3580 2921 l 3590 2887 l 3599 2852 l 3608 2817 l 3617 2780 l 3626 2743 l 3634 2705 l 3642 2667 l 3649 2627 l 3656 2588 l 3662 2547 l 3668 2506 l 3673 2465 l 3677 2424 l 3681 2383 l 3684 2341 l 3687 2300 l 3688 2259 l 3689 2218 l 3690 2177 l 3689 2137 l 3688 2097 l 3687 2058 l 3684 2020 l 3681 1982 l 3677 1944 l 3672 1907 l 3667 1871 l 3661 1836 l 3654 1800 l 3647 1765 l 3639 1731 l 3630 1697 l 3620 1663 l 3609 1628 l 3597 1594 l 3585 1560 l 3572 1526 l 3557 1491 l 3542 1457 l 3525 1422 l 3507 1387 l 3489 1353 l 3469 1318 l 3448 1284 l 3426 1249 l 3403 1215 l 3380 1182 l 3355 1148 l 3329 1116 l 3303 1084 l 3276 1052 l 3248 1022 l 3219 992 l 3190 963 l 3160 935 l 3130 908 l 3100 882 l 3069 857 l 3038 834 l 3006 811 l 2974 789 l 2942 769 l 2910 749 l 2877 731 l 2844 713 l 2810 697 l 2776 681 l 2743 667 l 2710 653 l 2675 641 l 2640 629 l 2605 617 l 2568 607 l 2531 597 l 2492 587 l 2453 579 l 2413 571 l 2372 564 l 2331 558 l 2289 552 l 2246 547 l 2202 543 l 2159 540 l 2115 538 l 2070 537 l 2026 536 l 1982 537 l 1937 538 l 1893 540 l 1850 543 l 1806 547 l 1763 552 l 1721 558 l 1680 564 l 1639 571 l 1599 579 l 1560 587 l 1521 597 l 1484 607 l 1447 617 l 1412 629 l 1377 641 l 1342 653 l 1309 667 l 1276 681 l 1242 697 l 1208 713 l 1175 731 l 1142 749 l 1110 769 l 1078 789 l 1046 811 l 1014 834 l 983 857 l 952 882 l 922 908 l 892 935 l 862 963 l 833 992 l 804 1022 l 776 1052 l 749 1084 l 723 1116 l 697 1148 l 672 1182 l 649 1215 l 626 1249 l 604 1284 l 583 1318 l 563 1353 l 545 1387 l 527 1422 l 510 1457 l 495 1491 l 480 1526 l 467 1560 l 455 1594 l 443 1628 l 432 1663 l 422 1697 l 414 1731 l 405 1765 l 398 1800 l 391 1836 l 385 1871 l 380 1907 l 375 1944 l 371 1982 l 368 2020 l 365 2058 l 364 2097 l 363 2137 l 362 2177 l 363 2218 l 364 2259 l 365 2300 l 368 2341 l 371 2383 l 375 2424 l 379 2465 l 384 2506 l 390 2547 l 396 2588 l 403 2627 l 410 2667 l 418 2705 l 426 2743 l 435 2780 l 444 2817 l 453 2852 l 462 2887 l 472 2921 l 482 2954 l 493 2987 l 504 3019 l 515 3050 l 526 3081 l 539 3115 l 553 3149 l 567 3182 l 581 3216 l 596 3249 l 612 3282 l 628 3315 l 644 3349 l 661 3382 l 679 3415 l 697 3448 l 715 3481 l 733 3514 l 752 3546 l 771 3578 l 790 3610 l 809 3642 l 828 3672 l 847 3703 l 866 3732 l 885 3761 l 903 3789 l 921 3816 l 939 3843 l 956 3869 l 973 3894 l 989 3918 l 1005 3942 l 1020 3965 l 1035 3987 l 1049 4009 l 1064 4031 l 1080 4057 l 1097 4083 l 1113 4109 l 1129 4135 l 1145 4161 l 1160 4187 l 1176 4213 l 1191 4239 l 1205 4265 l 1220 4291 l 1234 4317 l 1247 4342 l 1260 4367 l 1273 4392 l 1285 4416 l 1296 4439 l 1307 4462 l 1317 4484 l 1327 4505 l 1335 4525 l 1344 4545 l 1351 4563 l 1358 4581 l 1365 4598 l 1371 4615 l 1376 4631 l 1383 4654 l 1390 4675 l 1395 4697 l 1400 4719 l 1405 4741 l 1408 4765 l 1412 4789 l 1415 4815 l 1417 4842 l 1420 4869 l 1422 4896 l 1423 4920 l 1424 4942 l 1425 4959 l 1426 4971 l 1426 4978 l 1426 4981 l gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 2476 2731 m 2476 2732 l 2475 2735 l 2473 2744 l 2469 2760 l 2463 2781 l 2456 2806 l 2449 2834 l 2441 2862 l 2434 2889 l 2426 2914 l 2420 2937 l 2413 2958 l 2407 2978 l 2401 2996 l 2395 3014 l 2389 3031 l 2383 3046 l 2377 3062 l 2370 3078 l 2363 3094 l 2356 3111 l 2349 3128 l 2341 3145 l 2333 3163 l 2324 3181 l 2316 3199 l 2307 3217 l 2299 3234 l 2291 3251 l 2282 3268 l 2274 3284 l 2266 3300 l 2259 3316 l 2251 3331 l 2243 3346 l 2236 3362 l 2228 3378 l 2220 3394 l 2211 3411 l 2203 3428 l 2195 3446 l 2186 3464 l 2178 3483 l 2169 3501 l 2161 3520 l 2153 3538 l 2146 3556 l 2139 3574 l 2132 3592 l 2125 3609 l 2119 3626 l 2114 3644 l 2108 3661 l 2102 3679 l 2097 3697 l 2092 3716 l 2086 3735 l 2081 3755 l 2076 3775 l 2072 3795 l 2067 3815 l 2063 3835 l 2059 3854 l 2055 3873 l 2051 3891 l 2048 3909 l 2045 3925 l 2043 3940 l 2041 3955 l 2039 3969 l 2036 3988 l 2034 4006 l 2032 4025 l 2030 4043 l 2029 4063 l 2028 4084 l 2027 4105 l 2027 4125 l 2026 4141 l 2026 4151 l 2026 4155 l 2026 4156 l gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 3526 3181 m 3525 3183 l 3522 3186 l 3517 3192 l 3511 3200 l 3502 3210 l 3491 3225 l 3476 3244 l 3468 3254 l 3459 3265 l 3449 3277 l 3438 3291 l 3426 3305 l 3414 3321 l 3400 3338 l 3386 3356 l 3371 3374 l 3356 3392 l 3340 3411 l 3325 3429 l 3310 3448 l 3295 3466 l 3280 3483 l 3266 3499 l 3252 3515 l 3239 3531 l 3225 3546 l 3212 3561 l 3198 3576 l 3185 3591 l 3171 3605 l 3156 3620 l 3142 3635 l 3127 3649 l 3112 3663 l 3097 3677 l 3081 3691 l 3066 3703 l 3051 3716 l 3036 3727 l 3021 3738 l 3006 3749 l 2991 3759 l 2976 3769 l 2962 3777 l 2948 3785 l 2932 3794 l 2917 3803 l 2900 3811 l 2882 3820 l 2864 3829 l 2844 3838 l 2824 3847 l 2803 3856 l 2782 3865 l 2760 3874 l 2737 3883 l 2715 3892 l 2692 3901 l 2669 3909 l 2646 3918 l 2623 3927 l 2600 3935 l 2576 3944 l 2556 3951 l 2535 3958 l 2513 3966 l 2490 3974 l 2465 3982 l 2439 3991 l 2411 4001 l 2381 4011 l 2348 4022 l 2313 4034 l 2276 4047 l 2237 4060 l 2196 4074 l 2156 4087 l 2116 4101 l 2078 4113 l 2044 4125 l 2014 4135 l 1990 4143 l 1972 4149 l 1960 4153 l 1954 4155 l 1951 4156 l gs col-1 s gr [] 0 sd % Polyline [15 90] 90 sd n 2476 2806 m 2478 2803 l 2483 2796 l 2491 2785 l 2501 2769 l 2514 2751 l 2529 2731 l 2544 2710 l 2558 2691 l 2571 2672 l 2584 2656 l 2596 2641 l 2607 2628 l 2617 2616 l 2628 2604 l 2639 2594 l 2649 2583 l 2661 2572 l 2673 2562 l 2685 2551 l 2699 2541 l 2713 2531 l 2727 2521 l 2742 2511 l 2757 2502 l 2773 2493 l 2788 2485 l 2803 2478 l 2819 2472 l 2834 2466 l 2849 2461 l 2864 2456 l 2879 2452 l 2894 2448 l 2911 2445 l 2928 2443 l 2945 2440 l 2964 2438 l 2982 2437 l 3001 2436 l 3020 2436 l 3038 2436 l 3057 2436 l 3074 2437 l 3091 2438 l 3108 2440 l 3123 2441 l 3139 2444 l 3156 2446 l 3173 2449 l 3190 2453 l 3207 2457 l 3225 2462 l 3243 2468 l 3260 2474 l 3277 2480 l 3294 2488 l 3309 2496 l 3324 2504 l 3338 2512 l 3351 2521 l 3364 2531 l 3376 2541 l 3388 2552 l 3400 2564 l 3411 2577 l 3423 2591 l 3435 2605 l 3446 2620 l 3456 2635 l 3466 2650 l 3475 2665 l 3483 2679 l 3490 2693 l 3496 2706 l 3501 2719 l 3506 2733 l 3511 2747 l 3515 2761 l 3518 2775 l 3521 2789 l 3523 2803 l 3524 2816 l 3525 2828 l 3526 2840 l 3526 2850 l 3526 2860 l 3526 2869 l 3526 2879 l 3526 2889 l 3526 2899 l 3526 2909 l 3526 2920 l 3526 2932 l 3526 2943 l 3526 2955 l 3526 2968 l 3526 2981 l 3526 2991 l 3526 3002 l 3526 3015 l 3526 3030 l 3526 3047 l 3526 3066 l 3526 3087 l 3526 3110 l 3526 3132 l 3526 3152 l 3526 3167 l 3526 3176 l 3526 3180 l 3526 3181 l gs col-1 s gr [] 0 sd /Symbol ff 390.00 scf sf 1921 5731 m gs 1 -1 sc (a) col-1 sh gr /Times-Roman ff 450.00 scf sf 1891 4373 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 2551 2929 a FI(S)2497 2994 y FL(\000)-42 b(\000)-18 b Fw( )2709 3423 y @beginspecial 0 @llx 0 @lly 76 @urx 103 @ury 760 @rwi @setspecial %%BeginDocument: figures/smove3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: smv3.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Aug 11 11:05:09 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 76 103 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -9.0 103.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 6176 m -1000 -1000 l 5248 -1000 l 5248 6176 l cp clip 0.01980 0.01980 sc /Times-Italic ff 390.00 scf sf 3960 1576 m gs 1 -1 sc (c) col-1 sh gr /Times-Roman ff 270.00 scf sf 4110 1681 m gs 1 -1 sc (1) col-1 sh gr % Arc 15.000 slw gs n 3286.0 1291.0 664.2 25.4 154.6 arc gs col-1 s gr gr % Arc gs [90] 0 sd n 3286.0 2026.0 750.0 -36.9 -143.1 arcn gs col-1 s gr gr [] 0 sd % Ellipse n 2161 4501 600 300 0 360 DrawEllipse gs col-1 s gr % Ellipse n 3361 1936 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 2199 1949 562 750 0 360 DrawEllipse gs col-1 s gr % Ellipse n 2191 4216 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd gs clippath 2541 4110 m 2254 4178 l 2490 4002 l 2140 4166 l 2191 4274 l cp clip n 3136 3526 m 2686 3976 l 2206 4201 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2541 4110 m 2254 4178 l 2490 4002 l 2472 4076 l 2541 4110 l cp gs 0.00 setgray ef gr col-1 s % Polyline n 2761 4501 m 2761 4498 l 2761 4491 l 2762 4479 l 2763 4462 l 2764 4440 l 2765 4416 l 2767 4389 l 2770 4362 l 2772 4335 l 2775 4309 l 2779 4285 l 2782 4261 l 2787 4239 l 2792 4217 l 2797 4195 l 2804 4174 l 2811 4151 l 2816 4135 l 2822 4118 l 2829 4101 l 2836 4083 l 2843 4065 l 2852 4045 l 2860 4025 l 2870 4004 l 2880 3982 l 2891 3959 l 2902 3936 l 2914 3912 l 2927 3887 l 2940 3862 l 2953 3837 l 2967 3811 l 2982 3785 l 2996 3759 l 3011 3733 l 3027 3707 l 3042 3681 l 3058 3655 l 3074 3629 l 3090 3603 l 3107 3577 l 3124 3551 l 3138 3529 l 3152 3507 l 3167 3485 l 3182 3462 l 3198 3438 l 3214 3414 l 3231 3389 l 3248 3363 l 3266 3336 l 3284 3309 l 3302 3281 l 3321 3252 l 3340 3223 l 3359 3192 l 3378 3162 l 3397 3130 l 3416 3098 l 3435 3066 l 3454 3034 l 3472 3001 l 3490 2968 l 3508 2935 l 3526 2902 l 3543 2869 l 3559 2835 l 3575 2802 l 3591 2769 l 3606 2736 l 3620 2702 l 3634 2669 l 3648 2635 l 3661 2601 l 3672 2570 l 3683 2539 l 3694 2507 l 3705 2474 l 3715 2441 l 3725 2407 l 3734 2372 l 3743 2337 l 3752 2300 l 3761 2263 l 3769 2225 l 3777 2187 l 3784 2147 l 3791 2108 l 3797 2067 l 3803 2026 l 3808 1985 l 3812 1944 l 3816 1903 l 3819 1861 l 3822 1820 l 3823 1779 l 3824 1738 l 3825 1697 l 3824 1657 l 3823 1617 l 3822 1578 l 3819 1540 l 3816 1502 l 3812 1464 l 3807 1427 l 3802 1391 l 3796 1356 l 3789 1320 l 3782 1285 l 3774 1251 l 3765 1217 l 3755 1183 l 3744 1148 l 3732 1114 l 3720 1080 l 3707 1046 l 3692 1011 l 3677 977 l 3660 942 l 3642 907 l 3624 873 l 3604 838 l 3583 804 l 3561 769 l 3538 735 l 3515 702 l 3490 668 l 3464 636 l 3438 604 l 3411 572 l 3383 542 l 3354 512 l 3325 483 l 3295 455 l 3265 428 l 3235 402 l 3204 377 l 3173 354 l 3141 331 l 3109 309 l 3077 289 l 3045 269 l 3012 251 l 2979 233 l 2945 217 l 2911 201 l 2878 187 l 2845 173 l 2810 161 l 2775 149 l 2740 137 l 2703 127 l 2666 117 l 2627 107 l 2588 99 l 2548 91 l 2507 84 l 2466 78 l 2424 72 l 2381 67 l 2337 63 l 2294 60 l 2250 58 l 2205 57 l 2161 56 l 2117 57 l 2072 58 l 2028 60 l 1985 63 l 1941 67 l 1898 72 l 1856 78 l 1815 84 l 1774 91 l 1734 99 l 1695 107 l 1656 117 l 1619 127 l 1582 137 l 1547 149 l 1512 161 l 1477 173 l 1444 187 l 1411 201 l 1377 217 l 1343 233 l 1310 251 l 1277 269 l 1245 289 l 1213 309 l 1181 331 l 1149 354 l 1118 377 l 1087 402 l 1057 428 l 1027 455 l 997 483 l 968 512 l 939 542 l 911 572 l 884 604 l 858 636 l 832 668 l 807 702 l 784 735 l 761 769 l 739 804 l 718 838 l 698 873 l 680 907 l 662 942 l 645 977 l 630 1011 l 615 1046 l 602 1080 l 590 1114 l 578 1148 l 567 1183 l 557 1217 l 549 1251 l 540 1285 l 533 1320 l 526 1356 l 520 1391 l 515 1427 l 510 1464 l 506 1502 l 503 1540 l 500 1578 l 499 1617 l 498 1657 l 497 1697 l 498 1738 l 499 1779 l 500 1820 l 503 1861 l 506 1903 l 510 1944 l 514 1985 l 519 2026 l 525 2067 l 531 2108 l 538 2147 l 545 2187 l 553 2225 l 561 2263 l 570 2300 l 579 2337 l 588 2372 l 597 2407 l 607 2441 l 617 2474 l 628 2507 l 639 2539 l 650 2570 l 661 2601 l 674 2635 l 688 2669 l 702 2702 l 716 2736 l 731 2769 l 747 2802 l 763 2835 l 779 2869 l 796 2902 l 814 2935 l 832 2968 l 850 3001 l 868 3034 l 887 3066 l 906 3098 l 925 3130 l 944 3162 l 963 3192 l 982 3223 l 1001 3252 l 1020 3281 l 1038 3309 l 1056 3336 l 1074 3363 l 1091 3389 l 1108 3414 l 1124 3438 l 1140 3462 l 1155 3485 l 1170 3507 l 1184 3529 l 1199 3551 l 1215 3577 l 1232 3603 l 1248 3629 l 1264 3655 l 1280 3681 l 1295 3707 l 1311 3733 l 1326 3759 l 1340 3785 l 1355 3811 l 1369 3837 l 1382 3862 l 1395 3887 l 1408 3912 l 1420 3936 l 1431 3959 l 1442 3982 l 1452 4004 l 1462 4025 l 1470 4045 l 1479 4065 l 1486 4083 l 1493 4101 l 1500 4118 l 1506 4135 l 1511 4151 l 1518 4174 l 1525 4195 l 1530 4217 l 1535 4239 l 1540 4261 l 1543 4285 l 1547 4309 l 1550 4335 l 1552 4362 l 1555 4389 l 1557 4416 l 1558 4440 l 1559 4462 l 1560 4479 l 1561 4491 l 1561 4498 l 1561 4501 l gs col-1 s gr % Polyline 30.000 slw [15 45] 45 sd n 2236 3676 m 2234 3674 l 2231 3671 l 2225 3664 l 2215 3654 l 2201 3640 l 2183 3622 l 2161 3600 l 2136 3575 l 2108 3546 l 2077 3515 l 2045 3483 l 2012 3449 l 1979 3415 l 1946 3382 l 1914 3349 l 1883 3317 l 1853 3286 l 1825 3257 l 1798 3229 l 1772 3202 l 1748 3177 l 1725 3152 l 1703 3129 l 1682 3106 l 1662 3085 l 1642 3063 l 1623 3042 l 1604 3022 l 1586 3001 l 1566 2979 l 1547 2957 l 1527 2934 l 1508 2911 l 1488 2888 l 1469 2864 l 1449 2839 l 1429 2814 l 1410 2789 l 1390 2763 l 1371 2736 l 1352 2709 l 1333 2681 l 1314 2653 l 1296 2625 l 1278 2596 l 1262 2568 l 1245 2539 l 1230 2510 l 1215 2481 l 1201 2452 l 1187 2424 l 1175 2395 l 1163 2366 l 1152 2338 l 1142 2309 l 1132 2280 l 1124 2251 l 1116 2223 l 1108 2195 l 1102 2166 l 1095 2136 l 1090 2106 l 1084 2075 l 1079 2043 l 1075 2010 l 1071 1976 l 1068 1942 l 1065 1908 l 1063 1872 l 1061 1837 l 1061 1801 l 1060 1765 l 1061 1729 l 1061 1694 l 1063 1658 l 1065 1624 l 1068 1589 l 1071 1556 l 1075 1523 l 1079 1491 l 1084 1459 l 1090 1429 l 1095 1399 l 1102 1370 l 1108 1342 l 1116 1315 l 1124 1289 l 1132 1262 l 1141 1237 l 1150 1211 l 1160 1186 l 1171 1161 l 1183 1136 l 1196 1112 l 1209 1088 l 1223 1064 l 1238 1040 l 1254 1016 l 1271 993 l 1289 971 l 1307 948 l 1326 927 l 1346 906 l 1367 886 l 1388 867 l 1409 848 l 1432 830 l 1454 814 l 1477 798 l 1500 783 l 1524 769 l 1548 755 l 1572 743 l 1597 731 l 1622 721 l 1647 710 l 1674 701 l 1700 692 l 1728 684 l 1756 676 l 1785 669 l 1815 662 l 1846 656 l 1878 650 l 1911 645 l 1945 640 l 1980 636 l 2015 632 l 2050 629 l 2086 627 l 2123 625 l 2159 624 l 2196 623 l 2232 623 l 2268 623 l 2303 624 l 2338 625 l 2372 627 l 2405 630 l 2437 632 l 2469 636 l 2499 639 l 2528 643 l 2557 648 l 2584 653 l 2610 658 l 2636 664 l 2667 671 l 2697 679 l 2726 688 l 2755 697 l 2783 708 l 2811 719 l 2837 731 l 2864 743 l 2889 757 l 2914 771 l 2939 785 l 2962 801 l 2984 816 l 3005 833 l 3025 849 l 3045 866 l 3063 882 l 3079 899 l 3095 916 l 3110 933 l 3124 950 l 3137 967 l 3149 984 l 3161 1001 l 3173 1020 l 3185 1039 l 3196 1059 l 3208 1080 l 3218 1102 l 3229 1124 l 3239 1147 l 3249 1171 l 3258 1196 l 3267 1221 l 3276 1247 l 3284 1273 l 3291 1300 l 3298 1327 l 3305 1354 l 3310 1380 l 3316 1407 l 3321 1433 l 3325 1460 l 3329 1486 l 3333 1512 l 3336 1539 l 3339 1561 l 3341 1584 l 3343 1608 l 3345 1632 l 3347 1657 l 3348 1683 l 3349 1709 l 3350 1737 l 3350 1765 l 3350 1793 l 3349 1822 l 3349 1851 l 3347 1881 l 3345 1911 l 3343 1941 l 3340 1971 l 3337 2001 l 3333 2030 l 3329 2059 l 3324 2088 l 3319 2116 l 3313 2144 l 3307 2171 l 3301 2198 l 3294 2225 l 3286 2251 l 3278 2276 l 3270 2300 l 3261 2325 l 3252 2351 l 3242 2376 l 3231 2402 l 3220 2429 l 3207 2456 l 3194 2483 l 3181 2511 l 3167 2539 l 3152 2567 l 3136 2596 l 3120 2624 l 3104 2653 l 3087 2681 l 3070 2709 l 3053 2737 l 3035 2764 l 3017 2791 l 3000 2817 l 2982 2843 l 2964 2868 l 2946 2893 l 2928 2918 l 2910 2941 l 2892 2965 l 2874 2989 l 2856 3010 l 2839 3032 l 2820 3054 l 2802 3076 l 2782 3099 l 2762 3122 l 2741 3146 l 2719 3171 l 2695 3197 l 2670 3224 l 2643 3253 l 2616 3283 l 2586 3314 l 2555 3346 l 2524 3380 l 2491 3414 l 2458 3448 l 2426 3482 l 2394 3514 l 2364 3546 l 2336 3574 l 2310 3600 l 2289 3622 l 2271 3640 l 2257 3654 l 2247 3664 l 2241 3671 l 2238 3674 l 2236 3676 l cp gs col-1 s gr [] 0 sd % Polyline [15 45] 45 sd n 2311 2701 m 2310 2701 l 2306 2704 l 2297 2709 l 2283 2718 l 2266 2730 l 2248 2742 l 2231 2755 l 2216 2768 l 2203 2781 l 2192 2795 l 2182 2810 l 2174 2826 l 2168 2838 l 2162 2851 l 2157 2865 l 2152 2880 l 2147 2896 l 2142 2914 l 2138 2933 l 2134 2953 l 2130 2974 l 2127 2995 l 2125 3018 l 2123 3040 l 2121 3063 l 2121 3085 l 2120 3108 l 2121 3131 l 2122 3153 l 2124 3176 l 2125 3195 l 2128 3214 l 2130 3234 l 2134 3256 l 2138 3278 l 2142 3302 l 2148 3328 l 2154 3356 l 2161 3386 l 2169 3418 l 2177 3452 l 2186 3486 l 2195 3521 l 2204 3555 l 2212 3587 l 2219 3615 l 2226 3638 l 2230 3655 l 2233 3667 l 2235 3673 l 2236 3676 l gs col-1 s gr [] 0 sd % Polyline [15 90] 90 sd n 3136 3526 m 3136 3525 l 3137 3522 l 3139 3513 l 3142 3497 l 3147 3476 l 3152 3451 l 3157 3423 l 3162 3395 l 3167 3368 l 3170 3343 l 3173 3320 l 3175 3299 l 3176 3279 l 3176 3261 l 3175 3243 l 3174 3226 l 3171 3209 l 3168 3191 l 3163 3173 l 3158 3155 l 3152 3136 l 3145 3117 l 3136 3097 l 3127 3078 l 3118 3058 l 3107 3039 l 3096 3021 l 3085 3003 l 3073 2986 l 3061 2969 l 3049 2954 l 3036 2939 l 3024 2925 l 3012 2912 l 2999 2899 l 2985 2885 l 2971 2872 l 2955 2859 l 2939 2846 l 2922 2833 l 2904 2820 l 2886 2808 l 2867 2797 l 2849 2786 l 2830 2776 l 2811 2767 l 2792 2759 l 2774 2751 l 2755 2745 l 2736 2739 l 2719 2734 l 2701 2729 l 2682 2725 l 2662 2722 l 2640 2719 l 2617 2716 l 2592 2713 l 2564 2711 l 2534 2709 l 2503 2707 l 2470 2706 l 2437 2705 l 2406 2703 l 2377 2703 l 2353 2702 l 2334 2701 l 2322 2701 l 2314 2701 l 2311 2701 l gs col-1 s gr [] 0 sd /Symbol ff 390.00 scf sf 2040 5176 m gs 1 -1 sc (a) col-1 sh gr /Times-Roman ff 450.00 scf sf 2123 3886 m gs 1 -1 sc (*) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1153 3638 a FP(Figure)32 b(5.13.)40 b FQ(The)28 b(relation)f FJ(S)2233 3608 y FM(2)2293 3638 y FQ(=)22 b FJ(Z)2443 3608 y FE(\000)p FM(1)2532 3638 y FJ(B)2595 3650 y FI(\013;c)2688 3658 y FF(1)2724 3638 y FQ(.)612 3847 y FK(MF9:)41 b(Relation)30 b(for)j FJ(g)25 b FQ(=)e(1)p FJ(;)14 b(n)22 b FQ(=)h(2)p FK(:)40 b FQ(Let)e(\006)f(b)r(e)h(a)f(mark) n(ed)f(torus)h(with)g(t)n(w)n(o)g(holes)711 3947 y FJ(\013;)14 b(\014)t FQ(,)29 b(isomorphic)d(to)h(the)h(one)g(sho)n(wn)e(in)i (Figure)f(5.14.)36 b(Then)28 b(w)n(e)f(require)1092 4086 y FJ(Z)1155 4052 y FE(\000)p FM(1)1244 4086 y FJ(B)1307 4098 y FI(\013;\014)1415 4086 y FJ(F)1480 4052 y FE(\000)p FM(1)1468 4106 y FI(c)1498 4114 y FF(6)1569 4086 y FJ(F)1622 4098 y FI(c)1652 4106 y FF(1)1711 4086 y FQ(=)c FJ(S)1855 4052 y FE(\000)p FM(1)1944 4086 y FJ(F)2009 4052 y FE(\000)p FM(1)1997 4106 y FI(c)2027 4114 y FF(6)2098 4086 y FJ(F)2151 4098 y FI(c)2181 4106 y FF(4)2218 4086 y FJ(T)2267 4098 y FI(c)2297 4106 y FF(3)2332 4086 y FJ(T)2393 4052 y FE(\000)p FM(1)2381 4106 y FI(c)2411 4114 y FF(4)2481 4086 y FJ(F)2546 4052 y FE(\000)p FM(1)2534 4106 y FI(c)2564 4114 y FF(4)2635 4086 y FJ(F)2688 4098 y FI(c)2718 4106 y FF(5)2755 4086 y FJ(S)5 b(F)2876 4052 y FE(\000)p FM(1)2864 4106 y FI(c)2894 4114 y FF(5)2965 4086 y FJ(F)3018 4098 y FI(c)3048 4106 y FF(2)456 4086 y FQ(\(5.2.12\))711 4226 y(|)26 b(see)f(Figure)g(5.15,)g(where)g(all)h(unmark)n(ed)e(arro)n (ws)g(are)g(comp)r(ositions)h(of)h(the)g(form)711 4325 y FJ(F)12 b(F)841 4295 y FE(\000)p FM(1)958 4325 y FQ(\(see)27 b(also)g([)p FK(BK)p FQ(,)g(App)r(endix)i(B]\).)605 4445 y(Note)34 b(that,)h(b)n(y)f(their)f(construction,)i(the)f(ab)r(o)n(v)n (e)e(relations)g(are)h(in)n(v)-5 b(arian)n(t)33 b(under)g(the)456 4544 y(action)27 b(of)g(the)h(mapping)g(class)e(group.)605 4697 y FP(Remark)32 b FQ(5.2.7)p FP(.)39 b FQ(It)29 b(is)f(not)g (trivial)g(that)g(relations)f(\(5.2.11,)g(5.2.12\))g(mak)n(e)g(sense,)h (i.e.,)456 4796 y(that)d(they)h(are)e(indeed)i(closed)e(paths)i(in)f FL(M)p FQ(\(\006\).)37 b(This)25 b(is)g(equiv)-5 b(alen)n(t)25 b(to)g(c)n(hec)n(king)f(that)i(the)456 4896 y(corresp)r(onding)j(iden)n (tities)j(hold)f(in)h(the)g(mapping)f(class)g(group)f(\000\(\006\).)49 b(This)32 b(is)f(indeed)h(so)456 4996 y(\(see,)27 b(e.g.,)f([)p FK(B1,)31 b(MS2)o FQ(]\).)37 b(Of)27 b(course,)f(these)h(relations)e (can)i(also)f(b)r(e)h(c)n(hec)n(k)n(ed)f(b)n(y)g(explicitly)456 5095 y(dra)n(wing)e(the)i(corresp)r(onding)e(sequence)h(of)g(cuts)h (and)f(graphs)g(and)g(c)n(hec)n(king)g(that)h(the)g(\014nal)456 5195 y(one)h(coincides)g(with)h(the)g(original)e(one,)h(as)g(done)g(in) h([)p FK(BK)p FQ(].)p eop %%Page: 105 13 105 108 bop 1599 226 a FM(5.2.)29 b(THE)g(LEGO)g(GAME)1021 b(105)1488 1185 y @beginspecial 0 @llx 0 @lly 111 @urx 96 @ury 1110 @rwi @setspecial %%BeginDocument: figures/g1n2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: b1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Wed Aug 12 19:17:59 1998 %%For: shurik@localhost.localdomain (Alexander Kirillov,,,) %%Orientation: Portrait %%BoundingBox: 0 0 111 96 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -50.0 131.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7601 m -1000 -1000 l 9116 -1000 l 9116 7601 l cp clip 0.01980 0.01980 sc % Arc 15.000 slw gs n 3537.5 4200.0 912.5 -138.9 138.9 arcn gs col-1 s gr gr % Arc gs n 8637.5 4200.0 912.5 -138.9 138.9 arcn gs col-1 s gr gr % Arc gs [120] 0 sd n 1725.0 4200.0 1275.0 -28.1 28.1 arc gs col-1 s gr gr [] 0 sd % Arc gs n 6825.0 4200.0 1275.0 -28.1 28.1 arc gs col-1 s gr gr % Arc gs n 6087.5 3000.0 912.5 -138.9 138.9 arcn gs col-1 s gr gr % Arc gs [120] 0 sd n 4275.0 3000.0 1275.0 -28.1 28.1 arc gs col-1 s gr gr [] 0 sd % Arc gs [120] 0 sd n 4275.0 5400.0 1275.0 -28.1 28.1 arc gs col-1 s gr gr [] 0 sd % Arc gs n 6087.5 5400.0 912.5 -138.9 138.9 arcn gs col-1 s gr gr % Ellipse n 5400 4200 586 586 0 360 DrawEllipse gs col-1 s gr 7.500 slw % Ellipse n 2625 4200 70 70 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 7725 4200 70 70 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 5175 5400 70 70 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 5175 3000 70 70 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr 30.000 slw [15 75] 75 sd 1 slc % Ellipse n 5400 4200 1209 1209 0 360 DrawEllipse gs col-1 s gr [] 0 sd % Polyline 0 slc [15 45] 45 sd gs clippath 7383 4140 m 7671 4200 l 7383 4260 l 7770 4260 l 7770 4140 l cp clip n 6600 4200 m 7725 4200 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 7383 4140 m 7671 4200 l 7383 4260 l 7431 4200 l 7383 4140 l cp gs 0.00 setgray ef gr col-1 s % Polyline 30.000 slw [15 45] 45 sd gs clippath 2967 4260 m 2679 4200 l 2967 4140 l 2580 4140 l 2580 4260 l cp clip n 2625 4200 m 4200 4200 l gs col-1 s gr gr [] 0 sd % arrowhead 15.000 slw n 2967 4260 m 2679 4200 l 2967 4140 l 2919 4200 l 2967 4260 l cp gs 0.00 setgray ef gr col-1 s % Polyline 0.000 slw n 5100 1800 m 5775 1800 l % Polyline n 5175 6600 m 5850 6600 l % Polyline 15.000 slw n 2850 3600 m 2853 3600 l 2858 3600 l 2868 3600 l 2883 3601 l 2903 3601 l 2927 3602 l 2956 3602 l 2988 3603 l 3023 3604 l 3057 3604 l 3092 3605 l 3125 3605 l 3157 3605 l 3186 3605 l 3213 3605 l 3238 3604 l 3260 3603 l 3281 3602 l 3300 3600 l 3323 3597 l 3345 3594 l 3366 3591 l 3386 3588 l 3405 3584 l 3424 3581 l 3442 3577 l 3461 3573 l 3478 3569 l 3496 3565 l 3514 3560 l 3531 3554 l 3549 3548 l 3566 3542 l 3583 3534 l 3600 3525 l 3616 3515 l 3631 3504 l 3646 3493 l 3660 3481 l 3673 3469 l 3685 3456 l 3697 3443 l 3709 3430 l 3721 3417 l 3733 3403 l 3746 3388 l 3760 3373 l 3774 3356 l 3790 3339 l 3807 3320 l 3825 3300 l 3838 3286 l 3851 3270 l 3865 3254 l 3879 3237 l 3893 3219 l 3907 3201 l 3922 3182 l 3937 3162 l 3952 3141 l 3967 3121 l 3983 3100 l 3998 3079 l 4014 3057 l 4030 3036 l 4046 3015 l 4062 2995 l 4078 2975 l 4095 2955 l 4112 2936 l 4129 2917 l 4146 2900 l 4163 2882 l 4181 2866 l 4200 2850 l 4219 2835 l 4238 2820 l 4258 2805 l 4279 2791 l 4299 2777 l 4320 2764 l 4341 2750 l 4362 2737 l 4383 2724 l 4405 2711 l 4427 2699 l 4448 2686 l 4470 2674 l 4492 2661 l 4515 2649 l 4537 2637 l 4560 2625 l 4582 2614 l 4605 2602 l 4629 2591 l 4652 2580 l 4676 2570 l 4700 2560 l 4725 2550 l 4748 2542 l 4772 2533 l 4796 2526 l 4821 2518 l 4846 2511 l 4871 2503 l 4897 2496 l 4923 2489 l 4949 2482 l 4975 2475 l 5002 2468 l 5029 2461 l 5055 2454 l 5082 2447 l 5109 2441 l 5136 2435 l 5163 2429 l 5190 2424 l 5216 2419 l 5243 2414 l 5269 2410 l 5296 2407 l 5322 2404 l 5348 2402 l 5374 2400 l 5400 2400 l 5426 2400 l 5452 2402 l 5478 2404 l 5504 2407 l 5531 2410 l 5557 2414 l 5584 2419 l 5610 2424 l 5637 2429 l 5664 2435 l 5691 2441 l 5718 2447 l 5745 2454 l 5771 2461 l 5798 2468 l 5825 2475 l 5851 2482 l 5877 2489 l 5903 2496 l 5929 2503 l 5954 2511 l 5979 2518 l 6004 2526 l 6028 2533 l 6052 2542 l 6075 2550 l 6100 2560 l 6124 2570 l 6148 2580 l 6171 2591 l 6195 2602 l 6218 2614 l 6240 2625 l 6263 2637 l 6285 2649 l 6308 2661 l 6330 2674 l 6352 2686 l 6373 2699 l 6395 2711 l 6417 2724 l 6438 2737 l 6459 2750 l 6480 2764 l 6501 2777 l 6521 2791 l 6542 2805 l 6562 2820 l 6581 2835 l 6600 2850 l 6619 2866 l 6637 2882 l 6654 2900 l 6671 2917 l 6688 2936 l 6705 2955 l 6722 2975 l 6738 2995 l 6754 3015 l 6770 3036 l 6786 3057 l 6802 3079 l 6817 3100 l 6833 3121 l 6848 3141 l 6863 3162 l 6878 3182 l 6893 3201 l 6907 3219 l 6921 3237 l 6935 3254 l 6949 3270 l 6962 3286 l 6975 3300 l 6993 3320 l 7010 3339 l 7026 3356 l 7040 3373 l 7054 3388 l 7067 3403 l 7079 3417 l 7091 3430 l 7103 3443 l 7115 3456 l 7127 3469 l 7140 3481 l 7154 3493 l 7169 3504 l 7184 3515 l 7200 3525 l 7217 3534 l 7234 3542 l 7251 3548 l 7269 3554 l 7286 3560 l 7304 3565 l 7322 3569 l 7339 3573 l 7358 3577 l 7376 3581 l 7395 3584 l 7414 3588 l 7434 3591 l 7455 3594 l 7477 3597 l 7500 3600 l 7519 3602 l 7540 3603 l 7562 3604 l 7587 3605 l 7614 3605 l 7643 3605 l 7675 3605 l 7708 3605 l 7743 3604 l 7778 3604 l 7812 3603 l 7844 3602 l 7873 3602 l 7897 3601 l 7917 3601 l 7932 3600 l 7942 3600 l 7947 3600 l 7950 3600 l gs col-1 s gr % Polyline n 2850 4800 m 2853 4800 l 2858 4800 l 2868 4800 l 2883 4799 l 2903 4799 l 2927 4798 l 2956 4798 l 2988 4797 l 3023 4796 l 3057 4796 l 3092 4795 l 3125 4795 l 3157 4795 l 3186 4795 l 3213 4795 l 3238 4796 l 3260 4797 l 3281 4798 l 3300 4800 l 3323 4803 l 3345 4806 l 3366 4809 l 3386 4812 l 3405 4816 l 3424 4819 l 3442 4823 l 3461 4827 l 3478 4831 l 3496 4835 l 3514 4840 l 3531 4846 l 3549 4852 l 3566 4858 l 3583 4866 l 3600 4875 l 3616 4885 l 3631 4896 l 3646 4907 l 3660 4919 l 3673 4931 l 3685 4944 l 3697 4957 l 3709 4970 l 3721 4983 l 3733 4997 l 3746 5012 l 3760 5027 l 3774 5044 l 3790 5061 l 3807 5080 l 3825 5100 l 3838 5114 l 3851 5130 l 3865 5146 l 3879 5163 l 3893 5181 l 3907 5199 l 3922 5218 l 3937 5238 l 3952 5259 l 3967 5279 l 3983 5300 l 3998 5321 l 4014 5343 l 4030 5364 l 4046 5385 l 4062 5405 l 4078 5425 l 4095 5445 l 4112 5464 l 4129 5483 l 4146 5500 l 4163 5518 l 4181 5534 l 4200 5550 l 4219 5565 l 4238 5580 l 4258 5595 l 4279 5609 l 4299 5623 l 4320 5636 l 4341 5650 l 4362 5663 l 4383 5676 l 4405 5689 l 4427 5701 l 4448 5714 l 4470 5726 l 4492 5739 l 4515 5751 l 4537 5763 l 4560 5775 l 4582 5786 l 4605 5798 l 4629 5809 l 4652 5820 l 4676 5830 l 4700 5840 l 4725 5850 l 4748 5858 l 4772 5867 l 4796 5874 l 4821 5882 l 4846 5889 l 4871 5897 l 4897 5904 l 4923 5911 l 4949 5918 l 4975 5925 l 5002 5932 l 5029 5939 l 5055 5946 l 5082 5953 l 5109 5959 l 5136 5965 l 5163 5971 l 5190 5976 l 5216 5981 l 5243 5986 l 5269 5990 l 5296 5993 l 5322 5996 l 5348 5998 l 5374 6000 l 5400 6000 l 5426 6000 l 5452 5998 l 5478 5996 l 5504 5993 l 5531 5990 l 5557 5986 l 5584 5981 l 5610 5976 l 5637 5971 l 5664 5965 l 5691 5959 l 5718 5953 l 5745 5946 l 5771 5939 l 5798 5932 l 5825 5925 l 5851 5918 l 5877 5911 l 5903 5904 l 5929 5897 l 5954 5889 l 5979 5882 l 6004 5874 l 6028 5867 l 6052 5858 l 6075 5850 l 6100 5840 l 6124 5830 l 6148 5820 l 6171 5809 l 6195 5798 l 6218 5786 l 6240 5775 l 6263 5763 l 6285 5751 l 6308 5739 l 6330 5726 l 6352 5714 l 6373 5701 l 6395 5689 l 6417 5676 l 6438 5663 l 6459 5650 l 6480 5636 l 6501 5623 l 6521 5609 l 6542 5595 l 6562 5580 l 6581 5565 l 6600 5550 l 6619 5534 l 6637 5518 l 6654 5500 l 6671 5483 l 6688 5464 l 6705 5445 l 6722 5425 l 6738 5405 l 6754 5385 l 6770 5364 l 6786 5343 l 6802 5321 l 6817 5300 l 6833 5279 l 6848 5259 l 6863 5238 l 6878 5218 l 6893 5199 l 6907 5181 l 6921 5163 l 6935 5146 l 6949 5130 l 6962 5114 l 6975 5100 l 6993 5080 l 7010 5061 l 7026 5044 l 7040 5027 l 7054 5012 l 7067 4997 l 7079 4983 l 7091 4970 l 7103 4957 l 7115 4944 l 7127 4931 l 7140 4919 l 7154 4907 l 7169 4896 l 7184 4885 l 7200 4875 l 7217 4866 l 7234 4858 l 7251 4852 l 7269 4846 l 7286 4840 l 7304 4835 l 7322 4831 l 7339 4827 l 7358 4823 l 7376 4819 l 7395 4816 l 7414 4812 l 7434 4809 l 7455 4806 l 7477 4803 l 7500 4800 l 7519 4798 l 7540 4797 l 7562 4796 l 7587 4795 l 7614 4795 l 7643 4795 l 7675 4795 l 7708 4795 l 7743 4796 l 7778 4796 l 7812 4797 l 7844 4798 l 7873 4798 l 7897 4799 l 7917 4799 l 7932 4800 l 7942 4800 l 7947 4800 l 7950 4800 l gs col-1 s gr /Times-Roman ff 495.00 scf sf 6510 4440 m gs 1 -1 sc (*) col-1 sh gr /Times-Roman ff 495.00 scf sf 4080 4440 m gs 1 -1 sc (*) col-1 sh gr /Times-Roman ff 210.00 scf sf 5475 2250 m gs 1 -1 sc (1) col-1 sh gr /Times-Italic ff 360.00 scf sf 5325 2175 m gs 1 -1 sc (c) col-1 sh gr /Times-Italic ff 360.00 scf sf 5325 6450 m gs 1 -1 sc (c) col-1 sh gr /Times-Roman ff 210.00 scf sf 5475 6525 m gs 1 -1 sc (2) col-1 sh gr /Symbol ff 345.00 scf sf 7800 5250 m gs 1 -1 sc (b) col-1 sh gr /Symbol ff 345.00 scf sf 2775 5250 m gs 1 -1 sc (a) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1102 1386 a FP(Figure)32 b(5.14.)40 b FQ(A)28 b(mark)n(ed)f(torus)g(with)h(t)n(w)n(o)f(holes.)951 3583 y @beginspecial 0 @llx 0 @lly 273 @urx 244 @ury 2730 @rwi @setspecial %%BeginDocument: figures/g1n2max.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2max.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Jun 10 17:06:21 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 273 244 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2800 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -118.0 265.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /reencdict 12 dict def /ReEncode { reencdict begin /newcodesandnames exch def /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName newfontname put newcodesandnames aload pop 128 1 255 { newfont /Encoding get exch /.notdef put } for newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat newfontname newfont definefont pop end } def /isovec [ 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde 8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis 8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron 8#220 /dotlessi 8#230 /oe 8#231 /OE 8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling 8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis 8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot 8#255 /endash 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus 8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph 8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine 8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf 8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute 8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring 8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute 8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute 8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve 8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply 8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex 8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave 8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring 8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute 8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute 8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve 8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide 8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex 8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def /Times-Italic /Times-Italic-iso isovec ReEncode /Times-Roman /Times-Roman-iso isovec ReEncode /Times-Roman /Times-Roman-iso isovec ReEncode /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 16746 m -1000 -1000 l 24231 -1000 l 24231 16746 l cp clip 0.01680 0.01680 sc 30.000 slw % Ellipse n 9482 3698 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 9482 2163 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 7579 2931 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 11490 2947 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Polyline [15 45] 45 sd gs clippath 11135 2876 m 11423 2936 l 11135 2996 l 11522 2996 l 11522 2876 l cp clip n 10284 2936 m 11477 2936 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 11135 2876 m 11423 2936 l 11135 2996 l 11183 2936 l 11135 2876 l cp gs 0.00 setgray ef gr col0 s % Polyline 30.000 slw [15 45] 45 sd gs clippath 7957 2981 m 7669 2921 l 7957 2861 l 7570 2861 l 7570 2981 l cp clip n 7615 2921 m 8642 2921 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 7957 2981 m 7669 2921 l 7957 2861 l 7909 2921 l 7957 2981 l cp gs 0.00 setgray ef gr col0 s /Times-Italic-iso ff 420.00 scf sf 9549 4009 m gs 1 -1 sc (c) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 9549 2036 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 10120 3154 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 8597 3154 m gs 1 -1 sc (*) col0 sh gr /Symbol ff 450.00 scf sf 7524 2809 m gs 1 -1 sc (a) col0 sh gr /Symbol ff 450.00 scf sf 11303 2778 m gs 1 -1 sc (b) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 9735 2133 m gs 1 -1 sc (1) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 9720 4098 m gs 1 -1 sc (2) col0 sh gr % Arc 30.000 slw gs [15 45] 45 sd n 15548.0 3635.0 767.4 83.9 96.2 arcn gs col0 s gr gr [] 0 sd % Rotated Ellipse gs 15540 4391 tr -180.000 rot n 0 0 50 50 0 360 DrawEllipse 180.000 rot gs 0.00 setgray ef gr gs col0 s gr gr % Rotated Ellipse gs 17073 1691 tr -180.000 rot n 0 0 50 50 0 360 DrawEllipse 180.000 rot gs 0.00 setgray ef gr gs col0 s gr gr % Rotated Ellipse gs 14000 1713 tr -180.000 rot n 0 0 50 50 0 360 DrawEllipse 180.000 rot gs 0.00 setgray ef gr gs col0 s gr gr % Rotated Ellipse gs 15546 2246 tr -180.000 rot n 0 0 50 50 0 360 DrawEllipse 180.000 rot gs 0.00 setgray ef gr gs col0 s gr gr % Polyline [15 45] 45 sd gs clippath 14383 1776 m 14093 1718 l 14381 1656 l 13994 1659 l 13996 1779 l cp clip n 17025 1689 m 14040 1719 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 14383 1776 m 14093 1718 l 14381 1656 l 14334 1716 l 14383 1776 l cp gs 0.00 setgray ef gr col0 s % Polyline 30.000 slw [15 45] 45 sd gs clippath 15496 2607 m 15557 2318 l 15616 2607 l 15618 2220 l 15498 2220 l cp clip n 15555 2814 m 15558 2265 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 15496 2607 m 15557 2318 l 15616 2607 l 15556 2559 l 15496 2607 l cp gs 0.00 setgray ef gr col0 s % Polyline 30.000 slw [15 45] 45 sd n 15557 2244 m 15560 1695 l gs col0 s gr [] 0 sd /Times-Italic-iso ff 450.00 scf sf 15449 4728 m gs 1 -1 sc (c) col0 sh gr /Symbol ff 450.00 scf sf 17271 1826 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 450.00 scf sf 13543 1795 m gs 1 -1 sc (a) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 15427 1968 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 15420 3138 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 15649 4818 m gs 1 -1 sc (2) col0 sh gr % Arc gs [15 45] 45 sd n 8968.5 13568.8 767.2 -96.2 -83.8 arcn gs col0 s gr gr [] 0 sd % Ellipse n 8976 12813 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 8951 14958 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 7443 15513 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 10516 15491 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Polyline [15 45] 45 sd gs clippath 7834 15572 m 7544 15514 l 7832 15452 l 7445 15455 l 7447 15575 l cp clip n 7491 15515 m 10476 15485 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 7834 15572 m 7544 15514 l 7832 15452 l 7785 15512 l 7834 15572 l cp gs 0.00 setgray ef gr col0 s % Polyline 30.000 slw [15 45] 45 sd n 8958 14970 m 8961 15500 l gs col0 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 9017 14598 m 8957 14886 l 8897 14598 l 8898 14985 l 9018 14985 l cp clip n 8957 14325 m 8958 14940 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 9017 14598 m 8957 14886 l 8897 14598 l 8958 14646 l 9017 14598 l cp gs 0.00 setgray ef gr col0 s /Times-Roman-iso ff 510.00 scf sf 8856 15746 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 8856 14591 m gs 1 -1 sc (*) col0 sh gr /Symbol ff 450.00 scf sf 10700 15641 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 450.00 scf sf 7070 15641 m gs 1 -1 sc (a) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 9073 12626 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 9236 12723 m gs 1 -1 sc (3) col0 sh gr /Times-Italic-iso ff 420.00 scf sf 14419 15090 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 14590 15179 m gs 1 -1 sc (4) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 17389 13564 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 17575 13661 m gs 1 -1 sc (3) col0 sh gr /Times-Italic-iso ff 420.00 scf sf 18248 13661 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 18419 13750 m gs 1 -1 sc (4) col0 sh gr % Arc 30.000 slw gs [15 45] 45 sd n 21038.5 14037.8 767.2 -96.2 -83.8 arcn gs col0 s gr gr [] 0 sd % Ellipse n 21046 14817 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 21046 13282 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 19143 14050 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 23054 14066 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Polyline [15 45] 45 sd gs clippath 22699 13995 m 22987 14055 l 22699 14115 l 23086 14115 l 23086 13995 l cp clip n 21848 14055 m 23041 14055 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 22699 13995 m 22987 14055 l 22699 14115 l 22747 14055 l 22699 13995 l cp gs 0.00 setgray ef gr col0 s % Polyline 30.000 slw [15 45] 45 sd gs clippath 19521 14100 m 19233 14040 l 19521 13980 l 19134 13980 l 19134 14100 l cp clip n 19179 14040 m 20206 14040 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 19521 14100 m 19233 14040 l 19521 13980 l 19473 14040 l 19521 14100 l cp gs 0.00 setgray ef gr col0 s /Times-Italic-iso ff 420.00 scf sf 21113 15128 m gs 1 -1 sc (c) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 21113 13155 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 21684 14273 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 20161 14273 m gs 1 -1 sc (*) col0 sh gr /Symbol ff 450.00 scf sf 19088 13928 m gs 1 -1 sc (a) col0 sh gr /Symbol ff 450.00 scf sf 22867 13897 m gs 1 -1 sc (b) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 21299 13252 m gs 1 -1 sc (3) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 21284 15217 m gs 1 -1 sc (4) col0 sh gr % Arc 30.000 slw gs [15 45] 45 sd n 14344.5 13999.8 767.2 -96.2 -83.8 arcn gs col0 s gr gr [] 0 sd % Ellipse n 14352 14779 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 14352 13244 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 12449 14012 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 16360 14028 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Polyline gs clippath 11754 13841 m 11933 13931 l 11754 14021 l 12019 14021 l 12019 13841 l cp clip n 10444 13931 m 11044 13931 l 11149 13826 l 11359 14036 l 11569 13826 l 11674 13931 l 11974 13931 l gs col0 s gr gr % arrowhead n 11754 13841 m 11933 13931 l 11754 14021 l col0 s % Polyline gs clippath 18544 13972 m 18723 14062 l 18544 14152 l 18809 14152 l 18809 13972 l cp clip n 17234 14062 m 17834 14062 l 17939 13957 l 18149 14167 l 18359 13957 l 18464 14062 l 18764 14062 l gs col0 s gr gr % arrowhead n 18544 13972 m 18723 14062 l 18544 14152 l col0 s % Polyline [15 45] 45 sd gs clippath 16005 13957 m 16293 14017 l 16005 14077 l 16392 14077 l 16392 13957 l cp clip n 15154 14017 m 16347 14017 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 16005 13957 m 16293 14017 l 16005 14077 l 16053 14017 l 16005 13957 l cp gs 0.00 setgray ef gr col0 s % Polyline 30.000 slw [15 45] 45 sd gs clippath 12827 14062 m 12539 14002 l 12827 13942 l 12440 13942 l 12440 14062 l cp clip n 12485 14002 m 13512 14002 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 12827 14062 m 12539 14002 l 12827 13942 l 12779 14002 l 12827 14062 l cp gs 0.00 setgray ef gr col0 s % Arc 30.000 slw gs [15 45] 45 sd n 9474.5 2918.8 767.2 -96.2 -83.8 arcn gs col0 s gr gr [] 0 sd /Times-Italic-iso ff 480.00 scf sf 17221 13444 m gs 1 -1 sc (T) col0 sh gr /Times-Italic-iso ff 480.00 scf sf 17550 2869 m gs 1 -1 sc (Z) col0 sh gr /Times-Italic-iso ff 480.00 scf sf 18070 13481 m gs 1 -1 sc (T) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 14990 14235 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 13467 14235 m gs 1 -1 sc (*) col0 sh gr /Symbol ff 450.00 scf sf 12394 13890 m gs 1 -1 sc (a) col0 sh gr /Symbol ff 450.00 scf sf 16173 13859 m gs 1 -1 sc (b) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 14605 13214 m gs 1 -1 sc (3) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 14419 13117 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 360.00 scf sf 18468 13264 m gs 1 -1 sc (-1) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 9128 7020 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 9291 7117 m gs 1 -1 sc (1) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 21655 9592 m gs 1 -1 sc (6) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 21492 9495 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 21465 2392 m gs 1 -1 sc (6) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 21302 2295 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 15915 2392 m gs 1 -1 sc (6) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 15752 2295 m gs 1 -1 sc (c) col0 sh gr % Arc gs [15 45] 45 sd n 21023.0 3598.0 767.4 83.9 96.2 arcn gs col0 s gr gr [] 0 sd % Rotated Ellipse gs 21015 4354 tr -180.000 rot n 0 0 50 50 0 360 DrawEllipse 180.000 rot gs 0.00 setgray ef gr gs col0 s gr gr % Rotated Ellipse gs 22548 1654 tr -180.000 rot n 0 0 50 50 0 360 DrawEllipse 180.000 rot gs 0.00 setgray ef gr gs col0 s gr gr % Rotated Ellipse gs 19475 1676 tr -180.000 rot n 0 0 50 50 0 360 DrawEllipse 180.000 rot gs 0.00 setgray ef gr gs col0 s gr gr % Rotated Ellipse gs 21021 2209 tr -180.000 rot n 0 0 50 50 0 360 DrawEllipse 180.000 rot gs 0.00 setgray ef gr gs col0 s gr gr % Polyline [15 45] 45 sd gs clippath 20971 2577 m 21032 2288 l 21091 2577 l 21093 2190 l 20973 2190 l cp clip n 21030 2777 m 21033 2235 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 20971 2577 m 21032 2288 l 21091 2577 l 21031 2529 l 20971 2577 l cp gs 0.00 setgray ef gr col0 s % Polyline 30.000 slw [15 45] 45 sd n 21032 2177 m 21035 1635 l gs col0 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 22158 1594 m 22446 1654 l 22158 1714 l 22545 1715 l 22545 1595 l cp clip n 19500 1649 m 22500 1655 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 22158 1594 m 22446 1654 l 22158 1714 l 22206 1654 l 22158 1594 l cp gs 0.00 setgray ef gr col0 s /Times-Italic-iso ff 450.00 scf sf 20924 4691 m gs 1 -1 sc (c) col0 sh gr /Symbol ff 450.00 scf sf 22648 1586 m gs 1 -1 sc (a) col0 sh gr /Symbol ff 450.00 scf sf 19146 1729 m gs 1 -1 sc (b) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 20924 4691 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 20902 1931 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 20895 3101 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 21124 4804 m gs 1 -1 sc (2) col0 sh gr % Arc 30.000 slw gs [15 45] 45 sd n 9023.5 7962.8 767.2 -96.2 -83.8 arcn gs col0 s gr gr [] 0 sd % Arc gs [15 45] 45 sd n 21284.5 8056.8 767.2 -96.2 -83.8 arcn gs col0 s gr gr [] 0 sd % Ellipse n 9031 7207 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 9006 9352 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 7498 9907 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 10571 9885 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 21292 7301 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 21267 9446 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 19759 10001 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 22832 9979 50 50 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Polyline gs clippath 13329 2929 m 13508 3019 l 13329 3109 l 13594 3109 l 13594 2929 l cp clip n 12019 3019 m 12619 3019 l 12724 2914 l 12934 3124 l 13144 2914 l 13249 3019 l 13549 3019 l gs col0 s gr gr % arrowhead n 13329 2929 m 13508 3019 l 13329 3109 l col0 s % Polyline gs clippath 18635 3229 m 18814 3319 l 18635 3409 l 18900 3409 l 18900 3229 l cp clip n 17325 3319 m 17925 3319 l 18030 3214 l 18240 3424 l 18450 3214 l 18555 3319 l 18855 3319 l gs col0 s gr gr % arrowhead n 18635 3229 m 18814 3319 l 18635 3409 l col0 s % Polyline gs clippath 20924 5321 m 21014 5140 l 21104 5321 l 21104 5055 l 20924 5055 l cp clip n 21014 6630 m 21014 6030 l 20909 5925 l 21119 5715 l 20909 5505 l 21014 5400 l 21014 5100 l gs col0 s gr gr % arrowhead n 20924 5321 m 21014 5140 l 21104 5321 l col0 s % Polyline gs clippath 9063 11767 m 8973 11946 l 8883 11767 l 8883 12032 l 9063 12032 l cp clip n 8973 10457 m 8973 11057 l 9078 11162 l 8868 11372 l 9078 11582 l 8973 11687 l 8973 11987 l gs col0 s gr gr % arrowhead n 9063 11767 m 8973 11946 l 8883 11767 l col0 s % Polyline gs clippath 9215 5930 m 9125 6109 l 9035 5930 l 9035 6195 l 9215 6195 l cp clip n 9125 4620 m 9125 5220 l 9230 5325 l 9020 5535 l 9230 5745 l 9125 5850 l 9125 6150 l gs col0 s gr gr % arrowhead n 9215 5930 m 9125 6109 l 9035 5930 l col0 s % Polyline gs clippath 21069 10966 m 21159 10785 l 21249 10966 l 21249 10700 l 21069 10700 l cp clip n 21159 12275 m 21159 11675 l 21054 11570 l 21264 11360 l 21054 11150 l 21159 11045 l 21159 10745 l gs col0 s gr gr % arrowhead n 21069 10966 m 21159 10785 l 21249 10966 l col0 s % Polyline [15 45] 45 sd gs clippath 7889 9966 m 7599 9908 l 7887 9846 l 7500 9849 l 7502 9969 l cp clip n 7546 9909 m 10531 9879 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 7889 9966 m 7599 9908 l 7887 9846 l 7840 9906 l 7889 9966 l cp gs 0.00 setgray ef gr col0 s % Polyline 30.000 slw [15 45] 45 sd gs clippath 9076 8946 m 9016 9234 l 8956 8946 l 8956 9333 l 9076 9333 l cp clip n 9016 8784 m 9016 9288 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 9076 8946 m 9016 9234 l 8956 8946 l 9016 8994 l 9076 8946 l cp gs 0.00 setgray ef gr col0 s % Polyline 30.000 slw [15 45] 45 sd n 9016 9376 m 9016 9880 l gs col0 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 20150 10060 m 19860 10002 l 20148 9940 l 19761 9943 l 19763 10063 l cp clip n 19807 10003 m 22792 9973 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 20150 10060 m 19860 10002 l 20148 9940 l 20101 10000 l 20150 10060 l cp gs 0.00 setgray ef gr col0 s % Polyline 30.000 slw [15 45] 45 sd n 21273 9495 m 21277 9988 l gs col0 s gr [] 0 sd % Polyline [15 45] 45 sd gs clippath 21347 9031 m 21289 9319 l 21227 9031 l 21230 9418 l 21350 9418 l cp clip n 21286 8880 m 21290 9373 l gs col0 s gr gr [] 0 sd % arrowhead 15.000 slw n 21347 9031 m 21289 9319 l 21227 9031 l 21288 9079 l 21347 9031 l cp gs 0.00 setgray ef gr col0 s /Times-Italic-iso ff 480.00 scf sf 21444 6000 m gs 1 -1 sc (S) col0 sh gr /Times-Roman-iso ff 360.00 scf sf 21782 5813 m gs 1 -1 sc (-1) col0 sh gr /Times-Italic-iso ff 480.00 scf sf 9363 11331 m gs 1 -1 sc (S) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 8911 10140 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 8911 8985 m gs 1 -1 sc (*) col0 sh gr /Symbol ff 450.00 scf sf 10755 10035 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 450.00 scf sf 7125 10035 m gs 1 -1 sc (a) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 21172 10234 m gs 1 -1 sc (*) col0 sh gr /Times-Roman-iso ff 510.00 scf sf 21172 9079 m gs 1 -1 sc (*) col0 sh gr /Symbol ff 450.00 scf sf 23016 10129 m gs 1 -1 sc (b) col0 sh gr /Symbol ff 450.00 scf sf 19386 10129 m gs 1 -1 sc (a) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 21552 7211 m gs 1 -1 sc (3) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 21389 7114 m gs 1 -1 sc (c) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 9317 9395 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 9480 9492 m gs 1 -1 sc (5) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 9142 14995 m gs 1 -1 sc (c) col0 sh gr /Times-Roman-iso ff 240.00 scf sf 9305 15092 m gs 1 -1 sc (5) col0 sh gr /Times-Roman-iso ff 360.00 scf sf 17850 2700 m gs 1 -1 sc (-1) col0 sh gr /Times-Italic-iso ff 480.00 scf sf 18375 2869 m gs 1 -1 sc (B) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 1146 3783 a FP(Figure)32 b(5.15.)41 b FQ(The)27 b(relation)g(for)g FJ(g)f FQ(=)c(1)p FJ(;)14 b(n)23 b FQ(=)f(2.)605 4035 y FP(Example)31 b FQ(5.2.8)p FP(.)40 b FQ(Let)27 b(\006)f(b)r(e)i(a)e(mark)n(ed)f(torus)h(with)i(one)e(cut)h FJ(c)2675 4047 y FM(1)2739 4035 y FQ(and)g(one)f(hole)g FJ(\013)i FQ(\(see)456 4135 y(the)g(left)g(hand)f(side)h(of)f(Figure)g (5.12\).)36 b(Then)28 b(w)n(e)f(ha)n(v)n(e:)1691 4285 y(\()p FJ(S)5 b(T)12 b FQ(\))1872 4251 y FM(3)1932 4285 y FQ(=)22 b FJ(S)2075 4251 y FM(2)2112 4285 y FJ(;)-1679 b FQ(\(5.2.13\))1756 4424 y FJ(S)1812 4390 y FM(2)1848 4424 y FJ(T)35 b FQ(=)22 b FJ(T)12 b(S)2136 4390 y FM(2)2172 4424 y FJ(;)-1739 b FQ(\(5.2.14\))1816 4563 y FJ(S)1872 4529 y FM(4)1932 4563 y FQ(=)22 b FJ(T)2080 4529 y FE(\000)p FM(1)2068 4584 y FI(\013)2168 4563 y FJ(:)-1735 b FQ(\(5.2.15\))456 4717 y(Indeed,)38 b(\(5.2.13\))e(is)g(exactly)h(\(5.2.11\))n(.)64 b(Equation)35 b(\(5.2.14\))g(follo)n(ws)h(from)g(\(5.2.10\))n(,)j(the) 456 4817 y(Cylinder)21 b(axiom,)g(and)h(the)f(comm)n(utativit)n(y)g(of) h(disjoin)n(t)f(union,)i(and)e(\(5.2.15\))f(easily)g(follo)n(ws)456 4917 y(from)27 b(\(5.2.10\))f(and)i(the)g(braiding)e(axiom.)605 5016 y(In)36 b(particular,)h(this)f(implies)g(that)g(the)g(elemen)n(ts) g FJ(t;)14 b(s)36 b FL(2)i FQ(\000)2568 5028 y FM(1)p FI(;)p FM(1)2693 5016 y FQ(\(cf.)f(Example)e(5.1.11\))456 5116 y(satisfy)g(relations)g(\(5.2.13{5.2.15\).)59 b(In)37 b(fact,)h(it)f(is)f(kno)n(wn)f(that)i(these)f(are)f(the)h(de\014ning) 456 5216 y(relations)26 b(of)i(the)g(group)e(\000)1318 5228 y FM(1)p FI(;)p FM(1)1436 5216 y FQ(\(see)h([)p FK(B1)p FQ(]\).)p eop %%Page: 106 14 106 109 bop 456 226 a FM(106)1010 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FQ(No)n(w)e(w)n(e)g(can)h(form)n(ulate)e(our)h(main)h(result)f (for)g(arbitrary)f(gen)n(us.)605 572 y FP(Theorem)32 b FQ(5.2.9)p FP(.)40 b FO(L)l(et)d FQ(\006)g FO(b)l(e)h(an)f(extende)l (d)h(surfac)l(e.)62 b(L)l(et)38 b FL(M)p FQ(\(\006\))f FO(b)l(e)h(the)g(2-c)l(omplex)456 671 y(with)27 b(a)h(set)f(of)h (vertic)l(es)f FJ(M)9 b FQ(\(\006\))p FO(,)28 b(e)l(dges)g(given)g(by)g (the)f(the)g(Z-,)h(F-,)g(B-,)g(and)g(S-moves,)g(and)f(2-)456 771 y(c)l(el)t(ls)f(given)g(by)g(r)l(elations)32 b FQ(MF1{MF9)p FO(.)37 b(Then)26 b FL(M)p FQ(\(\006\))f FO(is)h(c)l(onne)l(cte)l(d)f (and)h(simply-c)l(onne)l(cte)l(d.)605 918 y FQ(Again,)35 b(this)f(theorem)g(w)n(as)e(stated)i(\(with)h(minor)e(inaccuracies\))f (in)j([)p FK(MS1)o FQ(],)h(but)e(the)456 1017 y(pro)r(of)24 b(giv)n(en)f(there)i(w)n(as)f(seriously)f(\015a)n(w)n(ed.)35 b(An)25 b(accurate)e(pro)r(of)h(w)n(as)g(found)h(indep)r(enden)n(tly) 456 1117 y(in)g([)p FK(BK)p FQ(])g(and,)h(in)f(a)g(di\013eren)n(t)g (form,)g([)p FK(F)m(G)q FQ(].)36 b(The)25 b(form)n(ulation)f(ab)r(o)n (v)n(e)g(is)h(tak)n(en)g(from)f([)p FK(BK)p FQ(].)1067 1286 y FK(5.3.)46 b(Ribb)s(on)30 b(categories)i(via)g(the)g FQ(Hom)f FK(spaces)605 1436 y FQ(In)38 b(this)g(section)f FL(C)42 b FQ(will)c(b)r(e)g(a)f(semisimple)h(ab)r(elian)f(category)f (with)i(represen)n(tativ)n(es)456 1535 y(of)c(the)g(equiv)-5 b(alence)34 b(classes)f(of)h(simple)h(ob)5 b(jects)34 b FJ(V)2128 1547 y FI(i)2156 1535 y FQ(,)i FJ(i)d FL(2)i FJ(I)7 b FQ(.)57 b(W)-7 b(e)34 b(use)h(the)f(notations)g(and)456 1635 y(con)n(v)n(en)n(tions)25 b(of)j(Section)g(2.4.)605 1734 y(In)c(a)g(semisimple)g(ab)r(elian)f(category)-7 b(,)23 b(an)n(y)g(ob)5 b(ject)24 b FJ(A)f FL(2)h(C)k FQ(is)c(determined)g(b)n(y)g(the)g(collec-)456 1834 y(tion)30 b(of)f(v)n(ector)g(spaces)g(Hom\()p FJ(A;)14 b FL(\001)p FQ(\).)45 b(More)29 b(formally)-7 b(,)29 b(w)n(e)h(ha)n(v)n(e)f(the)h (follo)n(wing)f(w)n(ell-kno)n(wn)456 1934 y(lemma.)605 2080 y FP(Lemma)i FQ(5.3.1)p FP(.)40 b FQ(\(i\))29 b FO(Every)h(functor)f FJ(F)21 b FQ(:)28 b FL(C)g(!)23 b(V)7 b FJ(ec)2231 2092 y FI(f)2302 2080 y FO(is)29 b(exact)37 b FQ(\()p FO(r)l(e)l(c)l(al)t(l)29 b(that)g(we)g(ar)l(e)h(c)l(on-)456 2180 y(sidering)h(only)f(additive)i(functors)7 b FQ(\))p FO(.)605 2279 y FQ(\(ii\))30 b FO(L)l(et)f FJ(F)21 b FQ(:)28 b FL(C)f(!)c(V)7 b FJ(ec)1323 2291 y FI(f)1395 2279 y FO(b)l(e)29 b(a)h(functor)f(satisfying)i(the)f(fol)t(lowing)h (\014niteness)e(c)l(ondition)6 b FQ(:)1167 2414 y FJ(F)12 b FQ(\()p FJ(V)1312 2426 y FI(i)1340 2414 y FQ(\))24 b(=)e(0)85 b FO(for)30 b(al)t(l)h(but)e(a)h(\014nite)g(numb)l(er)f(of)h FJ(i:)-2277 b FQ(\(5.3.1\))456 2549 y FO(Then)39 b FJ(F)51 b FO(is)39 b(r)l(epr)l(esentable,)k(i.e.,)g(ther)l(e)c(exists)g(an)g (obje)l(ct)g FJ(X)2492 2561 y FI(F)2547 2549 y FO(,)j(unique)d(up)f(to) h(a)h(unique)456 2648 y(isomorphism,)33 b(such)e(that)g FJ(F)12 b FQ(\()p FJ(A)p FQ(\))26 b(=)e(Hom)1811 2660 y FE(C)1854 2648 y FQ(\()p FJ(X)1955 2660 y FI(F)2011 2648 y FJ(;)14 b(A)p FQ(\))p FO(.)42 b(Similarly,)33 b(for)f(a)f(functor)f FJ(G)9 b FQ(:)29 b FL(C)3263 2618 y FM(op)3361 2648 y FL(!)456 2748 y(V)7 b FJ(ec)589 2760 y FI(f)661 2748 y FO(ther)l(e)29 b(exists)h(a)g(unique)f FJ(Y)1482 2760 y FI(G)1561 2748 y FL(2)24 b(C)34 b FO(such)c(that)g FJ(G)p FQ(\()p FJ(A)p FQ(\))24 b(=)e(Hom)2552 2760 y FE(C)2595 2748 y FQ(\()p FJ(A;)14 b(Y)2774 2760 y FI(G)2831 2748 y FQ(\))p FO(.)605 2848 y FQ(\(iii\))26 b FO(F)-6 b(or)26 b(two)f(functors)h FJ(F)r(;)14 b(F)1542 2818 y FE(0)1575 2848 y FQ(:)28 b FL(C)f(!)c(V)7 b FJ(ec)1936 2860 y FI(f)2004 2848 y FO(satisfying)27 b(the)e(\014niteness)g(c)l (ondition)i(ab)l(ove,)456 2947 y(ther)l(e)21 b(is)h(a)f(bije)l(ction)i (b)l(etwe)l(en)e(the)g(sp)l(ac)l(e)h(of)g(functor)f(morphisms)i FJ(F)35 b FL(!)23 b FJ(F)2797 2917 y FE(0)2842 2947 y FO(and)30 b FQ(Hom)3176 2959 y FE(C)3219 2947 y FQ(\()p FJ(X)3320 2959 y FI(F)3371 2943 y Fx(0)3398 2947 y FJ(;)14 b(X)3504 2959 y FI(F)3558 2947 y FQ(\))p FO(.)456 3047 y(A)29 b(similar)i(statement)e(holds)i(for)g FJ(G;)14 b(G)1720 3017 y FE(0)1753 3047 y FQ(:)27 b FL(C)1852 3017 y FM(op)1949 3047 y FL(!)c(V)7 b FJ(ec)2188 3059 y FI(f)2230 3047 y FO(.)605 3193 y FQ(Therefore,)27 b(to)g(construct,)h (sa)n(y)-7 b(,)27 b(a)g(functor)h FJ(F)21 b FQ(:)28 b FL(C)g(!)23 b(C)5 b FQ(,)28 b(it)g(su\016ces)g(to)g(de\014ne)g(a)f (bifunc-)456 3293 y(tor)35 b FJ(A)9 b FQ(:)30 b FL(C)771 3263 y FM(op)869 3293 y FL(\002)23 b(C)41 b(!)36 b(V)7 b FJ(ec)1294 3305 y FI(f)1372 3293 y FQ(satisfying)35 b(suitable)g(\014niteness)h(conditions,)h(and)e(then)h(de\014ne)456 3393 y FJ(F)12 b FQ(\()p FJ(X)7 b FQ(\))30 b(b)n(y)g(the)h(iden)n(tit)n (y)g(Hom\()p FL(\001)p FJ(;)14 b(F)e FQ(\()p FJ(X)7 b FQ(\)\))28 b(=)g FJ(A)p FQ(\()p FL(\001)p FJ(;)14 b(X)7 b FQ(\);)32 b(more)e(formally)-7 b(,)31 b(one)f(w)n(ould)g(sa)n(y)g (\\let)456 3492 y FJ(F)12 b FQ(\()p FJ(X)7 b FQ(\))28 b(b)r(e)g(the)h(ob)5 b(ject)28 b(represen)n(ting)f(the)h(functor)h FJ(A)p FQ(\()p FL(\001)p FJ(;)14 b(X)7 b FQ(\)".)38 b(Similarly)-7 b(,)28 b(all)g(the)h(functorial)456 3592 y(isomorphisms)d(can)h(b)r(e)h (de\014ned)g(in)g(terms)f(of)h(v)n(ector)e(spaces.)605 3692 y(Our)h(goal)g(in)h(this)g(section)f(is)h(to)g(rewrite)f(the)h (axioms)f(of)h(a)f(ribb)r(on)h(category)e(in)i(terms)456 3791 y(of)f(the)h(v)n(ector)e(spaces)1175 3926 y FL(h)p FJ(W)1285 3938 y FM(1)1323 3926 y FJ(;)14 b(:)g(:)g(:)g(;)g(W)1586 3938 y FI(n)1631 3926 y FL(i)24 b FQ(:=)e(Hom)1970 3938 y FE(C)2013 3926 y FQ(\()p FK(1)p FJ(;)14 b(W)2208 3938 y FM(1)2264 3926 y FL(\012)k(\001)c(\001)g(\001)19 b(\012)f FJ(W)2624 3938 y FI(n)2669 3926 y FQ(\))p FJ(:)-2268 b FQ(\(5.3.2\))456 4065 y(This)35 b(w)n(as)f(\014rst)i(done)f(in)g([)p FK(MS1)p FQ(].)61 b(The)35 b(follo)n(wing)f(de\014nition)i(is)g(essen)n (tially)e(tak)n(en)h(from)456 4165 y([)p FK(MS1)o FQ(];)28 b(for)f(this)h(reason,)e(w)n(e)h(think)h(it)g(is)g(prop)r(er)e(to)i (commemorate)e(their)i(names.)605 4311 y FP(Definition)k FQ(5.3.2)p FP(.)40 b FO(Mo)l(or)l(e{Seib)l(er)l(g)e(data)43 b FQ(\(MS)36 b(data)f(for)g(short\))g(for)f(a)h(semisimple)456 4411 y(ab)r(elian)27 b(category)f FL(C)32 b FQ(is)27 b(the)h(follo)n(wing)f(collection)g(of)g(data:)612 4528 y FK(Conformal)j(blo)s(c)m(ks:)41 b FQ(A)29 b(collection)f(of)h (functors)g FL(h)14 b(i)9 b FQ(:)29 b FL(C)2476 4498 y Fv(\002)p FI(n)2598 4528 y FL(!)c(V)7 b FJ(ec)2839 4540 y FI(f)2911 4528 y FQ(\()p FJ(n)25 b FL(\025)g FQ(0\),)30 b(whic)n(h)711 4628 y(are)21 b(lo)r(cally)g(\014nite)i(in)f(the)h (\014rst)e(comp)r(onen)n(t:)34 b(for)22 b(ev)n(ery)e FJ(A)2553 4640 y FM(1)2591 4628 y FJ(;)14 b(:)g(:)g(:)f(;)h(A)2837 4640 y FI(n)p FE(\000)p FM(1)2991 4628 y FL(2)23 b(C)5 b FQ(,)23 b(w)n(e)f(ha)n(v)n(e)711 4729 y FL(h)p FJ(V)791 4741 y FI(i)819 4729 y FJ(;)14 b(A)918 4741 y FM(1)956 4729 y FJ(;)g(:)g(:)g(:)f(;)h(A)1202 4741 y FI(n)p FE(\000)p FM(1)1333 4729 y FL(i)30 b FQ(=)f(0)i(for)g(all)g(but)h(a)f(\014nite)h (n)n(um)n(b)r(er)f(of)h FJ(i)p FQ(.)48 b(\(Here)32 b FL(C)3044 4699 y Fv(\002)p FI(n)3172 4729 y FQ(denotes)711 4828 y(the)c(tensor)f(pro)r(duct)g FL(C)c Fw(\002)18 b FL(\001)c(\001)g(\001)19 b Fw(\002)f FL(C)32 b FQ(de\014ned)c(in)g (1.1.15.\))612 4928 y FK(Rotation)j(isomorphisms:)36 b FQ(F)-7 b(unctorial)27 b(isomorphisms)1229 5065 y FJ(Z)15 b FQ(:)28 b FL(h)p FJ(A)1446 5077 y FM(1)1483 5065 y FJ(;)14 b(:)g(:)g(:)g(;)g(A)1730 5077 y FI(n)1775 5065 y FL(i)1859 5018 y FE(\030)1831 5065 y FL(\000)-40 b(!)23 b(h)p FJ(A)2056 5077 y FI(n)2102 5065 y FJ(;)14 b(A)2201 5077 y FM(1)2239 5065 y FJ(;)g(:)g(:)g(:)f(;)h(A)2485 5077 y FI(n)p FE(\000)p FM(1)2616 5065 y FL(i)p FJ(:)612 5216 y FK(R:)40 b FQ(A)28 b(symmetric)f(ob)5 b(ject)28 b FJ(R)23 b FL(2)h FQ(ind)p FL(\000C)1891 5185 y Fv(\002)p FM(2)2007 5216 y FQ(\(see)k(Section)f(2.4\).)p eop %%Page: 107 15 107 110 bop 1144 226 a FM(5.3.)29 b(RIBBON)i(CA)-5 b(TEGORIES)28 b(VIA)i(THE)f(Hom)f(SP)-5 b(A)n(CES)566 b(107)612 425 y FK(Gluing)30 b(isomorphisms:)36 b FQ(F)-7 b(or)27 b(ev)n(ery)g FJ(k)s(;)14 b(l)24 b FL(2)f FH(Z)2200 437 y FM(+)2276 425 y FQ(functorial)k(isomorphisms)800 573 y FJ(G)9 b FQ(:)28 b FL(h)p FJ(A)1019 585 y FM(1)1057 573 y FJ(;)14 b(:)g(:)g(:)g(;)g(A)1304 585 y FI(k)1345 573 y FJ(;)g(R)1446 539 y FM(\(1\))1534 573 y FL(i)19 b(\012)f(h)p FJ(R)1764 539 y FM(\(2\))1853 573 y FJ(;)c(B)1953 585 y FM(1)1990 573 y FJ(;)g(:)g(:)g(:)g(;)g(B)2238 585 y FI(l)2263 573 y FL(i)2347 526 y FE(\030)2319 573 y FL(\000)-40 b(!)23 b(h)p FJ(A)2544 585 y FM(1)2582 573 y FJ(;)14 b(:)g(:)g(:)g(;)g(A)2829 585 y FI(k)2870 573 y FJ(;)g(B)2970 585 y FM(1)3007 573 y FJ(;)g(:)g(:)g(:)f(;)h(B)3254 585 y FI(l)3280 573 y FL(i)p FJ(:)612 716 y FK(Comm)m(utativit)m(y)29 b(isomorphism:)37 b FQ(A)28 b(functorial)f(isomorphism)1467 861 y FJ(\033)12 b FQ(:)29 b FL(h)p FJ(X)r(;)14 b(A;)g(B)t FL(i)1968 814 y FE(\030)1939 861 y FL(\000)-39 b(!)23 b(h)p FJ(X)r(;)14 b(B)t(;)g(A)p FL(i)p FJ(:)456 1004 y FQ(These)27 b(data)g(ha)n(v)n(e)f (to)i(satisfy)f(the)h(axioms)f(MS1{MS7)f(listed)i(b)r(elo)n(w.)612 1157 y FK(MS1:)41 b(Non-degeneracy:)g FQ(F)-7 b(or)41 b(ev)n(ery)g FJ(i)p FQ(,)46 b(there)c(exists)g(an)g(ob)5 b(ject)42 b FJ(X)48 b FQ(suc)n(h)42 b(that)711 1257 y FL(h)p FJ(X)r(;)14 b(V)899 1269 y FI(i)927 1257 y FL(i)23 b(6)p FQ(=)g(0.)612 1357 y FK(MS2:)41 b(Normalization:)e FQ(The)d(functor)g FL(h)14 b(i)9 b FQ(:)32 b FL(C)2201 1327 y FM(0)2275 1357 y FL(\021)37 b(V)7 b FJ(ec)2510 1369 y FI(f)2590 1357 y FL(!)37 b(V)7 b FJ(ec)2843 1369 y FI(f)2922 1357 y FQ(is)36 b(the)g(iden)n(tit)n(y)711 1456 y(functor.)612 1556 y FK(MS3:)41 b(Asso)s(ciativit)m(y)31 b(of)h FJ(G)p FK(:)41 b FQ(Let)28 b(us)g(consider)e(t)n(w)n(o)h (functorial)g(isomorphisms)630 1701 y FJ(G)695 1667 y FE(0)718 1701 y FJ(G)783 1667 y FE(0)q(0)826 1701 y FJ(;)14 b(G)928 1667 y FE(00)971 1701 y FJ(G)1036 1667 y FE(0)1069 1701 y FQ(:)27 b FL(h)p FJ(A)1213 1713 y FM(1)1251 1701 y FJ(;)14 b(:)g(:)g(:)g(;)g(R)1500 1667 y FE(0)o FM(\(1\))1608 1701 y FL(i)k(\012)g(h)p FJ(R)1837 1667 y FE(0)p FM(\(2\))1946 1701 y FJ(;)c(B)2046 1713 y FM(1)2083 1701 y FJ(;)g(:)g(:)g(:)f(;)h(R) 2331 1667 y FE(00)p FM(\(1\))2458 1701 y FL(i)19 b(\012)f(h)p FJ(R)2688 1667 y FE(00)p FM(\(2\))2815 1701 y FJ(;)c(C)2911 1713 y FM(1)2949 1701 y FJ(;)g(:)g(:)g(:)f(;)h(C)3192 1713 y FI(n)3238 1701 y FL(i)1254 1799 y FE(\030)1225 1846 y FL(\000)-39 b(!)23 b(h)p FJ(A)1451 1858 y FM(1)1489 1846 y FJ(;)14 b(:)g(:)g(:)f(;)h(B)1736 1858 y FM(1)1774 1846 y FJ(;)g(:)g(:)g(:)f(;)h(C)2017 1858 y FM(1)2055 1846 y FJ(;)g(:)g(:)g(:)f(;)h(C)2298 1858 y FI(n)2344 1846 y FL(i)p FJ(;)711 1993 y FQ(where)29 b FJ(R)1017 1963 y FE(0)1040 1993 y FJ(;)14 b(R)1141 1963 y FE(00)1213 1993 y FQ(are)29 b(t)n(w)n(o)g(copies)g(of)h FJ(R)q FQ(,)g(and)g FJ(G)2203 1963 y FE(0)2227 1993 y FJ(;)14 b(G)2329 1963 y FE(00)2401 1993 y FQ(are)29 b(the)h(corresp)r(onding)e(gluing)711 2093 y(isomorphisms.)36 b(Then)27 b FJ(G)1543 2063 y FE(0)1567 2093 y FJ(G)1632 2063 y FE(00)1698 2093 y FQ(=)22 b FJ(G)1850 2063 y FE(0)q(0)1893 2093 y FJ(G)1958 2063 y FE(0)1982 2093 y FQ(.)612 2195 y FK(MS4:)41 b(Rotation)31 b(axiom:)40 b FJ(Z)1653 2165 y FI(n)1721 2195 y FQ(=)22 b(id)10 b(:)27 b FL(h)p FJ(A)2031 2207 y FM(1)2069 2195 y FJ(;)14 b(:)g(:)g(:)g(;)g(A)2316 2207 y FI(n)2361 2195 y FL(i)2445 2148 y FE(\030)2416 2195 y FL(\000)-39 b(!)23 b(h)p FJ(A)2642 2207 y FM(1)2680 2195 y FJ(;)14 b(:)g(:)g(:)f(;)h(A) 2926 2207 y FI(n)2972 2195 y FL(i)p FQ(.)612 2295 y FK(MS5:)41 b(Symmetry)30 b(of)i FJ(G)p FK(:)41 b FQ(F)-7 b(or)30 b(an)n(y)g FJ(m;)14 b(n)28 b FL(\025)f FQ(0)k(the)g(follo)n(wing)e (diagram)h(is)g(comm)n(u-)711 2394 y(tativ)n(e:)573 2640 y FL(h)p FJ(A)667 2652 y FM(1)705 2640 y FJ(;)14 b(:)g(:)g(:)f(;)h(A) 951 2652 y FI(n)997 2640 y FJ(;)g(R)1098 2610 y FM(\(1\))1186 2640 y FL(i)19 b(\012)f(h)p FJ(R)1416 2610 y FM(\(2\))1505 2640 y FJ(;)c(B)1605 2652 y FM(1)1642 2640 y FJ(;)g(:)g(:)g(:)g(;)g(B) 1890 2652 y FI(m)1953 2640 y FL(i)2125 2593 y FI(G)2027 2640 y FL(\000)-28 b(\000)-19 b(\000)g(\000)-28 b(!)41 b(h)p FJ(A)2411 2652 y FM(1)2449 2640 y FJ(;)14 b(:)g(:)g(:)g(;)g(A) 2696 2652 y FI(n)2741 2640 y FJ(;)g(B)2841 2652 y FM(1)2878 2640 y FJ(;)g(:)g(:)g(:)g(;)g(B)3126 2652 y FI(m)3189 2640 y FL(i)920 2804 y FI(P)9 b FM(\()p FI(Z)t FE(\012)p FI(Z)1147 2779 y Fx(\000)p FF(1)1225 2804 y FM(\))1251 2711 y Fy(?)1251 2760 y(?)1251 2810 y(y)2637 2807 y FI(Z)2686 2782 y FG(m)2741 2711 y Fy(?)2741 2760 y(?)2741 2810 y(y)573 2980 y FL(h)p FJ(B)668 2992 y FM(1)705 2980 y FJ(;)14 b(:)g(:)g(:)g(;)g(B)953 2992 y FI(m)1016 2980 y FJ(;)g(R)1117 2950 y FM(\(2\))1206 2980 y FL(i)k(\012)g(h)p FJ(R)1435 2950 y FM(\(1\))1525 2980 y FJ(;)c(A)1624 2992 y FM(1)1661 2980 y FJ(;)g(:)g(:)g(:)g(;)g(A)1908 2992 y FI(n)1953 2980 y FL(i)2093 2933 y FI(G)p FE(\016)p FI(s)2027 2980 y FL(\000)-28 b(\000)-19 b(\000)g(\000)-28 b(!)41 b(h)p FJ(B)2412 2992 y FM(1)2450 2980 y FJ(;)14 b(:)g(:)g(:)f(;)h(B)2697 2992 y FI(m)2760 2980 y FJ(;)g(A)2859 2992 y FM(1)2897 2980 y FJ(;)g(:)g(:)g(:)f(;)h(A)3143 2992 y FI(n)3189 2980 y FL(i)3304 2794 y FJ(:)711 3114 y FQ(\(Here)36 b FJ(P)48 b FQ(is)36 b(the)h(p)r(erm)n(utation)f(of)g (the)g(t)n(w)n(o)f(factors)g(in)i(the)f(tensor)g(pro)r(duct)g(and)711 3221 y FJ(s)9 b FQ(:)28 b FJ(R)874 3191 y FM(op)999 3174 y FE(\030)971 3221 y FL(\000)-40 b(!)23 b FJ(R)29 b FQ(is)e(as)g(in)h (Section)g(2.4.\))612 3320 y FK(MS6:)41 b(Hexagon)31 b(axioms:)40 b FQ(\(i\))28 b(The)g(follo)n(wing)e(diagram)g(is)i(comm)n (utativ)n(e:)1242 3504 y FL(h)p FJ(X)r(;)14 b(A;)g(B)t(;)g(C)6 b FL(i)1565 3699 y FI(\033)1603 3707 y FG(A;B)1854 3749 y FD($)p FC($)1820 3726 y FB(I)1788 3704 y(I)1755 3682 y(I)1723 3660 y(I)1690 3638 y(I)1657 3616 y(I)1625 3594 y(I)1592 3572 y(I)1560 3550 y(I)1854 3442 y FI(\033)1892 3450 y FG(A;B)r(C)2198 3483 y FD(/)p FC(/)p 1707 3485 491 4 v 2222 3504 a FL(h)p FJ(X)r(;)14 b(B)t(;)g(C)q(;)g(A)p FL(i)1732 3836 y(h)p FJ(X)r(;)g(B)t(;)g(A;)g(C)6 b FL(i)2189 3699 y FI(\033)2227 3707 y FG(A;C)2343 3550 y FD(:)p FC(:)2309 3573 y FB(u)2276 3595 y(u)2244 3617 y(u)2212 3639 y(u)2179 3661 y(u)2147 3683 y(u)2115 3705 y(u)2082 3727 y(u)2050 3749 y(u)711 3990 y FQ(where)27 b FJ(\033)998 4002 y FI(A;B)s(C)1205 3990 y FQ(is)g(de\014ned)h(as)f(the)h(comp)r (osition)655 4173 y FL(h)p FJ(X)r(;)14 b(A;)g(B)t(;)g(C)6 b FL(i)1147 4126 y FI(G)1199 4101 y Fx(\000)p FF(1)1119 4173 y FL(\000)-36 b(\000)-19 b(\000)-37 b(!)23 b(h)p FJ(X)r(;)14 b(A;)g(R)1631 4139 y FM(\(1\))1720 4173 y FL(i)k(\012)g(h)p FJ(R)1949 4139 y FM(\(2\))2039 4173 y FJ(;)c(B)t(;)g(C)6 b FL(i)1147 4309 y FI(\033)r FE(\012)p FM(id)1119 4356 y FL(\000)-27 b(\000)-19 b(\000)-27 b(!)23 b(h)p FJ(X)r(;)14 b(R)1551 4321 y FM(\(1\))1639 4356 y FJ(;)g(A)p FL(i)19 b(\012)f(h)p FJ(R)1968 4321 y FM(\(2\))2057 4356 y FJ(;)c(B)t(;)g(C)6 b FL(i)2347 4302 y FI(Z)2396 4276 y Fx(\000)p FF(1)2474 4302 y FI(G)p FM(\()p FI(Z)t FE(\012)p FM(id)o(\))2319 4356 y FL(\000)-23 b(\000)k(\000)g(\000)g (\000)h(\000)f(\000)g(\000)c(!)23 b(h)p FJ(X)r(;)14 b(B)t(;)g(C)q(;)g (A)p FL(i)p FJ(;)711 4498 y FQ(and)28 b FJ(\033)920 4510 y FI(A;B)1074 4498 y FQ(is)g(de\014ned)g(as)f(the)h(comp)r(osition)754 4681 y FL(h)p FJ(X)r(;)14 b(A;)g(B)t(;)g(C)6 b FL(i)1246 4634 y FI(G)1298 4609 y Fx(\000)p FF(1)1375 4634 y FI(Z)1218 4681 y FL(\000)-35 b(\000)-19 b(\000)g(\000)-35 b(!)23 b(h)p FJ(C)q(;)14 b(X)r(;)g(R)1777 4647 y FM(\(1\))1866 4681 y FL(i)19 b(\012)f(h)p FJ(R)2096 4647 y FM(\(2\))2185 4681 y FJ(;)c(A;)g(B)t FL(i)1246 4810 y FM(id)d FE(\012)p FI(\033)1218 4857 y FL(\000)-22 b(\000)j(\000)e(!)23 b(h)p FJ(C)q(;)14 b(X)r(;)g(R)1758 4822 y FM(\(1\))1847 4857 y FL(i)19 b(\012)f(h)p FJ(R)2077 4822 y FM(\(2\))2166 4857 y FJ(;)c(B)t(;)g(A)p FL(i)2453 4810 y FI(Z)2502 4784 y Fx(\000)p FF(1)2579 4810 y FI(G)2424 4857 y FL(\000)-35 b(\000)-18 b(\000)f(\000)-36 b(!)23 b(h)p FJ(X)r(;)14 b(B)t(;)g(A;)g(C)6 b FL(i)p FJ(:)861 5009 y FQ(\(ii\))28 b(The)g(same,)f(but)h(with)g FJ(\033)j FQ(replaced)c(b)n(y)g FJ(\033)2313 4979 y FE(\000)p FM(1)2403 5009 y FQ(.)612 5116 y FK(MS7:)41 b(Dehn)32 b(t)m(wist)f(axiom:)40 b FJ(Z)6 b(\033)1792 5128 y FI(A;B)1942 5116 y FQ(=)23 b FJ(\033)2077 5128 y FI(B)s(;A)2204 5116 y FJ(Z)15 b FQ(:)27 b FL(h)p FJ(A;)14 b(B)t FL(i)2609 5069 y FE(\030)2580 5116 y FL(\000)-39 b(!)23 b(h)p FJ(A;)14 b(B)t FL(i)p FQ(,)21 b(where)d FJ(\033)3264 5128 y FI(A;B)3414 5116 y FQ(=)711 5216 y FJ(G)p FQ(\()p FJ(\033)23 b FL(\012)18 b FQ(id\))p FJ(G)1127 5185 y FE(\000)p FM(1)1244 5216 y FQ(is)28 b(de\014ned)g(similarly)e(to)i(MS6.)p eop %%Page: 108 16 108 111 bop 456 226 a FM(108)1010 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FQ(No)n(w)c(w)n(e)g(describ)r(e)g(ho)n(w)f(the)i(MS)g(data)e(are) h(related)f(with)i(the)g(tensor)e(structure)h(on)g(the)456 525 y(category)-7 b(.)35 b(Let)27 b FL(C)33 b FQ(b)r(e)28 b(a)f(semisimple)g(ribb)r(on)h(category)-7 b(.)35 b(De\014ne:)858 678 y FL(h)p FJ(A)952 690 y FM(1)990 678 y FJ(;)14 b(:)g(:)g(:)g(;)g(A) 1237 690 y FI(n)1282 678 y FL(i)23 b FQ(=)g(Hom)1598 690 y FE(C)1641 678 y FQ(\()p FK(1)p FJ(;)14 b(A)1820 690 y FM(1)1876 678 y FL(\012)k(\001)c(\001)g(\001)k(\012)g FJ(A)2219 690 y FI(n)2265 678 y FQ(\))p FJ(;)-1864 b FQ(\(5.3.3\))858 832 y FJ(R)24 b FQ(=)1033 754 y Fy(M)1172 832 y FJ(V)1239 798 y FE(\003)1220 853 y FI(i)1295 832 y FL(\012)18 b FJ(V)1426 844 y FI(i)1454 832 y FJ(;)208 b FQ(cf.)37 b(\(2.4.7\))p FJ(;)-1610 b FQ(\(5.3.4\))858 989 y FJ(Z)15 b FQ(:)42 b(Hom\()p FK(1)p FJ(;)14 b(A)1347 1001 y FM(1)1402 989 y FL(\012)k(\001)c(\001)g(\001)19 b(\012)f FJ(A)1746 1001 y FI(n)1791 989 y FQ(\))1875 942 y FE(\030)1847 989 y FL(\000)-40 b(!)23 b FQ(Hom\()2183 955 y FE(\003)2222 989 y FJ(A)2284 1001 y FI(n)2329 989 y FJ(;)14 b(A)2428 1001 y FM(1)2484 989 y FL(\012)k(\001)c(\001)g(\001) k(\012)g FJ(A)2827 1001 y FI(n)p FE(\000)p FM(1)2958 989 y FQ(\))-2534 b(\(5.3.5\))993 1087 y FE(\030)964 1134 y FL(\000)-39 b(!)23 b FQ(Hom\()p FK(1)p FJ(;)1386 1100 y FE(\003\003)1458 1134 y FJ(A)1520 1146 y FI(n)1584 1134 y FL(\012)18 b FJ(A)1729 1146 y FM(1)1785 1134 y FL(\012)g(\001)c(\001)g(\001)k(\012)g FJ(A)2128 1146 y FI(n)p FE(\000)p FM(1)2259 1134 y FQ(\))993 1232 y FE(\030)964 1279 y FL(\000)-39 b(!)23 b FQ(Hom\()p FK(1)p FJ(;)14 b(A)1448 1291 y FI(n)1512 1279 y FL(\012)k FJ(A)1657 1291 y FM(1)1713 1279 y FL(\012)g(\001)c(\001)g(\001)k(\012)g FJ(A)2056 1291 y FI(n)p FE(\000)p FM(1)2186 1279 y FQ(\))p FJ(;)858 1433 y(G)9 b FQ(:)997 1354 y Fy(M)1137 1433 y FQ(Hom\()p FK(1)p FJ(;)14 b(A)1489 1445 y FM(1)1544 1433 y FL(\012)k(\001)c(\001)g(\001)19 b(\012)f FJ(A)1888 1445 y FI(n)1952 1433 y FL(\012)g FJ(V)2102 1399 y FE(\003)2083 1454 y FI(i)2140 1433 y FQ(\))g FL(\012)g FQ(Hom\()p FK(1)p FJ(;)c(V)2611 1445 y FI(i)2658 1433 y FL(\012)k FJ(B)2804 1445 y FM(1)2860 1433 y FL(\012)g(\001)c(\001)g(\001)k(\012)g FJ(B)3204 1445 y FI(k)3245 1433 y FQ(\))-2821 b(\(5.3.6\))993 1543 y FE(\030)964 1590 y FL(\000)-39 b(!)23 b FQ(Hom\()p FK(1)p FJ(;)14 b(A)1448 1602 y FM(1)1504 1590 y FL(\012)k(\001)c(\001)g (\001)k(\012)g FJ(A)1847 1602 y FI(n)1911 1590 y FL(\012)g FJ(V)2061 1556 y FE(\003)2042 1610 y FI(i)2099 1590 y FQ(\))h FL(\012)f FQ(Hom\()p FJ(V)2505 1556 y FE(\003)2486 1610 y FI(i)2543 1590 y FJ(;)c(B)2643 1602 y FM(1)2699 1590 y FL(\012)k(\001)c(\001)g(\001)k(\012)g FJ(B)3043 1602 y FI(k)3084 1590 y FQ(\))993 1688 y FE(\030)964 1735 y FL(\000)-39 b(!)23 b FQ(Hom\()p FK(1)p FJ(;)14 b(A)1448 1747 y FM(1)1504 1735 y FL(\012)k(\001)c(\001)g(\001)k(\012)g FJ(A)1847 1747 y FI(n)1911 1735 y FL(\012)g FJ(B)2057 1747 y FM(1)2113 1735 y FL(\012)g(\001)c(\001)g(\001)k(\012)g FJ(B)2457 1747 y FI(k)2498 1735 y FQ(\))p FJ(;)858 1880 y(\033)12 b FQ(:)42 b(Hom\()p FK(1)p FJ(;)14 b(X)25 b FL(\012)18 b FJ(A)h FL(\012)f FJ(B)t FQ(\))1764 1833 y FE(\030)1735 1880 y FL(\000)-39 b(!)23 b FQ(Hom\()p FK(1)p FJ(;)14 b(X)25 b FL(\012)18 b FJ(B)k FL(\012)c FJ(A)p FQ(\))p FJ(:)-2163 b FQ(\(5.3.7\))456 2053 y(Here)25 b(w)n(e)g(used)g(the)h(rigidit)n(y)e(isomorphisms)g(\(2.1.13,)h (2.1.14\),)f(the)i(isomorphisms)e FJ(\016)12 b FQ(:)28 b FJ(V)3364 2006 y FE(\030)3336 2053 y FL(\000)-40 b(!)456 2153 y FJ(V)522 2123 y FE(\003\003)595 2153 y FQ(,)35 b(and)e(the)h(fact)g(that)g(in)g(a)f(semisimple)g(category)-7 b(,)34 b(Hom\()p FJ(X)r(;)14 b(Y)k FQ(\))34 b FL(')2830 2091 y Fy(L)2936 2153 y FQ(Hom\()p FJ(X)r(;)14 b(V)3297 2165 y FI(i)3325 2153 y FQ(\))23 b FL(\012)456 2253 y FQ(Hom\()p FJ(V)709 2265 y FI(i)737 2253 y FJ(;)14 b(Y)k FQ(\).)605 2413 y FP(Pr)n(oposition)31 b FQ(5.3.3)p FP(.)40 b FO(If)g FL(C)45 b FO(is)c(a)g(semisimple)h(ribb)l(on)f(c)l(ate)l (gory,)k(formulas)j FQ(\(5.3.3\))o FO({)456 2512 y FQ(\(5.3.7\))29 b FO(de\014ne)g(MS)h(data.)605 2672 y FQ(The)38 b(pro)r(of)f(of)h(this) g(prop)r(osition)f(is)h(straigh)n(tforw)n(ard:)54 b(if)38 b(w)n(e)g(use)f(the)i(tec)n(hnique)f(of)456 2772 y(ribb)r(on)27 b(graphs)f(dev)n(elop)r(ed)h(in)h(Chapter)f(1,)h(then)g(all)f(the)h (axioms)e(are)h(ob)n(vious.)p 3384 2772 4 57 v 3388 2719 50 4 v 3388 2772 V 3437 2772 4 57 v 605 2872 a(A)k(natural)f(question)h (is)g(whether)g(this)g(prop)r(osition)f(can)g(b)r(e)h(rev)n(ersed,)f (i.e.,)i(is)f(it)h(true)456 2971 y(that)h(ev)n(ery)g(collection)f(of)i (MS)g(data)f(on)g(a)g(semisimple)g(ab)r(elian)g(category)f(comes)h (from)g(a)456 3071 y(structure)28 b(of)h(a)f(ribb)r(on)g(category)-7 b(.)39 b(It)29 b(turns)g(out)f(that)h(it)h(is)e(almost)g(true;)i(to)e (get)h(a)f(precise)456 3171 y(statemen)n(t,)f(w)n(e)g(m)n(ust)h (somewhat)f(w)n(eak)n(en)f(the)i(rigidit)n(y)f(axiom.)605 3270 y(Let)34 b FL(C)k FQ(b)r(e)c(a)f(monoidal)f(category)-7 b(.)53 b(W)-7 b(e)34 b(sa)n(y)e(that)i(an)f(ob)5 b(ject)33 b FJ(V)52 b FL(2)33 b FQ(Ob)13 b FL(C)39 b FQ(has)32 b(a)i(w)n(eak)456 3370 y(dual)27 b(if)h(the)g(functor)f(Hom\()p FK(1)p FJ(;)14 b(V)37 b FL(\012)18 b(\001)p FQ(\))28 b(is)f(represen)n(table.)35 b(In)28 b(this)g(case,)e(w)n(e)i(denote)f (the)h(cor-)456 3470 y(resp)r(onding)c(represen)n(ting)g(ob)5 b(ject)25 b(b)n(y)g FJ(V)1772 3439 y FE(\003)1819 3470 y FQ(:)42 b(Hom\()p FK(1)p FJ(;)14 b(V)33 b FL(\012)13 b FJ(X)7 b FQ(\))23 b(=)g(Hom\()p FJ(V)2824 3439 y FE(\003)2862 3470 y FJ(;)14 b(X)7 b FQ(\).)36 b(Ob)n(viously)-7 b(,)456 3569 y FL(\003)35 b FQ(is)g(functorial:)52 b(ev)n(ery)34 b(morphism)h FJ(f)17 b FQ(:)31 b FJ(V)55 b FL(!)35 b FJ(W)48 b FQ(de\014nes)35 b(a)g(morphism)g FJ(f)2933 3539 y FE(\003)2980 3569 y FQ(:)30 b FJ(W)3123 3539 y FE(\003)3197 3569 y FL(!)36 b FJ(V)3383 3539 y FE(\003)3421 3569 y FQ(,)456 3669 y(pro)n(vided)26 b(that)i FJ(V)1044 3639 y FE(\003)1082 3669 y FJ(;)14 b(W)1209 3639 y FE(\003)1275 3669 y FQ(exist.)605 3829 y FP(Definition)32 b FQ(5.3.4)p FP(.)40 b FQ(A)25 b(monoidal)g(category)e FL(C)30 b FQ(is)25 b(called)g FO(we)l(akly)k(rigid)e FQ(if)f(ev)n(ery)e(ob)5 b(ject)456 3929 y(has)27 b(a)g(w)n(eak)f(dual)i(and)f FL(\003)9 b FQ(:)28 b FL(C)f(!)c(C)1554 3898 y FM(op)1656 3929 y FQ(is)k(an)g(equiv)-5 b(alence)28 b(of)f(categories.)605 4089 y(Of)34 b(course,)g(ev)n(ery)e(rigid)h(category)f(is)h(w)n(eakly)g (rigid;)j(the)e(con)n(v)n(erse,)f(ho)n(w)n(ev)n(er,)g(is)g(not)456 4188 y(true.)h(It)22 b(is)e(also)g(useful)i(to)e(note)h(that)h(in)f(ev) n(ery)f(w)n(eakly)f(rigid)i(category)e(w)n(e)h(ha)n(v)n(e)g(a)h (canonical)456 4288 y(morphism)g FJ(i)867 4300 y FI(V)934 4288 y FQ(:)27 b FK(1)c FL(!)g FJ(V)j FL(\012)7 b FJ(V)1374 4258 y FE(\003)1412 4288 y FQ(,)23 b(corresp)r(onding)d(to)i(id)i FL(2)f FQ(Hom\()p FJ(V)2525 4258 y FE(\003)2563 4288 y FJ(;)14 b(V)2667 4258 y FE(\003)2705 4288 y FQ(\))24 b(=)e(Hom\()p FK(1)p FJ(;)14 b(V)26 b FL(\012)7 b FJ(V)3351 4258 y FE(\003)3389 4288 y FQ(\).)456 4388 y(If)29 b(the)g(category)e (is)h(rigid,)h(then)g FJ(i)1542 4400 y FI(V)1628 4388 y FQ(de\014ned)g(in)g(this)h(w)n(a)n(y)d(coincides)h(with)i(the)f(one)f (de\014ned)456 4487 y(b)n(y)f(the)h(rigidit)n(y)f(axioms.)605 4647 y FP(Definition)32 b FQ(5.3.5)p FP(.)40 b FQ(A)33 b FO(we)l(akly)k(ribb)l(on)d FQ(category)e(is)h(a)g(w)n(eakly)g(rigid)f (braided)h(tensor)456 4749 y(category)23 b FL(C)31 b FQ(endo)n(w)n(ed)24 b(with)j(a)e(family)h(of)f(functorial)g (isomorphisms)g FJ(\022)12 b FQ(:)27 b FJ(V)2906 4702 y FE(\030)2878 4749 y FL(\000)-40 b(!)24 b FJ(V)44 b FQ(satisfying)456 4849 y(\(2.2.8\))o({\(2.2.10\))n(.)605 5009 y(As)32 b(discussed)g(in)g(Section)h(2.2,)f(for)g(a)g(rigid)f (category)f(de\014ning)i FJ(\022)j FQ(satisfying)e(\(2.2.8\))o({)456 5116 y(\(2.2.10\))i(is)i(equiv)-5 b(alen)n(t)36 b(to)h(de\014ning)g FJ(\016)12 b FQ(:)31 b FJ(V)1935 5069 y FE(\030)1907 5116 y FL(\000)-40 b(!)39 b FJ(V)2121 5086 y FE(\003\003)2193 5116 y FQ(,)g(so)d(ev)n(ery)g(ribb)r(on)g(category)f(is)i(also)456 5216 y(w)n(eakly)26 b(ribb)r(on.)p eop %%Page: 109 17 109 112 bop 1144 226 a FM(5.3.)29 b(RIBBON)i(CA)-5 b(TEGORIES)28 b(VIA)i(THE)f(Hom)f(SP)-5 b(A)n(CES)566 b(109)605 425 y FP(Exer)n(cise)32 b FQ(5.3.6)p FP(.)40 b FQ(\(i\))f(Sho)n(w)f(that)h (in)h(ev)n(ery)d(semisimple)i(w)n(eakly)f(ribb)r(on)g(category)-7 b(,)456 525 y(the)37 b(map)g FJ(\036)9 b FQ(:)45 b(Hom\()p FJ(V)1201 495 y FE(\003)1239 525 y FJ(;)14 b(X)7 b FQ(\))38 b FL(!)h FQ(Hom\()p FK(1)p FJ(;)14 b(X)31 b FL(\012)24 b FJ(V)2090 495 y FE(\003\003)2162 525 y FQ(\))38 b(giv)n(en)e(b)n(y)h FJ( )42 b FL(7!)d FQ(\()p FJ( )28 b FL(\012)c FQ(id\))p FJ(i)3134 537 y FI(V)3188 521 y Fx(\003)3264 525 y FQ(is)37 b(an)456 624 y(isomorphism.)605 724 y(\(ii\))g(Sho)n(w)f(that)h(in)f (ev)n(ery)f(semisimple)i(w)n(eakly)e(ribb)r(on)h(category)e(one)i(can)g (de\014ne)h(a)456 831 y(family)26 b(of)h(functorial)f(isomorphisms)f FJ(\016)12 b FQ(:)28 b FJ(V)1912 784 y FE(\030)1884 831 y FL(\000)-40 b(!)24 b FJ(V)2082 801 y FE(\003\003)2181 831 y FQ(b)n(y)j(the)f(condition)h(that)g(the)g(follo)n(wing)456 930 y(diagram)f(b)r(e)i(comm)n(utativ)n(e:)1389 1074 y FL(h)p FJ(V)5 b(;)14 b(X)7 b FL(i)1763 1027 y FE(')1665 1074 y FL(\000)-28 b(\000)-19 b(\000)g(\000)-28 b(!)41 b FQ(Hom\()p FJ(V)2227 1044 y FE(\003)2265 1074 y FJ(;)14 b(X)7 b FQ(\))1435 1232 y FI(\033)1476 1144 y Fy(?)1476 1194 y(?)1476 1244 y(y)2155 1144 y(?)2155 1194 y(?)2155 1244 y(y)2210 1234 y FI(\036)1384 1414 y FL(h)p FJ(X)r(;)14 b(V)19 b FL(i)1714 1367 y FM(id)10 b FE(\012)p FI(\016)1665 1414 y FL(\000)-28 b(\000)-19 b(\000)g(\000)-28 b(!)113 b(h)p FJ(X)r(;)14 b(V)2234 1384 y FE(\003\003)2306 1414 y FL(i)2493 1233 y FJ(:)605 1541 y FQ(\(iii\))21 b(Sho)n(w)e(that)h(in) g(ev)n(ery)f(semisimple)h(w)n(eakly)f(ribb)r(on)g(category)-7 b(,)20 b(one)f(has)h(\()p FJ(\022)3081 1553 y FI(A)3138 1541 y FL(\012)s FQ(id\))p FJ(f)32 b FQ(=)456 1640 y(\(id)14 b FL(\012)p FJ(\022)675 1652 y FI(B)732 1640 y FQ(\))p FJ(f)36 b FQ(for)27 b(ev)n(ery)g FJ(f)17 b FQ(:)28 b FK(1)23 b FL(!)g FJ(A)c FL(\012)f FJ(B)t FQ(.)37 b(\(Hin)n(t:)g(use)28 b FJ(\022)2203 1610 y FE(\003)2201 1663 y FI(V)2282 1640 y FQ(=)22 b FJ(\022)2408 1652 y FI(V)2462 1636 y Fx(\003)2501 1640 y FQ(.\))605 1781 y(Note,)30 b(ho)n(w)n(ev)n(er,)e(that)i(in)g (general,)e(\()p FJ(V)39 b FL(\012)20 b FJ(W)12 b FQ(\))2093 1751 y FE(\003)2157 1781 y FL(6')26 b FJ(W)2338 1751 y FE(\003)2396 1781 y FL(\012)19 b FJ(V)2547 1751 y FE(\003)2585 1781 y FQ(,)30 b(so)f(the)h(axiom)f FJ(\016)3173 1793 y FI(V)14 b FE(\012)p FI(W)3380 1781 y FQ(=)456 1881 y FJ(\016)493 1893 y FI(V)569 1881 y FL(\012)k FJ(\016)689 1893 y FI(W)792 1881 y FQ(do)r(es)27 b(not)h(mak)n(e)e(sense.)605 2021 y FP(Remark)32 b FQ(5.3.7)p FP(.)39 b FQ(The)24 b(authors)f(do)h(not)g(kno)n(w)f(an)n(y)g(example)g(of)h(a)g (semisimple)g(ab)r(elian)456 2121 y(category)h(whic)n(h)j(is)f(w)n (eakly)g(rigid)g(but)h(not)f(rigid.)605 2262 y(No)n(w)g(w)n(e)g(can)h (form)n(ulate)e(the)i(main)g(theorem)f(of)h(this)f(section.)605 2402 y FP(Theorem)32 b FQ(5.3.8)p FP(.)40 b FO(L)l(et)28 b FL(C)33 b FO(b)l(e)c(a)g(semisimple)i(we)l(akly)f(ribb)l(on)f(c)l (ate)l(gory)h(with)f(simple)h(ob-)456 2502 y(je)l(cts)j FJ(V)696 2514 y FI(i)724 2502 y FJ(;)14 b(i)28 b FL(2)h FJ(I)7 b FO(.)48 b(Then)34 b(formulas)40 b FQ(\(5.3.3\))o FO({)p FQ(\(5.3.7\))p FO(,)34 b(with)g FJ(\016)h FO(de\014ne)l(d)f(as)f (in)g(Exer)l(cise)g FQ(5.3.6)p FO(,)456 2602 y(de\014ne)j(MS)g(data)h (for)g FL(C)5 b FO(.)58 b(Conversely,)40 b(every)d(c)l(ol)t(le)l(ction) h(of)f(MS)f(data)h(for)g(a)g(semisimple)456 2701 y(ab)l(elian)31 b(c)l(ate)l(gory)f FL(C)k FO(is)d(obtaine)l(d)f(in)g(this)g(way.)605 2842 y FP(Pr)n(oof.)41 b FQ(The)d(\014rst)f(statemen)n(t)h(of)g(the)g (theorem)f(is)h(parallel)f(to)h(Prop)r(osition)e(5.3.3.)456 2942 y(The)27 b(pro)r(of)h(is)f(also)g(quite)h(parallel;)e(w)n(e)i (just)g(ha)n(v)n(e)f(to)g(c)n(hec)n(k)g(that)h(all)f(the)i(argumen)n (ts)d(w)n(ork)456 3041 y(in)h(a)g(w)n(eakly)g(rigid)f(category)g(as)g (w)n(ell)i(as)e(in)i(a)f(rigid)g(one.)36 b(This)28 b(is)f(left)h(to)f (the)h(reader)e(as)h(an)456 3141 y(exercise;)f(part)g(of)h(it)g(is)g (con)n(tained)f(in)h(Exercise)e(5.3.6.)35 b(In)27 b(particular,)f(the)h (iden)n(tit)n(y)h(\(2.2.8\))456 3240 y FJ(\022)495 3252 y FI(V)14 b FE(\012)p FI(W)699 3240 y FQ(=)22 b FJ(\033)833 3252 y FI(W)9 b(V)963 3240 y FJ(\033)1010 3252 y FI(V)15 b(W)1139 3240 y FQ(\()p FJ(\022)1210 3252 y FI(V)1275 3240 y FL(\012)7 b FJ(\022)1386 3252 y FI(W)1460 3240 y FQ(\))22 b(will)g(giv)n(e)f(the)h(Rotation)f(axiom,)h(and)g(the)g (iden)n(tit)n(y)h(\(2.2.10\))456 3340 y FJ(\022)495 3352 y FI(V)548 3336 y Fx(\003)610 3340 y FQ(=)g FJ(\022)739 3310 y FE(\003)737 3363 y FI(V)822 3340 y FQ(will)28 b(giv)n(e)e(the)i(Dehn)h(t)n(wist)e(axiom.)605 3440 y(The)g(pro)r(of)f (of)h(the)g(con)n(v)n(erse)e(statemen)n(t)i(is)g(more)f(complicated.)36 b(F)-7 b(or)26 b(con)n(v)n(enience,)g(w)n(e)456 3539 y(split)33 b(it)h(in)n(to)f(sev)n(eral)e(steps.)54 b(T)-7 b(o)33 b(simplify)h(the)f(notation,)i(w)n(e)d(will)i(write)f(just)h FL(h)p FJ(:)14 b(:)g(:)g(;)g(R)q FL(i)22 b(\012)456 3639 y(h)p FJ(R)q(;)14 b(:)g(:)g(:)o FL(i)p FQ(,)28 b(omitting)g(the)g(sup)r (erscripts.)37 b(Since)28 b FJ(R)g FQ(is)g(symmetric,)f(this)h(causes)f (no)g(problems.)456 3739 y(The)19 b(symmetry)g(of)h FJ(G)g FQ(axiom)e(MS5)i(implies)f(that)h(the)g(order)e(of)i(the)f(factors)g (is)g(not)h(imp)r(ortan)n(t)456 3838 y(for)27 b(de\014ning)g FJ(G)p FQ(.)38 b(W)-7 b(e)28 b(will)f(implicitly)i(use)e(this.)605 3938 y(Let)g(us)g(start)g(b)n(y)g(constructing)f(the)i(dualit)n(y)f (and)g(tensor)f(pro)r(duct)h(on)g FL(C)32 b FQ(from)27 b(the)g(MS)456 4038 y(data.)605 4178 y FP(Lemma)k FQ(5.3.9)p FP(.)40 b FO(Given)32 b(MS)g(data)h(for)f FL(C)5 b FO(,)33 b(ther)l(e)f(exists)f(an)h(involution)g FL(\003)9 b FQ(:)28 b FJ(I)34 b FL(!)27 b FJ(I)38 b FO(such)456 4278 y(that)29 b FQ(dim)q FL(h)p FJ(V)844 4290 y FI(i)872 4278 y FJ(;)14 b(V)957 4290 y FI(j)992 4278 y FL(i)24 b FQ(=)e FJ(\016)1172 4290 y FI(i;j)1245 4274 y Fx(\003)1285 4278 y FO(.)39 b(A)n(lso,)30 b FJ(R)h FO(is)f(isomorphic)37 b FQ(\()p FO(non-c)l(anonic)l(al)t(ly)7 b FQ(\))32 b FO(to)2942 4216 y Fy(L)3048 4278 y FJ(V)3096 4290 y FI(i)3142 4278 y Fw(\002)18 b FJ(V)3273 4290 y FI(i)3296 4274 y Fx(\003)3336 4278 y FO(.)605 4419 y FP(Pr)n(oof.)41 b FQ(De\014ne)35 b FJ(A)1259 4431 y FI(ij)1353 4419 y FQ(=)f(dim)p FL(h)p FJ(V)1670 4431 y FI(i)1699 4419 y FJ(;)14 b(V)1784 4431 y FI(j)1819 4419 y FL(i)p FQ(,)37 b(and)d(de\014ne)h FJ(B)2389 4431 y FI(ij)2483 4419 y FQ(b)n(y)f FJ(R)i FL(')2803 4356 y Fy(L)2909 4419 y FJ(B)2972 4431 y FI(ij)3031 4419 y FJ(V)3079 4431 y FI(i)3130 4419 y Fw(\002)23 b FJ(V)3266 4431 y FI(j)3301 4419 y FQ(.)58 b(It)456 4518 y(follo)n(ws)19 b(from)h(the)h(non-degeneracy)d(axiom)i(and)g(the)h (existence)f(of)h FJ(Z)26 b FQ(that)21 b FJ(A)f FQ(is)h(a)f(symmetric) 456 4618 y(matrix)29 b(with)h(no)g(zero)e(ro)n(ws)h(or)g(columns.)43 b(F)-7 b(rom)29 b(the)h(symmetry)g(of)f FJ(R)q FQ(,)i(w)n(e)e(get)h (that)g FJ(B)k FQ(is)456 4717 y(a)27 b(symmetric)g(matrix.)605 4817 y(W)-7 b(riting)32 b(the)f(iden)n(tit)n(y)h FL(h)p FJ(V)1451 4829 y FI(i)1479 4817 y FJ(;)14 b(V)1564 4829 y FI(j)1600 4817 y FL(i)30 b FQ(=)f FL(h)p FJ(V)1836 4829 y FI(i)1864 4817 y FJ(;)14 b(R)1965 4787 y FM(\(1\))2054 4817 y FL(i)21 b(\012)g(h)p FJ(R)2289 4787 y FM(\(2\))2378 4817 y FJ(;)14 b(V)2463 4829 y FI(j)2498 4817 y FL(i)32 b FQ(w)n(e)f(get)g(the)h(iden)n(tit)n(y)g FJ(A)e FQ(=)456 4917 y FJ(AB)t(A)p FQ(.)40 b(W)-7 b(e)28 b(lea)n(v)n(e)f(it)i(to)f(the) h(reader)e(to)h(sho)n(w)g(that)g(if)h FJ(A;)14 b(B)33 b FQ(are)27 b(symmetric)h(matrices)g(with)456 5016 y(non-negativ)n(e)j (in)n(teger)h(en)n(tries)g(and)g FJ(A)h FQ(has)g(no)f(zero)g(columns,)i (then)f(suc)n(h)f(an)h(iden)n(tit)n(y)g(is)456 5116 y(p)r(ossible)g (only)g(if)i FJ(A)e FQ(=)g FJ(B)38 b FQ(is)c(a)f(p)r(erm)n(utation)g (of)h(order)e(2.)55 b(\(Hin)n(t:)50 b(use)34 b FJ(AB)k FQ(=)33 b(\()p FJ(AB)t FQ(\))3299 5086 y FM(2)3371 5116 y FQ(to)456 5216 y(pro)n(v)n(e)26 b(that)h FJ(AB)32 b FQ(either)c(has)f(a)g(zero)g(ro)n(w)f(or)h(column,)g(or)g(it)h(is)g (the)g(iden)n(tit)n(y)f(matrix.\))p 3384 5216 4 57 v 3388 5163 50 4 v 3388 5216 V 3437 5216 4 57 v eop %%Page: 110 18 110 113 bop 456 226 a FM(110)1010 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FK(1.)42 b(De\014ning)31 b(the)h(dualit)m(y)g(functor.)37 b FQ(De\014ne)28 b(the)g(functor)g FL(\003)f FQ(b)n(y)1559 568 y(Hom\()p FJ(V)1831 534 y FE(\003)1870 568 y FJ(;)14 b(X)7 b FQ(\))22 b(=)h FL(h)p FJ(V)5 b(;)14 b(X)7 b FL(i)-1899 b FQ(\(5.3.8\))456 716 y(\(see)30 b(Lemma)g(5.3.1\).)45 b(Then)30 b(the)h(previous)f(lemma)g(immediately)h(implies)f FJ(V)2992 686 y FE(\003)2973 738 y FI(i)3058 716 y FL(')e FJ(V)3199 728 y FI(i)3222 712 y Fx(\003)3292 716 y FQ(\(not)456 816 y(canonically!\).)35 b(It)28 b(is)f(easy)f(to)g(see)h(from)g(this)g (that)g FL(\003)g FQ(is)g(an)g(an)n(ti-equiv)-5 b(alence)26 b(of)g(categories.)456 915 y(In)f(particular,)g(this)h(implies)f(that)h (ev)n(ery)e(ob)5 b(ject)25 b FJ(V)42 b FL(2)24 b(C)30 b FQ(is)25 b(completely)g(determined)h(b)n(y)f(the)456 1015 y(functor)i FL(h)p FJ(V)5 b(;)14 b FL(\001i)24 b FQ(=)e(Hom\()p FJ(V)1305 985 y FE(\003)1343 1015 y FJ(;)14 b FL(\001)p FQ(\).)605 1115 y(Note)26 b(that)h(if)g(the)g(MS)f(data)g (come)g(from)g(the)h(structure)f(of)g(a)g(w)n(eakly)f(ribb)r(on)h (category)456 1214 y(on)32 b FL(C)37 b FQ(\(see)32 b(Prop)r(osition)f (5.3.3\),)i(then)f(the)h FL(\003)f FQ(functor)h(de\014ned)f(ab)r(o)n(v) n(e)f(coincides)h(with)h(the)456 1314 y(one)27 b(giv)n(en)g(b)n(y)g (the)h(rigidit)n(y)f(axioms.)605 1413 y FK(2.)76 b FJ(R)41 b FQ(=)964 1351 y Fy(L)1070 1413 y FJ(V)1137 1383 y FE(\003)1118 1435 y FI(i)1200 1413 y Fw(\002)25 b FJ(V)1338 1425 y FI(i)1366 1413 y FK(.)67 b FQ(T)-7 b(o)37 b(pro)n(v)n(e)f(this,)41 b(let)d(us)f(write)h FJ(R)i FL(')2700 1351 y Fy(P)2802 1413 y FJ(X)2871 1425 y FI(i)2923 1413 y Fw(\002)25 b FJ(V)3061 1425 y FI(i)3127 1413 y FQ(for)37 b(some)456 1513 y FJ(X)525 1525 y FI(i)575 1513 y FL(2)23 b FQ(ind)p FL(\000C)5 b FQ(.)37 b(The)28 b(isomorphism)e FJ(G)i FQ(giv)n(es,)e(in)i(particular,)f(an)g(isomorphism)1364 1668 y FL(h)p FJ(A;)14 b(V)1562 1634 y FE(\003)1543 1689 y FI(i)1600 1668 y FL(i)24 b(')1743 1589 y Fy(M)1869 1668 y FL(h)p FJ(A;)14 b(X)2069 1680 y FI(i)2097 1668 y FL(i)k(\012)g(h)p FJ(V)2310 1680 y FI(i)2339 1668 y FJ(;)c(V)2443 1634 y FE(\003)2424 1689 y FI(i)2481 1668 y FL(i)p FJ(:)456 1828 y FQ(Since)40 b FL(h)p FJ(V)765 1840 y FI(i)794 1828 y FJ(;)14 b(V)897 1798 y FE(\003)879 1849 y FI(i)936 1828 y FL(i)44 b FQ(=)g(Hom\()p FJ(V)1393 1798 y FE(\003)1374 1849 y FI(i)1432 1828 y FJ(;)14 b(V)1535 1798 y FE(\003)1517 1849 y FI(i)1574 1828 y FQ(\))44 b(=)g FJ(k)s FQ(,)g(w)n(e)c(get)g(canonical)g(isomorphisms)f FL(h)p FJ(A;)14 b(V)3265 1798 y FE(\003)3246 1849 y FI(i)3303 1828 y FL(i)45 b FQ(=)456 1927 y FL(h)p FJ(A;)14 b(X)656 1939 y FI(i)683 1927 y FL(i)p FQ(.)38 b(Th)n(us,)27 b(w)n(e)g(ha)n(v)n (e)g(constructed)g(an)g(isomorphism)f FJ(R)e FL(')2546 1865 y Fy(L)2652 1927 y FJ(V)2719 1897 y FE(\003)2700 1949 y FI(i)2775 1927 y Fw(\002)18 b FJ(V)2906 1939 y FI(i)2962 1927 y FQ(suc)n(h)27 b(that)h(the)456 2027 y(isomorphism)e FJ(G)9 b FQ(:)28 b FL(h)p FJ(X)r(;)14 b(Y)19 b FL(i)k(')g(h)p FJ(X)r(;)14 b(R)q FL(i)k(\012)g(h)p FJ(R)q(;)c(Y)19 b FL(i)28 b FQ(is)f(giv)n(en)g(b)n(y)h(\(5.3.6\).)605 2129 y FK(3.)42 b(T)-8 b(ensor)32 b(pro)s(duct.)k FQ(De\014ne)28 b(the)g(functor)g FL(\012)9 b FQ(:)28 b FL(C)2288 2099 y Fv(\002)p FM(2)2399 2129 y FL(!)23 b(C)33 b FQ(b)n(y)1505 2272 y FL(h)p FJ(X)r(;)14 b(A)19 b FL(\012)f FJ(B)t FL(i)24 b FQ(=)e FL(h)p FJ(X)r(;)14 b(A;)g(B)t FL(i)p FJ(;)-1924 b FQ(\(5.3.9\))456 2420 y(\(it)21 b(is)f(w)n(ell)g(de\014ned)g(b)n(y)g (the)h(results)e(of)h(Step)h(1\).)34 b(More)20 b(generally)-7 b(,)20 b(de\014ne)h(the)f(tensor)g(pro)r(duct)456 2520 y(of)27 b FJ(n)h FQ(ob)5 b(jects)27 b(b)n(y)g(the)h(follo)n(wing)f (form)n(ula:)1262 2663 y FL(h)p FJ(X)r(;)14 b(A)1464 2675 y FM(1)1520 2663 y FL(\012)k(\001)c(\001)g(\001)k(\012)g FJ(A)1863 2675 y FI(n)1908 2663 y FL(i)24 b FQ(=)e FL(h)p FJ(X)r(;)14 b(A)2253 2675 y FM(1)2291 2663 y FJ(;)g(:)g(:)g(:)f(;)h(A) 2537 2675 y FI(n)2583 2663 y FL(i)p FJ(:)456 2806 y FQ(Next,)28 b(de\014ne)f(isomorphisms)456 2974 y(\(5.3.10\))81 b FJ(A)877 2986 y FM(1)933 2974 y FL(\012)18 b(\001)c(\001)g(\001)19 b(\012)f FJ(A)1277 2986 y FI(i)1323 2974 y FL(\012)g FQ(\()p FJ(B)1501 2986 y FM(1)1557 2974 y FL(\012)g(\001)c(\001)g(\001) k(\012)g FJ(B)1901 2986 y FI(k)1942 2974 y FQ(\))h FL(\012)f FJ(A)2138 2986 y FI(i)p FM(+1)2268 2974 y FL(\012)g(\001)c(\001)g(\001) 19 b(\012)f FJ(A)2612 2986 y FI(n)1497 3099 y FL(')k FJ(A)1646 3111 y FM(1)1702 3099 y FL(\012)c(\001)c(\001)g(\001)k(\012)g FJ(A)2045 3111 y FI(i)2092 3099 y FL(\012)g FJ(B)2238 3111 y FM(1)2294 3099 y FL(\012)g(\001)c(\001)g(\001)k(\012)g FJ(B)2638 3111 y FI(k)2697 3099 y FL(\012)g FJ(A)2842 3111 y FI(i)p FM(+1)2973 3099 y FL(\012)g(\001)c(\001)g(\001)k(\012)g FJ(A)3316 3111 y FI(n)456 3242 y FQ(as)27 b(the)h(follo)n(wing)e(comp)r (osition:)881 3385 y FL(h)p FJ(X)6 b(;)14 b(A)1087 3397 y FM(1)1125 3385 y FJ(;)g(:)g(:)g(:)f(;)h(A)1371 3397 y FI(i)1399 3385 y FJ(;)g(B)1499 3397 y FM(1)1555 3385 y FL(\012)k(\001)c(\001)g(\001)k(\012)g FJ(B)1899 3397 y FI(k)1940 3385 y FJ(;)c(A)2039 3397 y FI(i)p FM(+1)2151 3385 y FJ(;)g(:)g(:)g(:)f(;)h(A)2397 3397 y FI(n)2443 3385 y FL(i)1012 3514 y(')22 b(h)p FJ(X)r(;)14 b(A)1301 3526 y FM(1)1339 3514 y FJ(;)g(:)g(:)g(:)f(;)h(A)1585 3526 y FI(i)1613 3514 y FJ(;)g(R)q(;)g(A)1813 3526 y FI(i)p FM(+1)1924 3514 y FJ(;)g(:)g(:)g(:)g(;)g(A)2171 3526 y FI(n)2216 3514 y FL(i)19 b(\012)f(h)p FJ(R)q(;)c(B)2546 3526 y FM(1)2602 3514 y FL(\012)k(\001)c(\001)g(\001)k(\012)g FJ(B)2946 3526 y FI(k)2987 3514 y FL(i)1012 3644 y(')k(h)p FJ(X)r(;)14 b(A)1301 3656 y FM(1)1339 3644 y FJ(;)g(:)g(:)g(:)f(;)h(A) 1585 3656 y FI(i)1613 3644 y FJ(;)g(R)q(;)g(A)1813 3656 y FI(i)p FM(+1)1924 3644 y FJ(;)g(:)g(:)g(:)g(;)g(A)2171 3656 y FI(n)2216 3644 y FL(i)19 b(\012)f(h)p FJ(R)q(;)c(B)2546 3656 y FM(1)2583 3644 y FJ(;)g(:)g(:)g(:)g(;)g(B)2831 3656 y FI(k)2872 3644 y FL(i)1012 3773 y(')22 b(h)p FJ(X)r(;)14 b(A)1301 3785 y FM(1)1339 3773 y FJ(;)g(:)g(:)g(:)f(;)h(A)1585 3785 y FI(i)1613 3773 y FJ(;)g(B)1713 3785 y FM(1)1750 3773 y FJ(;)g(:)g(:)g(:)g(;)g(B)1998 3785 y FI(k)2038 3773 y FJ(;)g(A)2137 3785 y FI(i)p FM(+1)2249 3773 y FJ(;)g(:)g(:)g(:)g(;)g(A)2496 3785 y FI(n)2541 3773 y FL(i)p FJ(;)456 3927 y FQ(where)35 b(the)h(isomorphisms)f(are,)i(resp)r (ectiv)n(ely)-7 b(,)37 b FJ(G)2098 3897 y FE(\000)p FM(1)2187 3927 y FQ(,)h(the)e(de\014nition)h(of)e(tensor)g(pro)r(duct,)456 4026 y(and)27 b FJ(G)p FQ(.)605 4181 y FP(Lemma)k FQ(5.3.10)p FP(.)40 b FO(L)l(et)29 b FJ(X)36 b FO(b)l(e)30 b(an)f(expr)l(ession)i (of)f(the)g(form)1432 4324 y FJ(X)f FQ(=)23 b(\()p FJ(A)1712 4336 y FM(1)1768 4324 y FL(\012)18 b FQ(\()p FJ(A)1945 4336 y FM(2)2001 4324 y FL(\012)g(\001)c(\001)g(\001)g FQ(\)\))19 b FL(\012)f FJ(A)2423 4336 y FI(n)456 4471 y FO(with)31 b(any)g(gr)l(ammatic)l(al)t(ly)h(c)l(orr)l(e)l(ct)f(p)l (ar)l(entheses)g(arr)l(angement)f FQ(\()p FO(p)l(ar)l(entheses)h(may)h (enclose)456 4571 y(any)e(numb)l(er)f(of)h(factors)p FQ(\))p FO(.)40 b(Then)31 b(any)f(two)g(isomorphisms)1528 4714 y FJ(')9 b FQ(:)28 b FJ(X)i FL(')22 b FJ(A)1890 4726 y FM(1)1946 4714 y FL(\012)c(\001)c(\001)g(\001)19 b(\012)f FJ(A)2290 4726 y FI(n)2335 4714 y FJ(;)456 4862 y FO(obtaine)l(d)30 b(as)h(a)f(c)l(omp)l(osition)h(of)f(the)g (morphisms)h(of)g(the)f(form)37 b FQ(\(5.3.10\))o FO(,)30 b(ar)l(e)g(e)l(qual.)605 5016 y FP(Pr)n(oof.)41 b FQ(Easy)20 b(induction)i(argumen)n(ts)e(sho)n(w)h(that)h(it)g(su\016ces)f(to)h (pro)n(v)n(e)e(this)h(statemen)n(t)456 5116 y(in)27 b(the)h(case)f (when)g(w)n(e)h(ha)n(v)n(e)e(just)i(t)n(w)n(o)f(pairs)f(of)i(paren)n (theses.)35 b(Th)n(us,)27 b(w)n(e)h(need)f(to)h(consider)456 5216 y(the)38 b(arrangemen)n(ts)e(of)i(the)h(form)f FL(\001)14 b(\001)g(\001)f FQ(\()p FL(\001)h(\001)g(\001)g FQ(\()p FL(\001)g(\001)g(\001)g FQ(\))g FL(\001)g(\001)g(\001)g FQ(\))g FL(\001)g(\001)g(\001)52 b FQ(and)38 b FL(\001)14 b(\001)g(\001)g FQ(\()p FL(\001)g(\001)g(\001)g FQ(\))g FL(\001)g(\001)g(\001)g FQ(\()p FL(\001)g(\001)g(\001)g FQ(\))g FL(\001)g(\001)g(\001)f FQ(.)69 b(F)-7 b(or)p eop %%Page: 111 19 111 114 bop 1144 226 a FM(5.3.)29 b(RIBBON)i(CA)-5 b(TEGORIES)28 b(VIA)i(THE)f(Hom)f(SP)-5 b(A)n(CES)566 b(111)456 425 y FQ(b)r(oth)24 b(of)h(them)g(the)g(statemen)n(t)f(easily)g(follo)n(ws) f(from)h(the)h(de\014nitions)g(and)f(the)h(asso)r(ciativit)n(y)456 525 y(of)i FJ(G)p FQ(.)p 3384 525 4 57 v 3388 472 50 4 v 3388 525 V 3437 525 4 57 v 605 688 a(This)32 b(sho)n(ws)f(that)i FL(\012)f FQ(is)g(indeed)g(asso)r(ciativ)n(e;)h(in)f(particular,)g(w)n (e)g(can)g(de\014ne)g(asso)r(cia-)456 788 y(tivit)n(y)27 b(constrain)n(t)g FJ(A)18 b FL(\012)g FQ(\()p FJ(B)23 b FL(\012)18 b FJ(C)6 b FQ(\))24 b FL(')f FQ(\()p FJ(A)c FL(\012)f FJ(B)t FQ(\))h FL(\012)f FJ(C)33 b FQ(whic)n(h)28 b(satis\014es)f(the)h(p)r(en)n(tagon)f(axiom.)605 888 y FK(4.)42 b(Unit.)36 b FQ(De\014ne)28 b(the)g(ob)5 b(ject)28 b FK(1)23 b FL(2)g(C)32 b FQ(b)n(y)1712 1032 y FL(h)p FK(1)p FJ(;)14 b(X)7 b FL(i)23 b FQ(=)g FL(h)p FJ(X)7 b FL(i)-1732 b FQ(\(5.3.11\))456 1181 y(\(as)27 b(b)r(efore,)g(it)h(is) g(w)n(ell)f(de\014ned)h(due)g(to)f(the)h(results)f(of)h(Step)g(1\).)605 1281 y(De\014ne)22 b(morphisms)f FL(h)p FJ(A)1365 1293 y FM(1)1403 1281 y FJ(;)14 b(:)g(:)g(:)f(;)h(A)1649 1293 y FI(i)1677 1281 y FJ(;)g FK(1)p FJ(;)g(A)1861 1293 y FI(i)p FM(+1)1972 1281 y FJ(;)g(:)g(:)g(:)g(;)g(A)2219 1293 y FI(n)2264 1281 y FL(i)24 b(')e(h)p FJ(A)2501 1293 y FM(1)2539 1281 y FJ(;)14 b(:)g(:)g(:)g(;)g(A)2786 1293 y FI(i)2814 1281 y FJ(;)g(A)2913 1293 y FI(i)p FM(+1)3024 1281 y FJ(;)g(:)g(:)g(:)g(;)g(A)3271 1293 y FI(n)3316 1281 y FL(i)22 b FQ(as)456 1380 y(the)28 b(follo)n(wing)e(comp)r (osition)644 1525 y FL(h)p FJ(A)738 1537 y FM(1)776 1525 y FJ(;)14 b(:)g(:)g(:)f(;)h(A)1022 1537 y FI(i)1050 1525 y FJ(;)g FK(1)p FJ(;)g(A)1234 1537 y FI(i)p FM(+1)1346 1525 y FJ(;)g(:)g(:)g(:)f(;)h(A)1592 1537 y FI(n)1638 1525 y FL(i)23 b(')g(h)p FJ(A)1875 1537 y FM(1)1912 1525 y FJ(;)14 b(:)g(:)g(:)g(;)g(A)2159 1537 y FI(i)2187 1525 y FJ(;)g(R)q(;)g(A)2387 1537 y FI(i)p FM(+1)2498 1525 y FJ(;)g(:)g(:)g(:)g(;)g(A)2745 1537 y FI(n)2790 1525 y FL(i)19 b(\012)f(h)p FK(1)p FJ(;)c(R)q FL(i)822 1654 y(')22 b(h)p FJ(A)1003 1666 y FM(1)1041 1654 y FJ(;)14 b(:)g(:)g(:)g(;)g(A)1288 1666 y FI(i)1316 1654 y FJ(;)g(R)q(;)g(A)1516 1666 y FI(i)p FM(+1)1627 1654 y FJ(;)g(:)g(:)g(:)g(;)g(A)1874 1666 y FI(n)1919 1654 y FL(i)19 b(\012)f(h)p FJ(R)q FL(i)23 b(')g(h)p FJ(A)2386 1666 y FM(1)2424 1654 y FJ(;)14 b(:)g(:)g(:)f(;)h (A)2670 1666 y FI(i)2698 1654 y FJ(;)g(A)2797 1666 y FI(i)p FM(+1)2909 1654 y FJ(;)g(:)g(:)g(:)f(;)h(A)3155 1666 y FI(n)3201 1654 y FL(i)p FJ(:)456 1799 y FQ(Note)41 b(that)g(this)h(construction)e(remains)g(v)-5 b(alid)41 b(for)g FJ(n)46 b FQ(=)f(0,)f(in)d(whic)n(h)h(case,)h(using)e(the)456 1899 y(normalization)26 b(axiom,)g(w)n(e)i(get)1804 2043 y FL(h)p FK(1)p FL(i)23 b FQ(=)g FJ(k)s(:)-1640 b FQ(\(5.3.12\))605 2188 y(Using)27 b(the)h(de\014nition)g(of)g(tensor)f(pro)r(duct,)g(w)n (e)h(see)f(that)h(the)g(isomorphism)942 2332 y FL(h)p FJ(X)r(;)14 b(A)1144 2344 y FM(1)1181 2332 y FJ(;)g(:)g(:)g(:)g(;)g(A) 1428 2344 y FI(i)1456 2332 y FJ(;)g FK(1)p FJ(;)g(A)1640 2344 y FI(i)p FM(+1)1751 2332 y FJ(;)g(:)g(:)g(:)g(;)g(A)1998 2344 y FI(n)2043 2332 y FL(i)23 b(')g(h)p FJ(X)r(;)14 b(A)2388 2344 y FM(1)2425 2332 y FJ(;)g(:)g(:)g(:)g(;)g(A)2672 2344 y FI(i)2700 2332 y FJ(;)g(A)2799 2344 y FI(i)p FM(+1)2911 2332 y FJ(;)g(:)g(:)g(:)f(;)h(A)3157 2344 y FI(n)3203 2332 y FL(i)456 2477 y FQ(giv)n(es)26 b(rise)h(to)g(an)h(isomorphism) 775 2621 y FJ(A)837 2633 y FM(1)893 2621 y FL(\012)18 b(\001)c(\001)g(\001)k(\012)g FJ(A)1236 2633 y FI(i)1283 2621 y FL(\012)g FK(1)g FL(\012)g FJ(A)1577 2633 y FI(i)p FM(+1)1707 2621 y FL(\012)g(\001)c(\001)g(\001)19 b(\012)f FJ(A)2051 2633 y FI(n)2119 2621 y FL(')23 b FJ(A)2269 2633 y FM(1)2325 2621 y FL(\012)18 b(\001)c(\001)g(\001)k(\012)g FJ(A)2668 2633 y FI(i)2714 2621 y FL(\012)g FJ(A)2859 2633 y FI(i)p FM(+1)2990 2621 y FL(\012)g(\001)c(\001)g(\001)k(\012)g FJ(A)3333 2633 y FI(n)3379 2621 y FJ(:)-2946 b FQ(\(5.3.13\))605 2776 y FP(Lemma)31 b FQ(5.3.11)p FP(.)40 b FO(The)d(fol)t(lowing)i (diagr)l(am,)g(with)e(the)g(horizontal)h(map)f(given)f(by)h(the)456 2876 y(asso)l(ciativity)30 b(isomorphism)h(and)e(the)g(two)f(others)h (by)g(the)g(unit)f(isomorphisms)37 b FQ(\(5.3.13\))o FO(,)29 b(is)456 2976 y(c)l(ommutative)6 b FQ(:)1349 3120 y FJ(A)19 b FL(\012)f FQ(\()p FK(1)h FL(\012)f FJ(B)t FQ(\))1891 3365 y FD(")p FC(")1859 3339 y FB(D)1830 3314 y(D)1800 3289 y(D)1770 3264 y(D)1741 3240 y(D)1711 3215 y(D)1681 3190 y(D)1651 3166 y(D)2100 3099 y FD(/)p FC(/)p 1819 3101 281 4 v 2124 3124 a FJ(A)h FL(\012)f FK(1)g FL(\012)g FJ(B)2022 3365 y FD(~)p FC(~)p FB(|)2050 3339 y(|)2079 3313 y(|)2107 3287 y(|)2136 3261 y(|)2164 3236 y(|)2193 3210 y(|)2221 3184 y(|)1844 3447 y FJ(A)h FL(\012)f FJ(B)2553 3120 y(:)605 3600 y FP(Pr)n(oof.)41 b FQ(Lo)r(oking)27 b(at)h(the)g(de\014nitions,)h(w)n(e)f(see)f(that)i(the)f(statemen)n(t)h (is)f(equiv)-5 b(alen)n(t)28 b(to)456 3699 y(the)g(comm)n(utativit)n(y) f(of)g(the)h(follo)n(wing)f(diagram:)456 3931 y FL(h)p FJ(X)r(;)14 b(A;)g(R)759 3900 y FE(0)782 3931 y FL(i)k(\012)g(h)p FJ(R)1011 3900 y FE(0)1035 3931 y FJ(;)c FK(1)k FL(\012)g FJ(B)t FL(i)42 b(\000)-28 b(\000)-19 b(\000)g(\000)-28 b(!)103 b(h)p FJ(X)r(;)14 b(A;)g(R)2017 3900 y FE(0)2040 3931 y FL(i)k(\012)g(h)p FJ(R)2269 3900 y FE(0)2293 3931 y FJ(;)c(B)t FL(i)103 b(\000)-28 b(\000)-19 b(\000)g(\000)-28 b(!)249 b(h)p FJ(X)r(;)14 b(A;)g(B)t FL(i)860 4001 y Fy(?)860 4051 y(?)860 4101 y(y)3172 4001 y(x)3172 4051 y(?)3172 4101 y(?)676 4263 y FL(h)p FJ(X)r(;)g(A;)g FK(1)p FJ(;)g(B)t FL(i)263 b(\000)-28 b(\000)-19 b(\000)g(\000)-28 b(!)41 b(h)p FJ(X)r(;)14 b(A;)g(R)1955 4233 y FE(00)1997 4263 y FJ(;)g(B)t FL(i)19 b(\012)f(h)p FK(1)p FJ(;)c(R)2416 4233 y FE(00)2458 4263 y FL(i)42 b(\000)-28 b(\000)-19 b(\000)g(\000)-28 b(!)42 b(h)p FJ(X)r(;)14 b(A;)g(R)3126 4233 y FE(0)o(0)3168 4263 y FJ(;)g(B)t FL(i)19 b(\012)f(h)p FJ(R)3502 4233 y FE(00)3544 4263 y FL(i)456 4399 y FQ(where,)30 b(as)f(b)r(efore,)h FJ(R)1165 4369 y FE(0)1218 4399 y FQ(and)g FJ(R)1446 4369 y FE(00)1518 4399 y FQ(are)f(t)n(w)n(o)g (copies)g(of)h FJ(R)q FQ(.)44 b(But)30 b(this)g(easily)g(follo)n(ws)e (from)i(the)456 4499 y(asso)r(ciativit)n(y)24 b(of)i FJ(G)g FQ(applied)g(to)g(the)g(space)f FL(h)p FJ(X)r(;)14 b(A;)g(R)2167 4468 y FE(00)2209 4499 y FJ(;)g(R)2310 4468 y FE(0)2333 4499 y FL(i)i(\012)e(h)p FK(1)p FJ(;)g(R)2641 4468 y FE(00)2683 4499 y FL(i)i(\012)f(h)p FJ(R)2907 4468 y FE(0)2930 4499 y FJ(;)f(B)t FL(i)p FQ(.)37 b(W)-7 b(e)26 b(lea)n(v)n(e)456 4598 y(the)i(details)f(to)g(the)h(reader.)p 3384 4598 4 57 v 3388 4545 50 4 v 3388 4598 V 3437 4598 4 57 v 605 4762 a FP(Cor)n(ollar)-6 b(y)33 b FQ(5.3.12)p FP(.)39 b FO(The)33 b(isomorphisms)i FK(1)20 b FL(\012)g FJ(X)2351 4715 y FE(\030)2323 4762 y FL(\000)-39 b(!)28 b FJ(X)38 b FO(and)33 b FJ(X)27 b FL(\012)20 b FK(1)3016 4715 y FE(\030)2987 4762 y FL(\000)-39 b(!)28 b FJ(X)7 b FO(,)33 b(given)456 4861 y(by)k FQ(\(5.3.13\))o FO(,)30 b(satisfy)h(the)f(triangle)g(axiom.)605 5016 y FQ(Com)n(bining)24 b(this)g(fact)h(with)g(the)g(MacLane)e(coherence)g(theorem)h(\(Theorem) g(1.1.9\),)g(w)n(e)456 5116 y(see)j(that)h(the)g(MS)g(data)f(indeed)h (de\014nes)f(a)g(structure)g(of)h(a)f(monoidal)g(category)f(on)h FL(C)5 b FQ(.)605 5216 y FK(5.)42 b(De\014nition)31 b(of)g FL(h)14 b(i)p FK(.)37 b FQ(Using)28 b(the)g(unit)g(isomorphisms)e (\(5.3.13\))o(,)h(w)n(e)h(can)f(iden)n(tify)p eop %%Page: 112 20 112 115 bop 456 226 a FM(112)1010 b(5.)29 b(MODULAR)g(FUNCTOR)990 571 y FL(h)p FJ(A)1084 583 y FM(1)1122 571 y FJ(;)14 b(:)g(:)g(:)g(;)g(A)1369 583 y FI(n)1414 571 y FL(i)1498 524 y FE(\030)1469 571 y FL(\000)-39 b(!)23 b(h)p FK(1)p FJ(;)14 b(A)1780 583 y FM(1)1817 571 y FJ(;)g(:)g(:)g(:)g(;)g(A)2064 583 y FI(n)2109 571 y FL(i)2193 524 y FE(\030)2165 571 y FL(\000)-40 b(!)23 b FQ(Hom\()p FK(1)2549 537 y FE(\003)2587 571 y FJ(;)14 b(A)2686 583 y FM(1)2742 571 y FL(\012)k(\001)c(\001)g (\001)19 b(\012)f FJ(A)3086 583 y FI(n)3131 571 y FQ(\))p FJ(:)456 737 y FQ(Next,)43 b(let)c(us)h(construct)f(an)g(isomorphism)g FK(1)2068 690 y FE(\030)2039 737 y FL(\000)-39 b(!)43 b FK(1)2239 707 y FE(\003)2277 737 y FQ(.)72 b(Using)41 b(\(5.3.12\))o(,)h(w)n(e)e(can)f(write)456 844 y(Hom\()p FK(1)709 814 y FE(\003)747 844 y FJ(;)14 b FK(1)p FQ(\))24 b(=)f FL(h)p FK(1)p FL(i)i FQ(=)f FJ(k)s FQ(.)38 b(Th)n(us,)28 b(1)c FL(2)g FJ(k)31 b FQ(giv)n(es)d(an)f(isomorphism)h FK(1)2669 797 y FE(\030)2640 844 y FL(\000)-39 b(!)24 b FK(1)2821 814 y FE(\003)2859 844 y FQ(;)29 b(com)n(bining)e(this)456 944 y(isomorphism)f(with)i(the)g(previous)f(iden)n(tit)n(y)-7 b(,)27 b(w)n(e)h(can)f(iden)n(tify)1241 1090 y FL(h)p FJ(A)1335 1102 y FM(1)1372 1090 y FJ(;)14 b(:)g(:)g(:)g(;)g(A)1619 1102 y FI(n)1664 1090 y FL(i)24 b(')e FQ(Hom\()p FK(1)p FJ(;)14 b(A)2159 1102 y FM(1)2215 1090 y FL(\012)k(\001)c(\001)g(\001) 19 b(\012)f FJ(A)2559 1102 y FI(n)2604 1090 y FQ(\))p FJ(:)-2203 b FQ(\(5.3.14\))605 1236 y FK(6.)57 b(Comm)m(utativit)m(y)36 b(isomorphism.)45 b FQ(De\014ne)33 b(the)f(comm)n(utativit)n(y)g (isomorphism)456 1336 y FJ(\033)12 b FQ(:)28 b FJ(A)19 b FL(\012)f FJ(B)27 b FL(!)c FJ(B)g FL(\012)18 b FJ(A)28 b FQ(using)f(the)h(follo)n(wing)e(comp)r(osition:)1015 1487 y FL(h)p FJ(X)r(;)14 b(A)k FL(\012)g FJ(B)t FL(i)24 b FQ(=)e FL(h)p FJ(X)r(;)14 b(A;)g(B)t FL(i)1918 1440 y FI(\033)1890 1487 y FL(\000)-51 b(!)23 b(h)p FJ(X)r(;)14 b(B)t(;)g(A)p FL(i)24 b FQ(=)e FL(h)p FJ(X)r(;)14 b(B)23 b FL(\012)18 b FJ(A)p FL(i)p FJ(:)456 1638 y FQ(Then)29 b(one)g(easily)g(sees)g(that)h(the)g(Hexagon)e(axioms)h(giv)n(en)f(in)i (Theorem)f(1.2.5\(iii\))g(are)f(im-)456 1737 y(mediate)c(corollaries)e (of)j(the)g(Hexagon)f(axioms)f(for)i(MS)g(data.)35 b(Th)n(us,)25 b(the)g(MS)g(data)f(de\014nes)456 1837 y(a)j(structure)g(of)g(a)h(BTC)f (on)g FL(C)5 b FQ(.)605 1936 y FK(7.)42 b(Balancing.)36 b FQ(Consider)27 b(the)h(functorial)f(isomorphism)1403 2115 y FL(h)p FJ(V)5 b(;)14 b(X)7 b FL(i)1684 2068 y FI(\033)1724 2043 y Fx(\000)p FF(1)1656 2115 y FL(\000)-19 b(\000)f(!)23 b(h)p FJ(X)r(;)14 b(V)19 b FL(i)2144 2068 y FI(Z)2115 2115 y FL(\000)-42 b(!)23 b(h)p FJ(V)5 b(;)14 b(X)7 b FL(i)p FJ(:)-2041 b FQ(\(5.3.15\))456 2282 y(By)28 b(Lemma)g(5.3.1,)g(there)g(exists)g(a)g(functorial)g(isomorphism)f FJ(\022)2522 2294 y FI(V)2589 2282 y FQ(:)h FJ(V)2760 2235 y FE(\030)2732 2282 y FL(\000)-40 b(!)25 b FJ(V)47 b FQ(suc)n(h)28 b(that)h(the)456 2381 y(ab)r(o)n(v)n(e)d(comp)r (osition)h(is)g(giv)n(en)g(b)n(y)g FJ(\022)1609 2393 y FI(V)1685 2381 y FL(\012)19 b FQ(id)1838 2393 y FI(X)1901 2381 y FQ(.)37 b(One)27 b(easily)g(c)n(hec)n(ks)f(that)i FJ(\022)2840 2393 y Fs(1)2905 2381 y FQ(=)23 b(id)k(and)h(that)540 2629 y FJ(\022)581 2594 y FE(\000)p FM(1)579 2654 y FI(W)641 2662 y FF(1)701 2629 y FQ(=)23 b FJ(Z)6 b(\033)899 2641 y FI(W)961 2649 y FF(1)994 2641 y FI(;W)1076 2649 y FF(2)1109 2641 y FE(\012\001\001\001)o(\012)p FI(W)1334 2649 y FG(n)1402 2629 y FQ(=)22 b FJ(\033)1536 2641 y FI(W)1598 2649 y FF(2)1632 2641 y FE(\012\001\001\001)o(\012)p FI(W)1857 2649 y FG(n)1898 2641 y FI(;W)1980 2649 y FF(1)2017 2629 y FJ(Z)2080 2595 y FE(\000)p FM(1)2178 2629 y FQ(:)27 b FL(h)p FJ(W)2338 2641 y FM(1)2376 2629 y FJ(;)14 b(:)g(:)g(:)g(;)g(W) 2639 2641 y FI(n)2684 2629 y FL(i)2768 2582 y FE(\030)2740 2629 y FL(\000)-40 b(!)23 b(h)p FJ(W)2981 2641 y FM(1)3019 2629 y FJ(;)14 b(:)g(:)g(:)g(;)g(W)3282 2641 y FI(n)3327 2629 y FL(i)456 2780 y FQ(\(this)28 b(is)f(where)g(w)n(e)h(need)f(the)h (Dehn)h(t)n(wist)e(axiom)g(MS7\).)605 2880 y(T)-7 b(o)26 b(pro)n(v)n(e)f(the)h(iden)n(tit)n(y)h FJ(\022)1435 2892 y FI(A)p FE(\012)p FI(B)1617 2880 y FQ(=)22 b FJ(\033)1751 2892 y FI(B)s(;A)1878 2880 y FJ(\033)1925 2892 y FI(A;B)2053 2880 y FQ(\()p FJ(\022)2124 2892 y FI(A)2194 2880 y FL(\012)15 b FJ(\022)2313 2892 y FI(B)2370 2880 y FQ(\),)27 b(note)f(that)h(it)f (is)h(equiv)-5 b(alen)n(t)26 b(to)1067 3036 y FJ(\033)1114 3048 y FI(B)s(;A)1241 3036 y FJ(\033)1288 3048 y FI(A;B)1416 3036 y FJ(\022)1455 3048 y FI(A)1509 3036 y FJ(\022)1550 3000 y FE(\000)p FM(1)1548 3060 y FI(C)1639 3036 y FJ(\022)1678 3048 y FI(B)1758 3036 y FQ(=)d(id)9 b(:)28 b FL(h)p FJ(A;)14 b(B)t(;)g(C)6 b FL(i)2360 2989 y FE(\030)2331 3036 y FL(\000)-39 b(!)23 b(h)p FJ(A;)14 b(B)t(;)g(C)6 b FL(i)p FJ(;)-2362 b FQ(\(5.3.16\))456 3182 y(whic)n(h)27 b(follo)n(ws)g(from)g (the)h(iden)n(tities)-2018 b Fq(?!)1406 3328 y FJ(\022)1447 3292 y FE(\000)p FM(1)1445 3352 y FI(A)1560 3328 y FQ(=)23 b FJ(Z)6 b(\033)1758 3340 y FI(A;B)s(C)1959 3328 y FQ(=)23 b FJ(Z)6 b(\033)2157 3340 y FI(A;C)2282 3328 y FJ(\033)2329 3340 y FI(A;B)2457 3328 y FJ(;)1406 3468 y(\022)1447 3433 y FE(\000)p FM(1)1445 3493 y FI(B)1560 3468 y FQ(=)23 b FJ(\033)1695 3480 y FI(B)s(;A)1822 3468 y FJ(Z)6 b(\033)1932 3480 y FI(B)s(;C)2060 3468 y FJ(;)1406 3608 y(\022)1447 3573 y FE(\000)p FM(1)1445 3633 y FI(C)1560 3608 y FQ(=)23 b FJ(Z)6 b(\033)1758 3620 y FI(A;C)1883 3608 y FJ(Z)g(\033)1993 3620 y FI(B)s(;C)2122 3608 y FJ(:)605 3755 y FQ(Finally)-7 b(,)34 b(w)n(e)e(lea)n(v)n(e)f(it)i(to)f(the)h(reader)e(to)h(sho)n(w)g (that)g(the)h(Dehn)g(t)n(wist)g(axiom)e(MF7)i(is)456 3854 y(essen)n(tially)26 b(equiv)-5 b(alen)n(t)26 b(to)h(the)g(iden)n (tit)n(y)g FJ(\022)1834 3866 y FI(V)1888 3850 y Fx(\003)1950 3854 y FQ(=)22 b FJ(\022)2078 3824 y FE(\003)2076 3877 y FI(V)2134 3854 y FQ(.)37 b(Th)n(us,)27 b(the)g(so)f(de\014ned)i FJ(\022)h FQ(satis\014es)d(the)456 3954 y(balancing)g(axioms)h (\(2.2.8\))o({\(2.2.10\))n(.)605 4054 y(This)h(completes)f(the)h(pro)r (of)f(of)g(Theorem)g(5.3.8.)p 3384 4054 4 57 v 3388 4001 50 4 v 3388 4054 V 3437 4054 4 57 v 605 4219 a(It)f(w)n(ould)e(b)r(e)i (nice)f(if)h(w)n(e)f(had)g(some)g(axiom)f(for)h(MS)h(data)f(whic)n(h)g (w)n(ould)g(automatically)456 4319 y(ensure)e(that)h(the)g(corresp)r (onding)e(BTC)i(is)f(rigid.)35 b(Ho)n(w)n(ev)n(er,)23 b(the)h(only)f(w)n(a)n(y)g(of)h(doing)f(it)h(that)456 4419 y(w)n(e)32 b(kno)n(w)h(of)g(is)g(explicitly)g(imp)r(osing)g(the)h (rigidit)n(y)e(condition.)54 b(\(It)33 b(is)g(claimed)g(in)h([)p FK(MS2)o FQ(])456 4518 y(that)c(rigidit)n(y)f(follo)n(ws)f(from)i(the)g (other)f(axioms;)h(ho)n(w)n(ev)n(er,)e(at)h(some)g(p)r(oin)n(t,)i(they) f(sa)n(y)e(\\w)n(e)456 4618 y(can)k(c)n(hec)n(k)g(the)i(univ)n(ersalit) n(y)d(prop)r(ert)n(y")h(without)h(doing)f(it)i(explicitly|w)n(e)f(w)n (ere)f(unable)456 4717 y(to)27 b(reconstruct)g(their)g(argumen)n(ts.\)) 605 4817 y(In)f(the)f(semisimple)h(case)e(the)i(rigidit)n(y)e (condition)h(is)h(equiv)-5 b(alen)n(t)25 b(to)g(the)g(non-v)-5 b(anishing)456 4917 y(of)26 b(certain)g(co)r(e\016cien)n(ts,)g(whic)n (h)h(sho)n(ws)e(that)i(\\almost)e(all")h(w)n(eakly)f(rigid)h (semisimple)g(cate-)456 5016 y(gories)g(are)g(rigid.)605 5116 y(Let)k FL(C)k FQ(b)r(e)c(a)f(semisimple)h(w)n(eakly)e(rigid)h (monoidal)g(category)f(suc)n(h)h(that)h FJ(V)3052 5086 y FE(\003\003)3150 5116 y FL(')c FJ(V)49 b FQ(\(as)456 5216 y(discussed)20 b(ab)r(o)n(v)n(e,)i(this)f(holds)g(for)g(an)n(y)f (category)f(obtained)i(from)g(MS)g(data\).)35 b(Let)21 b FJ(')3145 5228 y FI(i)3183 5216 y FQ(:)27 b FJ(V)3300 5185 y FE(\003)3281 5237 y FI(i)3361 5216 y FL(!)p eop %%Page: 113 21 113 116 bop 777 226 a FM(5.4.)29 b(MODULAR)g(FUNCTOR)h(IN)f(GENUS)g (ZER)n(O)g(AND)g(TENSOR)g(CA)-5 b(TEGORIES)199 b(113)456 425 y FJ(V)522 395 y FE(\003)504 447 y FI(i)582 425 y FL(\012)21 b FJ(V)716 437 y FI(i)765 425 y FL(\012)g FJ(V)918 395 y FE(\003)899 447 y FI(i)988 425 y FQ(b)r(e)32 b(giv)n(en)f(b)n(y)h FJ(')1500 437 y FI(i)1558 425 y FQ(=)d(id)14 b FL(\012)p FJ(i)1829 437 y FI(V)1868 445 y FG(i)1898 425 y FQ(.)50 b(Using)32 b(the)g(asso)r(ciativit)n(y)e (isomorphism,)i(w)n(e)456 525 y(can)27 b(write)1557 663 y FJ(')1611 675 y FI(i)1662 663 y FQ(=)22 b FJ(a)1793 675 y FI(i)1839 663 y FL(\012)c FQ(id)c(+)2084 584 y Fy(X)2086 763 y FI(j)s FE(6)p FM(=0)2217 663 y FJ( )2271 675 y FI(j)2306 663 y FJ(;)456 887 y FQ(where)30 b FJ(a)743 899 y FI(i)801 887 y FQ(are)f(certain)h(morphisms)g FK(1)e FL(!)g FJ(V)1900 856 y FE(\003)1881 908 y FI(i)1958 887 y FL(\012)20 b FJ(V)2091 899 y FI(i)2120 887 y FQ(,)31 b(and)f FJ( )2392 899 y FI(j)2458 887 y FQ(are)g(some)g(morphisms)g (whic)n(h)456 986 y(are)c(obtained)i(as)e(the)i(comp)r(osition)1257 1170 y FJ(V)1324 1135 y FE(\003)1305 1190 y FI(i)1385 1170 y FL(!)23 b FJ(V)1539 1182 y FI(j)1593 1170 y FL(\012)18 b FJ(V)1743 1135 y FE(\003)1724 1190 y FI(i)1833 1105 y( )1879 1080 y Fx(0)1877 1122 y FG(j)1907 1105 y FE(\012)p FM(id)1804 1170 y FL(\000)-33 b(\000)-19 b(\000)h(\000)-34 b(!)23 b FQ(\()p FJ(V)2165 1135 y FE(\003)2146 1190 y FI(i)2222 1170 y FL(\012)18 b FJ(V)2353 1182 y FI(i)2381 1170 y FQ(\))h FL(\012)f FJ(V)2582 1135 y FE(\003)2563 1190 y FI(i)2620 1170 y FJ(:)456 1308 y FQ(Note)26 b(that)g(since)g FJ(V)1102 1278 y FE(\003)1083 1330 y FI(i)1155 1308 y FL(\012)15 b FJ(V)1283 1320 y FI(i)1337 1308 y FQ(con)n(tains)25 b FK(1)h FQ(with)h(m)n(ultiplicit)n(y)f(one,)g(the)h(morphisms)e FJ(a)3145 1320 y FI(i)3198 1308 y FQ(lie)i(in)f(a)456 1408 y(one-dimensional)g(space.)605 1559 y FP(Pr)n(oposition)31 b FQ(5.3.13)p FP(.)39 b FO(L)l(et)i FL(C)46 b FO(b)l(e)c(a)f (semisimple)j(we)l(akly)e(rigid)h(monoidal)h(c)l(ate)l(gory)456 1659 y(such)32 b(that)g FJ(V)886 1629 y FE(\003\003)986 1659 y FL(')27 b FJ(V)19 b FO(,)34 b(and)f(let)f FJ(a)1531 1671 y FI(i)1568 1659 y FQ(:)c FK(1)g FL(!)f FJ(V)1872 1629 y FE(\003)1853 1680 y FI(i)1931 1659 y FL(\012)20 b FJ(V)2064 1671 y FI(i)2124 1659 y FO(b)l(e)32 b(de\014ne)l(d)h(as)g (ab)l(ove.)47 b(Then)33 b FL(C)k FO(is)c(rigid)456 1758 y(i\013)d FJ(a)606 1770 y FI(i)656 1758 y FL(6)p FQ(=)23 b(0)29 b FO(for)i(al)t(l)g FJ(i)22 b FL(2)i FJ(I)7 b FO(.)605 1910 y FP(Pr)n(oof.)41 b FQ(If)33 b FL(C)38 b FQ(is)32 b(rigid,)i(then)f FJ(e)1648 1922 y FI(V)1687 1930 y FG(i)1717 1910 y FJ(a)1761 1922 y FI(i)1821 1910 y FQ(=)e(1,)j(whic)n(h)f(immediately)g(follo)n(ws)f(from)g(taking)456 2009 y(comp)r(osition)g(of)h FJ(')1079 2021 y FI(i)1141 2009 y FQ(with)g FJ(e)1374 2021 y FI(V)1413 2029 y FG(i)1466 2009 y FL(\012)21 b FQ(id)q(.)53 b(Th)n(us,)35 b FJ(a)1983 2021 y FI(i)2042 2009 y FL(6)p FQ(=)d(0.)54 b(Con)n(v)n(ersely)-7 b(,)32 b(assume)h(that)g FJ(a)3223 2021 y FI(i)3283 2009 y FL(6)p FQ(=)f(0.)456 2109 y(Then)e(de\014ne)h FJ(e)957 2121 y FI(V)996 2129 y FG(i)1036 2109 y FQ(:)e FJ(V)1155 2079 y FE(\003)1136 2131 y FI(i)1213 2109 y FL(\012)20 b FJ(V)1346 2121 y FI(i)1403 2109 y FL(!)28 b FK(1)j FQ(b)n(y)f(the)h(condition)g FJ(e)2264 2121 y FI(V)2303 2129 y FG(i)2333 2109 y FJ(a)2377 2121 y FI(i)2433 2109 y FQ(=)c(1;)32 b(since)f FJ(V)2896 2079 y FE(\003)2877 2131 y FI(i)2954 2109 y FL(\012)21 b FJ(V)3088 2121 y FI(i)3146 2109 y FQ(con)n(tains)456 2209 y FK(1)30 b FQ(with)h(m)n(ultiplicit)n(y)h(one,)f(this)g(is)f(p)r(ossible.)46 b(F)-7 b(rom)30 b(this)h(condition,)h(w)n(e)e(immediately)h(see)456 2308 y(that)c(the)h(comp)r(osition)1292 2481 y FJ(V)1359 2447 y FE(\003)1340 2502 y FI(i)1449 2420 y FM(id)11 b FE(\012)p FI(i)1591 2428 y FG(V)1625 2441 y(i)1420 2481 y FL(\000)-20 b(\000)h(\000)g(\000)e(!)23 b FJ(V)1774 2447 y FE(\003)1755 2502 y FI(i)1831 2481 y FL(\012)18 b FJ(V)1962 2493 y FI(i)2008 2481 y FL(\012)g FJ(V)2158 2447 y FE(\003)2139 2502 y FI(i)2248 2420 y(e)2279 2428 y FG(V)2313 2441 y(i)2344 2420 y FE(\012)p FM(id)2219 2481 y FL(\000)-22 b(\000)j(\000)g(\000)d(!)23 b FJ(V)2570 2447 y FE(\003)2551 2502 y FI(i)456 2624 y FQ(is)k(equal)g(to)h(iden)n (tit)n(y;)f(th)n(us,)h(the)g(second)f(rigidit)n(y)g(axiom)g(\(2.1.6\))g (is)g(satis\014ed.)605 2724 y(T)-7 b(o)27 b(c)n(hec)n(k)g(the)h (\014rst)f(rigidit)n(y)g(axiom,)g(denote)g(the)h(comp)r(osition)1336 2896 y FJ(V)1384 2908 y FI(i)1463 2835 y(i)1486 2843 y FG(V)1520 2856 y(i)1552 2835 y FE(\012)p FM(id)1435 2896 y FL(\000)-26 b(\000)-19 b(\000)g(\000)-27 b(!)23 b FJ(V)1758 2908 y FI(i)1805 2896 y FL(\012)18 b FJ(V)1955 2862 y FE(\003)1936 2917 y FI(i)2011 2896 y FL(\012)g FJ(V)2142 2908 y FI(i)2222 2835 y FM(id)11 b FE(\012)p FI(e)2372 2843 y FG(V)2406 2856 y(i)2193 2896 y FL(\000)-16 b(\000)d(\000)g(\000)i(!)23 b FJ(V)2536 2908 y FI(i)456 3039 y FQ(b)n(y)k FJ(c)607 3051 y FI(i)634 3039 y FQ(;)h(since)g(End)o (\()p FJ(V)1117 3051 y FI(i)1146 3039 y FQ(\))23 b(=)g FJ(k)s FQ(,)k FJ(c)1421 3051 y FI(i)1477 3039 y FQ(is)g(a)g(n)n(um)n(b) r(er.)37 b(W)-7 b(e)28 b(need)g(to)f(sho)n(w)g(that)h FJ(c)2824 3051 y FI(i)2874 3039 y FQ(=)23 b(1.)605 3139 y(Consider)k(the)h(comp)r(osition)1099 3297 y(\010)9 b(:)28 b FK(1)1318 3250 y FI(i)p FE(\012)p FI(i)1290 3297 y FL(\000)-29 b(\000)g(!)23 b FJ(V)1516 3309 y FI(i)1563 3297 y FL(\012)18 b FJ(V)1713 3263 y FE(\003)1694 3318 y FI(i)1769 3297 y FL(\012)g FJ(V)1900 3309 y FI(i)1947 3297 y FL(\012)g FJ(V)2097 3263 y FE(\003)2078 3318 y FI(i)2186 3250 y FM(id)11 b FE(\012)p FI(e)p FE(\012)p FM(id)2158 3297 y FL(\000)-18 b(\000)f(\000)g(\000)g(\000)g(!)23 b FJ(V)2543 3309 y FI(i)2590 3297 y FL(\012)18 b FJ(V)2740 3263 y FE(\003)2721 3318 y FI(i)2778 3297 y FJ(:)456 3440 y FQ(F)-7 b(rom)35 b(the)i(second)e(rigidit)n(y)h(axiom)f (\(already)g(pro)n(v)n(ed\),)i(\010)g(=)g FJ(i)2563 3452 y FI(V)2602 3460 y FG(i)2632 3440 y FQ(.)63 b(On)35 b(the)i(other)e (hand,)456 3540 y(form)28 b(the)h(de\014nition)g(of)f FJ(c)1298 3552 y FI(i)1326 3540 y FQ(,)h(w)n(e)f(ha)n(v)n(e)f(\010)e(=) f FJ(c)1903 3552 y FI(i)1931 3540 y FJ(i)1960 3552 y FI(V)1999 3560 y FG(i)2029 3540 y FQ(.)40 b(This)28 b(pro)n(v)n(es)f FJ(c)2576 3552 y FI(i)2628 3540 y FQ(=)d(1)k(and)h(th)n(us,)g(the)g (\014rst)456 3640 y(rigidit)n(y)d(axiom)h(for)g FJ(V)1168 3652 y FI(i)1196 3640 y FQ(.)605 3739 y(Therefore,)g(if)i FJ(a)1126 3751 y FI(i)1177 3739 y FL(6)p FQ(=)23 b(0,)28 b(then)h FJ(V)1596 3751 y FI(i)1652 3739 y FQ(is)f(rigid.)38 b(But)28 b(since)g(a)f(direct)h(sum)h(of)f(rigid)f(ob)5 b(jects)28 b(is)456 3839 y(again)e(rigid,)h(ev)n(ery)f(ob)5 b(ject)28 b(in)g FL(C)k FQ(is)27 b(rigid.)p 3384 3839 4 57 v 3388 3786 50 4 v 3388 3839 V 3437 3839 4 57 v 755 4018 a FK(5.4.)47 b(Mo)s(dular)31 b(functor)i(in)e(gen)m(us)g(zero) h(and)h(tensor)e(categories)605 4168 y FQ(In)22 b(this)g(section)f(w)n (e)g(pro)n(v)n(e)f(the)i(\014rst)f(main)h(theorem)f(of)g(this)h(c)n (hapter,)g(establishing)f(that)456 4267 y(the)31 b(axioms)e(of)i(a)f (\(w)n(eakly\))g(ribb)r(on)h(category)d(are)i(essen)n(tially)g(equiv)-5 b(alen)n(t)30 b(to)h(the)g(axioms)456 4367 y(of)c(a)g(mo)r(dular)g (functor)h(in)g(gen)n(us)e(zero.)605 4466 y(Let)g FL(C)31 b FQ(b)r(e)c(a)f(semisimple)g(ab)r(elian)g(category)e(with)j(represen)n (tativ)n(es)d(of)i(the)h(equiv)-5 b(alence)456 4566 y(classes)20 b(of)h(simple)h(ob)5 b(jects)20 b FJ(V)1380 4578 y FI(i)1408 4566 y FQ(,)j FJ(i)g FL(2)g FJ(I)7 b FQ(.)35 b(Let)22 b(us)f(call)g(a)g FL(C)5 b FO(-extende)l(d)23 b(mo)l(dular)i(functor)f (in)g(genus)456 4666 y(zer)l(o)33 b FQ(the)g(same)f(data)h(as)f(in)h (De\014nition)h(5.1.12)d(but)i(with)g(the)h(spaces)e FJ(\034)9 b FQ(\(\006\))34 b(de\014ned)f(only)456 4765 y(for)26 b(\006)g(of)h(gen)n(us)e(zero;)h(therefore,)g(the)h(only)f (gluing)g(allo)n(w)n(ed)f(is)h(the)h(gluing)f(of)h(t)n(w)n(o)e (di\013eren)n(t)456 4865 y(connected)i(comp)r(onen)n(ts.)605 5016 y FP(Theorem)32 b FQ(5.4.1)e(\(Mo)r(ore{Seib)r(erg)c([)p FK(MS1)o FQ(]\))p FP(.)42 b FO(L)l(et)28 b FL(C)33 b FO(b)l(e)c(a)g(semisimple)i(we)l(akly)f(ribb)l(on)456 5116 y(c)l(ate)l(gory.)41 b(Then)31 b(ther)l(e)f(is)h(a)f(unique)g FL(C)5 b FO(-extende)l(d)30 b(genus)f(zer)l(o)i(mo)l(dular)g(functor)f (satisfying)456 5216 y(the)g(pr)l(op)l(erties)37 b FQ(\(i\){\(iii\))31 b FO(b)l(elow.)p eop %%Page: 114 22 114 117 bop 456 226 a FM(114)1010 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FQ(\(i\))h FO(F)-6 b(or)30 b(the)g(standar)l(d)h(spher)l(e)f FJ(S)1660 437 y FM(0)p FI(;n)1788 425 y FQ(\()p FO(se)l(e)36 b FQ(\(5.2.1\))o(\):)878 579 y FJ(\034)9 b FQ(\()p FJ(S)1006 591 y FM(0)p FI(;n)1105 579 y FQ(;)14 b FJ(W)1220 591 y FM(1)1257 579 y FJ(;)g(:)g(:)g(:)g(;)g(W)1520 591 y FI(n)1565 579 y FQ(\))24 b(=)e(Hom)1881 591 y FE(C)1924 579 y FQ(\()p FK(1)p FJ(;)14 b(W)2119 591 y FM(1)2175 579 y FL(\012)k(\001)c(\001)g(\001)19 b(\012)f FJ(W)2535 591 y FI(n)2580 579 y FQ(\))24 b(=:)e FL(h)p FJ(W)2856 591 y FM(1)2894 579 y FJ(;)14 b(:)g(:)g(:)g(;)g(W)3157 591 y FI(n)3202 579 y FL(i)p FJ(:)-2801 b FQ(\(5.4.1\))605 753 y(\(ii\))30 b FJ(R)24 b FQ(=)920 690 y Fy(L)1026 753 y FJ(V)1093 723 y FE(\003)1074 774 y FI(i)1149 753 y FL(\012)18 b FJ(V)1280 765 y FI(i)1308 753 y FO(,)31 b(and)f(the)g(isomorphism)i FJ(s)9 b FQ(:)28 b FJ(R)2366 706 y FE(\030)2337 753 y FL(\000)-39 b(!)23 b FJ(R)2533 723 y FM(op)2636 753 y FO(is)31 b(given)f(by)37 b FQ(\(2.4.8\))p FO(.)605 852 y FQ(\(iii\))31 b FO(We)e(have)6 b FQ(:)1633 1006 y FJ(z)1672 1018 y FE(\003)1733 1006 y FQ(=)22 b FJ(Z)q(;)99 b(b)2036 1018 y FE(\003)2097 1006 y FQ(=)23 b FJ(\033)n(;)-1797 b FQ(\(5.4.2\))456 1164 y FO(wher)l(e)32 b(the)h(home)l(omorphisms)h FJ(z)t(;)14 b(b)31 b FO(ar)l(e)i(de\014ne)l (d)f(by)40 b FQ(\(5.2.2\))p FO(,)33 b(and)f(the)h(isomorphisms)h FJ(Z)q(;)14 b(\033)456 1264 y FO(ar)l(e)30 b(de\014ne)l(d)g(by)37 b FQ(\(5.3.5\))p FO(,)30 b FQ(\(5.3.7\))o FO(.)39 b(A)n(lso,)30 b(for)h(every)f FJ(k)s(;)14 b(l)24 b FL(\025)f FQ(0)p FO(,)30 b(the)g(c)l(omp)l(osition)456 1553 y FJ(\034)9 b FQ(\()p FJ(S)584 1565 y FM(0)p FI(;k)q FM(+1)762 1553 y FQ(;)14 b FJ(:)g(:)g(:)g(;)g(R)1011 1518 y FM(\(1\))1100 1553 y FQ(\))k FL(\012)g FJ(\034)9 b FQ(\()p FJ(S)1361 1565 y FM(0)p FI(;l)p FM(+1)1525 1553 y FQ(;)14 b FJ(R)1626 1518 y FM(\(2\))1714 1553 y FJ(;)g(:)g(:)g(:)g FQ(\))23 b FL(!)g FJ(\034)9 b FQ(\()p FJ(S)2151 1565 y FM(0)p FI(;k)q FM(+1)2348 1553 y FL(t)2403 1565 y FI(k)q FM(+1)p FI(;)p FM(1)2600 1553 y FJ(S)2651 1565 y FM(0)p FI(;l)p FM(+1)2813 1553 y FQ(\))2897 1498 y FM(\()p FI(\013)2966 1507 y FG(k)q(l)3022 1498 y FM(\))3048 1506 y Fx(\003)2868 1553 y FL(\000)-31 b(\000)-19 b(\000)h(\000)-32 b(!)23 b FJ(\034)9 b FQ(\()p FJ(S)3262 1565 y FM(0)p FI(;k)q FM(+)p FI(l)3429 1553 y FQ(\))p FJ(;)456 1711 y FO(wher)l(e)36 b(the)g(\014rst)f(arr)l(ow)h(is)g(the)g(sewing)g(isomorphism)45 b FQ(\(5.1.1\))34 b FO(and)j FJ(\013)2765 1723 y FI(k)q(l)2863 1711 y FO(is)f(as)g(in)42 b FQ(\(5.2.3\))o FO(,)456 1811 y(c)l(oincides)31 b(with)f(the)g(isomorphism)i FJ(G)e FO(de\014ne)l(d)g(by)38 b FQ(\(5.3.6\))o FO(.)605 1910 y(This)31 b(mo)l(dular)f(functor)g(is)g(non-de)l(gener)l(ate)g(and)g (has)h(the)f(fol)t(lowing)i(pr)l(op)l(erties)7 b FQ(:)605 2010 y(\(iv\))34 b FO(L)l(et)g FJ(t)948 2022 y FI(i)985 2010 y FQ(:)29 b FJ(S)1088 2022 y FM(0)p FI(;n)1216 2010 y FL(!)i FJ(S)1381 2022 y FM(0)p FI(;n)1513 2010 y FO(b)l(e)j(the)g (Dehn)f(twist)h(ar)l(ound)g FJ(i)2500 1980 y FI(th)2602 2010 y FO(punctur)l(e.)50 b(Then,)36 b(under)456 2110 y(the)30 b(isomorphism)38 b FQ(\(5.4.1\))o FO(,)30 b FQ(\()p FJ(t)1441 2122 y FI(i)1469 2110 y FQ(\))1501 2122 y FE(\003)1569 2110 y FO(is)g(given)h(by)f(the)g(twist)984 2263 y FJ(\022)1023 2275 y FI(W)1085 2283 y FG(i)1125 2263 y FQ(:)42 b(Hom)1363 2275 y FE(C)1406 2263 y FQ(\()p FK(1)p FJ(;)14 b(W)1601 2275 y FM(1)1657 2263 y FL(\012)k(\001)c(\001)g (\001)k(\012)g FJ(W)2016 2275 y FI(n)2062 2263 y FQ(\))23 b FL(!)g FQ(Hom)2396 2275 y FE(C)2440 2263 y FQ(\()p FK(1)p FJ(;)14 b(W)2635 2275 y FM(1)2691 2263 y FL(\012)k(\001)c(\001)g (\001)k(\012)g FJ(W)3050 2275 y FI(n)3096 2263 y FQ(\))p FJ(:)605 2422 y FQ(\(v\))30 b FO(If)g FL(C)35 b FO(is)30 b(rigid,)h(then)f(this)g(mo)l(dular)h(functor)e(is)h(unitary,)g(with)h (the)f(p)l(airing)38 b FQ(\(5.1.2\))862 2575 y FL(h)p FJ(;)14 b FL(i)963 2587 y FI(S)1004 2595 y FF(0)p FG(;n)1106 2575 y FQ(:)42 b(Hom)1344 2587 y FE(C)1387 2575 y FQ(\()p FK(1)p FJ(;)14 b(W)1582 2587 y FM(1)1638 2575 y FL(\012)k(\001)c(\001)g (\001)k(\012)g FJ(W)1997 2587 y FI(n)2043 2575 y FQ(\))g FL(\012)g FQ(Hom)2349 2587 y FE(C)2393 2575 y FQ(\()p FK(1)p FJ(;)c(W)2600 2541 y FE(\003)2588 2596 y FI(n)2656 2575 y FL(\012)k(\001)c(\001)g(\001)k(\012)g FJ(W)3027 2541 y FE(\003)3015 2596 y FM(1)3065 2575 y FQ(\))24 b FL(!)f FJ(k)456 2729 y FO(given)30 b(by)981 2883 y FL(h)p FJ(';)14 b( )s FL(i)9 b FQ(:)29 b FK(1)23 b FL(!)g FK(1)18 b FL(\012)g FK(1)23 b FL(!)g FJ(W)1835 2895 y FM(1)1891 2883 y FL(\012)18 b(\001)c(\001)g(\001)19 b(\012)f FJ(W)2251 2895 y FI(n)2315 2883 y FL(\012)g FJ(W)2488 2848 y FE(\003)2476 2903 y FI(n)2544 2883 y FL(\012)g(\001)c(\001)g (\001)19 b(\012)f FJ(W)2916 2848 y FE(\003)2904 2903 y FM(1)2977 2883 y FL(!)23 b FK(1)p FJ(:)456 3041 y FO(Her)l(e)j(we)h (identify)i FJ(k)d FQ(=)c(End\()p FK(1)p FQ(\))27 b FO(and)h(use)e(the) h(fact)g(that)g(for)h(a)f(standar)l(d)h(spher)l(e)f FJ(S)3116 3053 y FM(0)p FI(;n)3214 3041 y FO(,)h(ther)l(e)456 3151 y(is)d(a)h(c)l(anonic)l(al)g(isomorphism)p 1453 3084 149 4 v 28 w FJ(S)1504 3163 y FM(0)p FI(;n)1653 3104 y FE(\030)1625 3151 y FL(\000)-39 b(!)23 b FJ(S)1808 3163 y FM(0)p FI(;n)1906 3151 y FO(,)j(which)h(r)l(everses)f(the)f(or)l (der)h(of)h(the)e(punctur)l(es.)456 3251 y(This)31 b(isomorphism)h(is)e (given)g(by)g(the)g(r)l(e\015e)l(ction)g(ar)l(ound)g(the)g(imaginary)h (axis.)605 3350 y(Conversely,)e(let)e FJ(\034)36 b FO(b)l(e)27 b(a)g(non-de)l(gener)l(ate)g(genus)f(zer)l(o)h FL(C)5 b FO(-extende)l(d)26 b(MF.)i(Then)f(ther)l(e)g(is)456 3450 y(a)k(unique)g(structur)l(e)f(of)i(a)g(we)l(akly)h(ribb)l(on)f(c)l (ate)l(gory)g(on)f FL(C)36 b FO(such)c(that)f(the)h(ab)l(ove)g(pr)l(op) l(erties)456 3549 y FQ(\(i\){\(iii\))e FO(hold.)605 3710 y FP(Pr)n(oof.)41 b FQ(The)35 b(pro)r(of)f(is)h(based)f(on)g(the)i (comparison)d(of)i(the)g(results)f(of)h(Sections)f(5.2)456 3809 y(and)e(5.3.)51 b(Since)33 b(b)n(y)f(Theorem)f(5.3.8)h(the)h (structure)f(of)g(a)g(w)n(eakly)g(ribb)r(on)g(category)f(on)h FL(C)456 3909 y FQ(is)c(equiv)-5 b(alen)n(t)28 b(to)g(what)h(w)n(e)f (called)g(MS)h(data,)f(it)h(su\016ces)f(to)g(sho)n(w)g(that)g(a)g (non-degenerate)456 4009 y(gen)n(us)e(zero)h(MF)h(de\014nes)f(MS)h (data)f(and)h(vice)f(v)n(ersa.)605 4108 y(Let)g(us)f(assume)g(w)n(e)g (are)f(giv)n(en)g(a)h(collection)g(of)h(MS)f(data.)36 b(T)-7 b(o)26 b(construct)g(a)g(gen)n(us)g(zero)456 4208 y(MF,)g(let)g(us)g(\014rst)f(consider)g(the)h(pairs)f(\(\006)p FJ(;)14 b(M)9 b FQ(\),)27 b(where)e FJ(M)32 b FQ(=)22 b(\()p FJ(C)q(;)14 b FL(f)p FJ( )2656 4220 y FI(a)2697 4208 y FL(g)p FQ(\))26 b(is)f(a)h(parameteriza-)456 4308 y(tion)e(of)g(\006)g(\(see)g(De\014nition)g(5.2.1\).)35 b(F)-7 b(or)23 b(eac)n(h)g(suc)n(h)h(pair,)g(de\014ne)g(the)h(v)n (ector)d(space)i FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\))456 4407 y(as)27 b(follo)n(ws.)35 b(F)-7 b(or)27 b(ev)n(ery)g(cut)h FJ(c)p FQ(,)f(tak)n(e)g(a)g(cop)n(y)g FJ(R)1966 4419 y FI(c)2028 4407 y FQ(of)g(the)h(ob)5 b(ject)28 b FJ(R)q FQ(,)f(and)g(de\014ne)1510 4573 y FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\))24 b(=)1918 4494 y Fy(O)1963 4668 y FI(a)2057 4573 y FJ(\034)9 b FQ(\()p FJ(S)2185 4585 y FM(0)p FI(;n)2279 4593 y FG(a)2320 4573 y FQ(\))p FJ(;)-1919 b FQ(\(5.4.3\))456 4801 y(where)26 b(the)i(index)f FJ(a)g FQ(runs)f(through)h(the)g(set)g(of)g(connected)g (comp)r(onen)n(ts)f(of)h(\006)18 b FL(n)f FJ(C)6 b FQ(,)27 b(and)g(for)456 4917 y(eac)n(h)e(connected)g(comp)r(onen)n(t)h(\006) 1509 4929 y FI(a)1549 4917 y FQ(,)g(w)n(e)g(assign)e FJ(R)2026 4874 y FM(\()p FI(")p FM(\))2025 4926 y FI(c)2140 4917 y FQ(to)h(ev)n(ery)g(b)r(oundary)g(comp)r(onen)n(t)g(of)h(\006) 3404 4929 y FI(a)456 5016 y FQ(whic)n(h)c(is)g(a)g(cut,)i(where)e FJ(")h FL(2)h(f)p FQ(1)p FJ(;)14 b FQ(2)p FL(g)20 b FQ(is)i(c)n(hosen)g (so)g(that)h(for)f(one)g(of)g(the)h(o)r(ccurrences)e(of)h FJ(R)3293 5028 y FI(c)3350 5016 y FQ(w)n(e)456 5116 y(tak)n(e)g FJ(")h FQ(=)f(1)h(and)g(for)g(the)g(other)g(w)n(e)g(tak)n(e)f FJ(")h FQ(=)f(2)h(\(note)g(that)h(eac)n(h)e FJ(R)2616 5128 y FI(c)2673 5116 y FQ(app)r(ears)g(exactly)h(t)n(wice)456 5216 y(in)k(\(5.4.3\)\).)37 b(Since)28 b FJ(R)g FQ(is)g(symmetric,)f (it)h(do)r(es)f(not)h(matter)f(whic)n(h)h(o)r(ccurrence)e(is)h(whic)n (h.)p eop %%Page: 115 23 115 118 bop 777 226 a FM(5.4.)29 b(MODULAR)g(FUNCTOR)h(IN)f(GENUS)g (ZER)n(O)g(AND)g(TENSOR)g(CA)-5 b(TEGORIES)199 b(115)605 425 y FQ(More)21 b(explicitly)-7 b(,)23 b(the)f(same)e(form)n(ula)h (can)g(b)r(e)h(written)g(as)e(follo)n(ws.)34 b(F)-7 b(or)21 b(eac)n(h)g(cut)h FJ(c)h FL(2)g FJ(C)6 b FQ(,)456 525 y(c)n(ho)r(ose)19 b(one)h(of)h(its)g(sides)g(as)f(\\p)r(ositiv)n(e")f (and)i(the)g(other)f(as)g(\\negativ)n(e".)33 b(Then)20 b(w)n(e)h(can)f(de\014ne)1358 672 y FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\))24 b(=)1848 593 y Fy(M)1766 771 y FI(i)1789 779 y FG(c)1820 771 y FE(2)p FI(I)5 b(;)11 b(c)p FE(2)p FI(C)2070 593 y Fy(O)2115 768 y FI(a)2209 672 y FJ(\034)e FQ(\()p FJ(S)2337 684 y FM(0)p FI(;n)2431 692 y FG(a)2472 672 y FQ(\))p FJ(;)-2071 b FQ(\(5.4.4\))456 893 y(where)27 b(the)i(sum)g(is)f(tak)n(en)f(o)n(v)n(er)g(all)h(w)n(a)n (ys)f(to)h(assign)f(an)h(index)h FJ(i)2542 905 y FI(c)2599 893 y FL(2)c FJ(I)35 b FQ(to)29 b(ev)n(ery)e(cut)h FJ(c)c FL(2)h FJ(C)6 b FQ(,)456 992 y(and)40 b(for)g(eac)n(h)f(connected)h (comp)r(onen)n(t)g(\006)1866 1004 y FI(a)1947 992 y FQ(of)g(\006)27 b FL(n)f FJ(C)47 b FQ(w)n(e)40 b(assign)f FJ(V)2756 1004 y FI(i)2779 1012 y FG(c)2856 992 y FQ(to)h(its)g(b)r(oundary)456 1092 y(comp)r(onen)n(t)27 b(if)h(it)f(is)h(the)f(p)r(ositiv)n(e)g(side) g(of)h(the)f(cut)h FJ(c)p FQ(,)g(and)f FJ(V)2432 1062 y FE(\003)2413 1113 y FI(i)2436 1121 y FG(c)2499 1092 y FQ(if)h(it)g(is)f(the)h(negativ)n(e)e(side)i(of)456 1191 y(the)k(cut)h FJ(c)p FQ(.)51 b(This)32 b(form)n(ula)f(dep)r(ends)i (on)f(the)h(c)n(hoice)e(of)h(\\p)r(ositiv)n(e")f(side)h(for)g(eac)n(h)g (cut;)j(to)456 1291 y(iden)n(tify)21 b(the)f(form)n(ulas)g(corresp)r (onding)e(to)j(di\013eren)n(t)f(c)n(hoices,)h(one)f(has)g(to)g(use)h (the)g(canonical)456 1393 y(isomorphism)26 b FJ(V)1008 1363 y FE(\003)989 1415 y FI(i)1065 1393 y Fw(\002)18 b FJ(V)1196 1405 y FI(i)1275 1346 y FE(\030)1247 1393 y FL(\000)-40 b(!)23 b FJ(V)1426 1405 y FI(i)1449 1389 y Fx(\003)1508 1393 y Fw(\002)18 b FJ(V)1657 1363 y FE(\003)1639 1415 y FI(i)1662 1398 y Fx(\003)1729 1393 y FQ(de\014ned)28 b(in)g(\(2.4.8\))o(.)605 1493 y(F)-7 b(or)24 b(example,)h(if)g(\006)f (is)h(a)f(sphere)g(with)h(4)f(holes)g(whic)n(h)g(w)n(e)g(index)h(b)n(y) f FJ(\013;)14 b(\014)t(;)g(\015)5 b(;)14 b(\016)s FQ(,)25 b(and)g FJ(')g FQ(is)456 1592 y(a)i(parameterization)e(with)j(one)g (cut)g FJ(c)f FQ(as)g(in)h(Figure)f(5.16,)f(then)i(the)g(ab)r(o)n(v)n (e)f(form)n(ula)f(giv)n(es)851 1730 y FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(')p FQ(;)g FJ(W)1194 1742 y FI(\013)1243 1730 y FJ(;)g(W)1358 1742 y FI(\014)1403 1730 y FJ(;)g(W)1518 1742 y FI(\015)1561 1730 y FJ(;)g(W)1676 1742 y FI(\016)1713 1730 y FQ(\))23 b(=)g FL(h)p FJ(W)1966 1742 y FI(\013)2014 1730 y FJ(;)14 b(W)2129 1742 y FI(\014)2174 1730 y FJ(;)g(R)2275 1696 y FM(\(1\))2364 1730 y FL(i)k(\012)h(h)p FJ(R)2594 1696 y FM(\(2\))2683 1730 y FJ(;)14 b(W)2798 1742 y FI(\015)2841 1730 y FJ(;)g(W)2956 1742 y FI(\016)2992 1730 y FL(i)1768 1885 y FQ(=)1856 1806 y Fy(M)1868 1984 y FI(i)p FE(2)p FI(I)1981 1885 y FL(h)p FJ(W)2091 1897 y FI(\013)2139 1885 y FJ(;)g(W)2254 1897 y FI(\014)2299 1885 y FJ(;)g(V)2384 1897 y FI(i)2412 1885 y FL(i)19 b(\012)f(h)p FJ(V)2645 1851 y FE(\003)2626 1905 y FI(i)2684 1885 y FJ(;)c(W)2799 1897 y FI(\015)2841 1885 y FJ(;)g(W)2956 1897 y FI(\016)2993 1885 y FL(i)p FJ(:)1592 2935 y @beginspecial 0 @llx 0 @lly 86 @urx 91 @ury 860 @rwi @setspecial %%BeginDocument: figures/ftaustand.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: ftaustand.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Jun 8 16:03:25 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 86 91 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -117.0 181.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 16016 m -1000 -1000 l 17898 -1000 l 17898 16016 l cp clip 0.01200 0.01200 sc % Arc 30.000 slw gs n 20340.0 11400.0 4215.0 -145.3 145.3 arcn gs col-1 s gr gr % Arc gs n 13321.9 7855.4 1969.8 141.7 35.5 arcn gs col-1 s gr gr % Arc gs n 13321.9 15019.6 1969.8 -141.7 -35.5 arc gs col-1 s gr gr % Ellipse n 10800 9000 975 375 0 360 DrawEllipse gs col-1 s gr % Ellipse n 10800 13800 975 375 0 360 DrawEllipse gs col-1 s gr % Ellipse n 15900 9000 975 375 0 360 DrawEllipse gs col-1 s gr % Arc gs n 6360.0 11400.0 4215.0 -34.7 34.7 arc gs col-1 s gr gr % Ellipse n 15900 13800 975 375 0 360 DrawEllipse gs col-1 s gr /Symbol ff 750.00 scf sf 10560 15000 m gs 1 -1 sc (d) col-1 sh gr % Polyline 15.000 slw n 10590 11370 m 10590 11371 l 10593 11374 l 10599 11381 l 10607 11393 l 10618 11407 l 10630 11421 l 10641 11435 l 10651 11448 l 10659 11459 l 10667 11468 l 10675 11477 l 10683 11485 l 10692 11495 l 10701 11504 l 10711 11514 l 10722 11524 l 10734 11534 l 10745 11543 l 10757 11552 l 10768 11560 l 10779 11568 l 10790 11575 l 10799 11581 l 10809 11586 l 10819 11592 l 10830 11598 l 10842 11604 l 10854 11609 l 10866 11615 l 10877 11620 l 10889 11626 l 10901 11631 l 10912 11635 l 10923 11640 l 10933 11645 l 10945 11649 l 10957 11654 l 10969 11659 l 10982 11665 l 10995 11670 l 11008 11675 l 11021 11681 l 11033 11686 l 11045 11691 l 11057 11695 l 11068 11700 l 11078 11705 l 11090 11709 l 11101 11714 l 11113 11719 l 11125 11725 l 11138 11730 l 11150 11735 l 11163 11741 l 11175 11746 l 11187 11751 l 11199 11755 l 11210 11760 l 11222 11765 l 11234 11769 l 11247 11774 l 11260 11779 l 11274 11784 l 11289 11789 l 11304 11794 l 11319 11799 l 11333 11803 l 11347 11808 l 11361 11811 l 11375 11815 l 11389 11818 l 11403 11822 l 11418 11825 l 11434 11828 l 11451 11831 l 11468 11834 l 11484 11837 l 11501 11840 l 11517 11843 l 11532 11845 l 11546 11848 l 11560 11850 l 11574 11852 l 11588 11855 l 11602 11857 l 11617 11860 l 11632 11862 l 11648 11865 l 11663 11868 l 11678 11870 l 11693 11873 l 11707 11875 l 11721 11878 l 11735 11880 l 11749 11882 l 11763 11885 l 11778 11887 l 11794 11890 l 11811 11893 l 11828 11895 l 11844 11898 l 11861 11901 l 11877 11904 l 11892 11907 l 11906 11910 l 11920 11913 l 11934 11915 l 11948 11919 l 11962 11922 l 11977 11925 l 11992 11929 l 12008 11933 l 12023 11936 l 12039 11940 l 12054 11943 l 12069 11946 l 12083 11950 l 12098 11953 l 12110 11955 l 12123 11957 l 12136 11960 l 12150 11962 l 12165 11965 l 12180 11967 l 12196 11969 l 12211 11972 l 12227 11974 l 12242 11976 l 12256 11978 l 12270 11979 l 12284 11981 l 12298 11983 l 12313 11984 l 12329 11986 l 12345 11987 l 12362 11989 l 12379 11991 l 12397 11992 l 12414 11994 l 12431 11995 l 12448 11996 l 12463 11998 l 12478 11999 l 12493 12000 l 12507 12001 l 12522 12002 l 12537 12004 l 12553 12005 l 12569 12006 l 12586 12007 l 12603 12008 l 12620 12009 l 12637 12010 l 12653 12011 l 12669 12012 l 12685 12013 l 12699 12013 l 12713 12013 l 12729 12014 l 12745 12014 l 12761 12014 l 12779 12014 l 12797 12015 l 12815 12015 l 12833 12015 l 12851 12015 l 12868 12015 l 12885 12015 l 12901 12015 l 12918 12015 l 12932 12015 l 12946 12015 l 12961 12015 l 12977 12015 l 12993 12015 l 13010 12015 l 13027 12015 l 13044 12015 l 13061 12015 l 13079 12016 l 13096 12016 l 13113 12016 l 13129 12016 l 13146 12017 l 13162 12017 l 13178 12018 l 13194 12018 l 13210 12018 l 13227 12019 l 13244 12020 l 13262 12020 l 13280 12021 l 13299 12022 l 13318 12022 l 13336 12023 l 13354 12023 l 13371 12024 l 13388 12024 l 13403 12025 l 13418 12025 l 13432 12025 l 13445 12025 l 13462 12025 l 13478 12025 l 13494 12024 l 13511 12024 l 13527 12023 l 13543 12022 l 13559 12021 l 13574 12020 l 13588 12018 l 13603 12017 l 13616 12016 l 13630 12015 l 13644 12014 l 13659 12013 l 13674 12011 l 13691 12010 l 13708 12009 l 13725 12008 l 13742 12007 l 13759 12006 l 13776 12005 l 13791 12004 l 13806 12003 l 13820 12003 l 13834 12002 l 13847 12002 l 13861 12001 l 13875 12001 l 13890 12001 l 13904 12000 l 13918 12000 l 13932 12000 l 13945 12000 l 13958 12000 l 13970 12000 l 13983 12000 l 13995 12000 l 14007 12000 l 14021 12000 l 14035 12000 l 14050 12000 l 14066 11999 l 14082 11999 l 14098 11998 l 14115 11998 l 14131 11997 l 14148 11996 l 14165 11995 l 14180 11994 l 14196 11993 l 14213 11991 l 14231 11990 l 14249 11988 l 14269 11986 l 14289 11984 l 14309 11982 l 14328 11980 l 14348 11978 l 14366 11976 l 14384 11974 l 14401 11972 l 14418 11970 l 14434 11968 l 14450 11966 l 14466 11964 l 14482 11962 l 14499 11960 l 14516 11958 l 14533 11955 l 14550 11953 l 14566 11951 l 14581 11949 l 14596 11947 l 14610 11946 l 14624 11944 l 14638 11943 l 14651 11941 l 14664 11940 l 14678 11938 l 14693 11937 l 14708 11935 l 14723 11934 l 14739 11932 l 14755 11930 l 14771 11928 l 14787 11926 l 14803 11924 l 14819 11922 l 14834 11920 l 14850 11918 l 14864 11915 l 14878 11913 l 14893 11910 l 14909 11907 l 14926 11904 l 14942 11901 l 14960 11898 l 14977 11894 l 14995 11890 l 15012 11887 l 15028 11883 l 15045 11879 l 15060 11875 l 15075 11872 l 15089 11868 l 15103 11865 l 15118 11861 l 15132 11857 l 15147 11853 l 15163 11849 l 15178 11844 l 15193 11840 l 15209 11835 l 15224 11830 l 15239 11826 l 15253 11821 l 15267 11817 l 15281 11813 l 15294 11809 l 15308 11805 l 15321 11801 l 15335 11797 l 15349 11793 l 15365 11789 l 15381 11784 l 15397 11779 l 15415 11775 l 15432 11770 l 15449 11765 l 15467 11760 l 15483 11756 l 15500 11751 l 15516 11747 l 15533 11743 l 15549 11738 l 15566 11733 l 15583 11729 l 15601 11723 l 15620 11718 l 15638 11713 l 15657 11707 l 15676 11702 l 15694 11696 l 15710 11690 l 15726 11685 l 15741 11680 l 15755 11675 l 15768 11670 l 15784 11663 l 15800 11656 l 15815 11649 l 15829 11641 l 15843 11634 l 15856 11626 l 15867 11619 l 15877 11613 l 15887 11608 l 15895 11603 l 15905 11597 l 15916 11591 l 15926 11586 l 15936 11580 l 15947 11575 l 15956 11570 l 15965 11565 l 15973 11560 l 15980 11555 l 15988 11549 l 15996 11542 l 16004 11535 l 16012 11528 l 16018 11521 l 16025 11515 l 16030 11510 l 16037 11503 l 16043 11497 l 16050 11489 l 16058 11482 l 16065 11474 l 16073 11465 l 16078 11459 l 16083 11452 l 16090 11444 l 16099 11434 l 16109 11422 l 16119 11410 l 16129 11398 l 16136 11390 l 16139 11386 l 16140 11385 l gs col-1 s gr % Polyline [90] 0 sd n 10590 11400 m 10590 11399 l 10593 11396 l 10599 11389 l 10607 11377 l 10618 11363 l 10630 11349 l 10641 11335 l 10651 11322 l 10659 11311 l 10667 11302 l 10675 11293 l 10683 11285 l 10692 11275 l 10701 11266 l 10711 11256 l 10722 11246 l 10734 11236 l 10745 11227 l 10757 11218 l 10768 11210 l 10779 11202 l 10790 11195 l 10799 11189 l 10809 11184 l 10819 11178 l 10830 11172 l 10842 11166 l 10854 11161 l 10866 11155 l 10877 11150 l 10889 11144 l 10901 11139 l 10912 11135 l 10923 11130 l 10933 11125 l 10945 11121 l 10957 11116 l 10969 11111 l 10982 11105 l 10995 11100 l 11008 11095 l 11021 11089 l 11033 11084 l 11045 11079 l 11057 11075 l 11068 11070 l 11078 11065 l 11090 11061 l 11101 11056 l 11113 11051 l 11125 11045 l 11138 11040 l 11150 11035 l 11163 11029 l 11175 11024 l 11187 11019 l 11199 11015 l 11210 11010 l 11222 11005 l 11234 11001 l 11247 10996 l 11260 10991 l 11274 10986 l 11289 10981 l 11304 10976 l 11319 10971 l 11333 10967 l 11347 10962 l 11361 10959 l 11375 10955 l 11389 10952 l 11403 10948 l 11418 10945 l 11434 10942 l 11451 10939 l 11468 10936 l 11484 10933 l 11501 10930 l 11517 10927 l 11532 10925 l 11546 10922 l 11560 10920 l 11574 10918 l 11588 10915 l 11602 10913 l 11617 10910 l 11632 10908 l 11648 10905 l 11663 10902 l 11678 10900 l 11693 10897 l 11707 10895 l 11721 10892 l 11735 10890 l 11749 10888 l 11763 10885 l 11778 10883 l 11794 10880 l 11811 10877 l 11828 10875 l 11844 10872 l 11861 10869 l 11877 10866 l 11892 10863 l 11906 10860 l 11920 10858 l 11934 10855 l 11948 10851 l 11962 10848 l 11977 10845 l 11992 10841 l 12008 10837 l 12023 10834 l 12039 10830 l 12054 10827 l 12069 10824 l 12083 10820 l 12098 10818 l 12110 10815 l 12123 10813 l 12136 10810 l 12150 10808 l 12165 10805 l 12180 10803 l 12196 10801 l 12211 10798 l 12227 10796 l 12242 10794 l 12256 10792 l 12270 10791 l 12284 10789 l 12298 10788 l 12313 10786 l 12329 10784 l 12345 10783 l 12362 10781 l 12379 10779 l 12397 10778 l 12414 10776 l 12431 10775 l 12448 10774 l 12463 10772 l 12478 10771 l 12493 10770 l 12507 10769 l 12522 10768 l 12537 10766 l 12553 10765 l 12569 10764 l 12586 10763 l 12603 10762 l 12620 10761 l 12637 10760 l 12653 10759 l 12669 10758 l 12685 10758 l 12699 10757 l 12713 10757 l 12729 10756 l 12745 10756 l 12761 10756 l 12779 10756 l 12797 10755 l 12815 10755 l 12833 10755 l 12851 10755 l 12868 10755 l 12885 10755 l 12901 10755 l 12918 10755 l 12932 10755 l 12946 10755 l 12961 10755 l 12977 10755 l 12993 10755 l 13010 10755 l 13027 10755 l 13044 10755 l 13061 10755 l 13079 10754 l 13096 10754 l 13113 10754 l 13129 10754 l 13146 10753 l 13162 10753 l 13178 10753 l 13194 10752 l 13210 10752 l 13227 10751 l 13244 10750 l 13262 10750 l 13280 10749 l 13299 10748 l 13318 10748 l 13336 10747 l 13354 10747 l 13371 10746 l 13388 10746 l 13403 10745 l 13418 10745 l 13432 10745 l 13445 10745 l 13462 10745 l 13478 10745 l 13494 10746 l 13511 10746 l 13527 10747 l 13543 10748 l 13559 10749 l 13574 10750 l 13588 10752 l 13603 10753 l 13616 10754 l 13630 10755 l 13644 10756 l 13659 10757 l 13674 10759 l 13691 10760 l 13708 10761 l 13725 10762 l 13742 10763 l 13759 10764 l 13776 10765 l 13791 10766 l 13806 10767 l 13820 10768 l 13834 10768 l 13847 10768 l 13861 10769 l 13875 10769 l 13890 10769 l 13904 10770 l 13918 10770 l 13932 10770 l 13945 10770 l 13958 10770 l 13970 10770 l 13983 10770 l 13995 10770 l 14007 10770 l 14021 10770 l 14035 10770 l 14050 10770 l 14066 10771 l 14082 10771 l 14098 10772 l 14115 10772 l 14131 10773 l 14148 10774 l 14165 10775 l 14180 10776 l 14196 10777 l 14213 10779 l 14231 10780 l 14249 10782 l 14269 10784 l 14289 10786 l 14309 10788 l 14328 10790 l 14348 10792 l 14366 10794 l 14384 10796 l 14401 10798 l 14418 10800 l 14434 10802 l 14450 10804 l 14466 10806 l 14482 10808 l 14499 10810 l 14516 10812 l 14533 10815 l 14550 10817 l 14566 10819 l 14581 10821 l 14596 10823 l 14610 10824 l 14624 10826 l 14638 10828 l 14651 10829 l 14664 10830 l 14678 10832 l 14693 10833 l 14708 10835 l 14723 10836 l 14739 10838 l 14755 10840 l 14771 10842 l 14787 10844 l 14803 10846 l 14819 10848 l 14834 10850 l 14850 10853 l 14864 10855 l 14878 10857 l 14893 10860 l 14909 10863 l 14926 10866 l 14942 10869 l 14960 10872 l 14977 10876 l 14995 10880 l 15012 10883 l 15028 10887 l 15045 10891 l 15060 10895 l 15075 10898 l 15089 10902 l 15103 10905 l 15118 10909 l 15132 10913 l 15147 10917 l 15163 10921 l 15178 10926 l 15193 10930 l 15209 10935 l 15224 10940 l 15239 10944 l 15253 10949 l 15267 10953 l 15281 10957 l 15294 10961 l 15308 10965 l 15321 10969 l 15335 10973 l 15349 10977 l 15365 10981 l 15381 10986 l 15397 10991 l 15415 10995 l 15432 11000 l 15449 11005 l 15467 11010 l 15483 11014 l 15500 11019 l 15516 11023 l 15533 11028 l 15549 11032 l 15566 11037 l 15583 11041 l 15601 11047 l 15620 11052 l 15638 11057 l 15657 11063 l 15676 11068 l 15694 11074 l 15710 11080 l 15726 11085 l 15741 11090 l 15755 11095 l 15768 11100 l 15781 11106 l 15795 11112 l 15807 11118 l 15820 11124 l 15832 11130 l 15843 11136 l 15854 11143 l 15863 11148 l 15872 11154 l 15880 11159 l 15888 11163 l 15895 11168 l 15905 11173 l 15916 11179 l 15926 11184 l 15936 11190 l 15947 11195 l 15956 11200 l 15965 11205 l 15973 11210 l 15980 11215 l 15988 11221 l 15996 11228 l 16004 11235 l 16012 11242 l 16018 11249 l 16025 11255 l 16030 11260 l 16037 11267 l 16043 11273 l 16050 11281 l 16058 11288 l 16065 11296 l 16073 11305 l 16078 11311 l 16083 11318 l 16090 11326 l 16099 11336 l 16109 11348 l 16119 11360 l 16129 11372 l 16136 11380 l 16139 11384 l 16140 11385 l gs col-1 s gr [] 0 sd /Times-Italic ff 750.00 scf sf 16425 11475 m gs 1 -1 sc (c) col-1 sh gr /Symbol ff 750.00 scf sf 15825 8250 m gs 1 -1 sc (b) col-1 sh gr /Symbol ff 750.00 scf sf 10575 8175 m gs 1 -1 sc (a) col-1 sh gr /Symbol ff 750.00 scf sf 15825 14850 m gs 1 -1 sc (g) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1710 3134 a FP(Figure)32 b(5.16)605 3301 y FQ(Of)27 b(course,)f(ev)n(ery)f(extended)i(surface)f(\006)h(can)f(b)r (e)i(parametrized)d(in)i(man)n(y)f(w)n(a)n(ys.)35 b(Ho)n(w-)456 3403 y(ev)n(er,)25 b(if)i(w)n(e)f(construct)g(a)g(system)g(of)g (isomorphisms)f FJ(f)2206 3415 y FI(M)s(;M)2361 3399 y Fx(0)2397 3403 y FQ(:)j FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)2712 3373 y FE(0)2736 3403 y FQ(\))2819 3356 y FE(\030)2791 3403 y FL(\000)-39 b(!)23 b FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\),)27 b(com-)456 3503 y(patible)j(in)g(the)g(follo)n(wing)f (sense:)41 b FJ(f)1623 3515 y FI(M)s(;M)1778 3498 y Fx(0)1805 3503 y FJ(f)1846 3515 y FI(M)1915 3498 y Fx(0)1937 3515 y FI(;M)2026 3498 y Fx(0)q(0)2099 3503 y FQ(=)26 b FJ(f)2231 3515 y FI(M)s(;M)2386 3498 y Fx(00)2431 3503 y FQ(,)31 b(then)f(w)n(e)g(can)f(iden)n(tify)i(all)f(of)456 3602 y(these)i(spaces)g(with)h(eac)n(h)e(other)h(and)g(de\014ne)h(the)g (space)f FJ(\034)9 b FQ(\(\006\),)35 b(whic)n(h)d(is)g(canonically)f (iso-)456 3702 y(morphic)24 b(to)h(eac)n(h)f(of)h FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\))26 b(\(see)f(a)g(formal)f (de\014nition)i(in)f(the)h(pro)r(of)e(of)h(Theorem)f(4.4.3\).)605 3802 y(Moreo)n(v)n(er,)f(suc)n(h)h(a)h(system)f(of)h(isomorphisms)f(w)n (ould)g(automatically)g(giv)n(e)g(a)g(represen-)456 3904 y(tation)j(of)h(the)g(extended)g(mapping)f(class)g(group)r(oid)f FL(T)7 b FJ(eich)p FQ(,)28 b(as)f(follo)n(ws.)36 b(Let)28 b FJ(f)17 b FQ(:)28 b(\006)3155 3916 y FM(1)3244 3857 y FE(\030)3215 3904 y FL(\000)-39 b(!)23 b FQ(\006)3407 3916 y FM(2)456 4003 y FQ(b)r(e)g(a)f(homeomorphism)f(of)h(extended)h (surfaces,)g(and)f(let)h FJ(M)2367 4015 y FM(2)2426 4003 y FQ(b)r(e)g(a)f(parameterization)f(of)h(\006)3384 4015 y FM(2)3421 4003 y FQ(.)456 4103 y(Then)32 b FJ(f)40 b FQ(giv)n(es)31 b(rise)g(to)g(a)h(parameterization)e FJ(M)2029 4115 y FM(1)2097 4103 y FQ(of)i(\006)2256 4115 y FM(1)2325 4103 y FQ(in)g(the)g(ob)n(vious)f(w)n(a)n(y)-7 b(.)48 b(Moreo)n(v)n(er,)456 4203 y FJ(f)41 b FQ(establishes)32 b(a)h(one-to-one)e(corresp)r(ondence)g(b)r(et)n(w)n(een)h(the)i(cuts)f FJ(C)2740 4215 y FM(1)2810 4203 y FQ(on)g(\006)2991 4215 y FM(1)3061 4203 y FQ(and)f FJ(C)3286 4215 y FM(2)3357 4203 y FQ(on)456 4302 y(\006)516 4314 y FM(2)553 4302 y FQ(,)f(and)f(b)r(et)n(w)n(een)g(the)g(comp)r(onen)n(ts)g(\(\006)1791 4314 y FM(1)1829 4302 y FQ(\))1861 4314 y FI(a)1931 4302 y FQ(and)g(\(\006)2187 4314 y FM(2)2225 4302 y FQ(\))2257 4314 y FI(a)2297 4302 y FQ(.)45 b(Th)n(us,)30 b FJ(f)39 b FQ(giv)n(es)29 b(rise)h(to)g(an)g(iden-)456 4402 y(ti\014cation)e FJ(\034)9 b FQ(\(\006)944 4414 y FM(1)983 4402 y FJ(;)14 b(M)1101 4414 y FM(1)1137 4402 y FQ(\))26 b(=)1285 4340 y Fy(L)1377 4427 y FI(i)1400 4435 y FG(c)1431 4427 y FE(2)p FI(I)5 b(;)11 b(c)p FE(2)p FI(C)1664 4435 y FF(1)1714 4340 y Fy(N)1806 4427 y FI(a)1860 4402 y FJ(\034)e FQ(\()p FJ(S)1988 4414 y FM(0)p FI(;n)2082 4422 y FG(a)2123 4402 y FQ(\))26 b(=)e FJ(\034)9 b FQ(\(\006)2407 4414 y FM(2)2446 4402 y FJ(;)14 b(M)2564 4414 y FM(2)2600 4402 y FQ(\).)41 b(Com)n(bining)29 b(this)g(with)456 4509 y(the)h(isomorphisms)e FJ(\034)9 b FQ(\(\006)1258 4521 y FM(1)1296 4509 y FQ(\))28 b(=)e FJ(\034)9 b FQ(\(\006)1584 4521 y FM(1)1622 4509 y FJ(;)14 b(M)1740 4521 y FM(1)1777 4509 y FQ(\),)31 b FJ(\034)9 b FQ(\(\006)2000 4521 y FM(2)2038 4509 y FQ(\))27 b(=)f FJ(\034)9 b FQ(\(\006)2325 4521 y FM(2)2363 4509 y FJ(;)14 b(M)2481 4521 y FM(2)2518 4509 y FQ(\),)31 b(w)n(e)e(get)h(an)g(isomorphism)456 4615 y FJ(f)497 4627 y FE(\003)544 4615 y FQ(:)h FJ(\034)9 b FQ(\(\006)735 4627 y FM(1)773 4615 y FQ(\))873 4568 y FE(\030)845 4615 y FL(\000)-40 b(!)40 b FJ(\034)9 b FQ(\(\006)1130 4627 y FM(2)1168 4615 y FQ(\).)67 b(W)-7 b(e)38 b(lea)n(v)n(e)e(it)i(to)g (the)g(reader)e(to)h(c)n(hec)n(k)g(that)h(this)g(isomorphism)456 4715 y(do)r(es)29 b(not)g(dep)r(end)i(on)e(the)h(c)n(hoice)f(of)g FJ(M)1773 4727 y FM(2)1840 4715 y FQ(and)g(satis\014es)g(\()p FJ(f)9 b(g)s FQ(\))2468 4727 y FE(\003)2532 4715 y FQ(=)26 b FJ(f)2664 4727 y FE(\003)2702 4715 y FJ(g)2742 4727 y FE(\003)2780 4715 y FJ(;)14 b FQ(id)2886 4727 y FE(\003)2950 4715 y FQ(=)26 b(id.)43 b(Also,)30 b(it)456 4815 y(is)i(immediately)g (ob)n(vious)f(from)h(\(5.4.3\))g(that)h(the)g(so)e(constructed)h(mo)r (dular)g(functor)g(will)456 4914 y(satisfy)27 b(the)h(gluing)f(axiom.) 605 5016 y(Therefore,)19 b(our)f(goal)f(is)h(to)g(construct)g(a)g (compatible)g(system)g(of)h(isomorphisms)e FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)3424 4986 y FE(0)3447 5016 y FQ(\))3531 4969 y FE(\030)3503 5016 y FL(\000)-40 b(!)456 5116 y FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\).)53 b(By)33 b(Theorem)f(5.2.3,)h(ev)n(ery)e(t)n(w)n(o)h(parameterizations)f (can)h(b)r(e)i(connected)e(b)n(y)h(a)456 5216 y(sequence)f(of)g(simple) h(mo)n(v)n(es)e FJ(Z)q(;)14 b(B)t(;)g(F)e FQ(;)35 b(let)e(us)g(assign)e (to)i(these)g(mo)n(v)n(es)e(the)i(isomorphisms)p eop %%Page: 116 24 116 119 bop 456 226 a FM(116)1010 b(5.)29 b(MODULAR)g(FUNCTOR)456 425 y FJ(Z)q(;)14 b(\033)n(;)g(G)31 b FQ(giv)n(en)f(b)n(y)h(the)g(MS)g (data.)45 b(A)31 b(comparison)e(of)i(the)g(axioms)f(MF1{MF7)g(and)g (MS1{)456 525 y(MS7)d(sho)n(ws)g(that)g(all)h(the)g(relations)e(among)h (the)h(mo)n(v)n(es)e FJ(Z)q(;)14 b(B)t(;)g(F)40 b FQ(also)26 b(hold)i(for)f(their)h(ana-)456 624 y(logues)j FJ(Z)q(;)14 b(\033)n(;)g(G)p FQ(;)36 b(the)c(only)g(relation)g(whic)n(h)g(is)g(not) g(immediately)h(ob)n(vious)e(is)h(the)h(cylinder)456 724 y(axiom)c(MF5,)h(but)h(it)f(follo)n(ws)f(from)g(the)h(functorialit) n(y)g(of)g(the)g(morphisms)f FJ(Z)q(;)14 b(\033)n(;)g(G)p FQ(.)45 b(Th)n(us,)456 824 y(ev)n(ery)26 b(MS)i(data)f(de\014nes)h(a)f (gen)n(us)f(zero)h(MF.)605 923 y(The)35 b(construction)f(in)i(the)f (opp)r(osite)g(direction)f(is)h(quite)g(similar.)59 b(Assume)35 b(that)g(w)n(e)456 1023 y(ha)n(v)n(e)30 b(a)h(gen)n(us)f(zero)g(MF.)i (De\014ne)g(the)f(functors)g FL(h)14 b(i)32 b FQ(and)f(the)h (isomorphisms)d FJ(Z)q(;)14 b(\033)n(;)g(G)33 b FQ(as)d(in)456 1123 y(the)g(statemen)n(t)f(of)h(the)g(theorem.)43 b(Again,)30 b(a)f(comparison)f(of)i(the)g(axioms)f(MF1{MF7)g(and)456 1222 y(MS1{MS7)j(sho)n(ws)g(that)i(these)f(data)g(satisfy)g(the)g (axioms)f(of)i(MS)f(data.)54 b(This)33 b(completes)456 1322 y(the)28 b(pro)r(of)f(of)g(Theorem)g(5.4.1.)p 3384 1322 4 57 v 3388 1269 50 4 v 3388 1322 V 3437 1322 4 57 v -383 1430 a Fq(?!)605 1602 y FP(Example)k FQ(5.4.2)p FP(.)40 b FQ(Consider)34 b(the)i(surface)f(\006)h(and)g(the)g(\\asso)r (ciativit)n(y)d(mo)n(v)n(e")h FJ(M)3366 1553 y FI(F)3408 1561 y FG(c)3361 1602 y Fw( )456 1756 y FJ(M)537 1768 y FM(0)609 1689 y FI(F)660 1662 y Fx(\000)p FF(1)651 1716 y FG(c)678 1704 y Fx(0)632 1756 y Fw( )59 b FJ(M)864 1726 y FE(0)922 1756 y FQ(sho)n(wn)34 b(in)i(Figure)f(5.17.)58 b(Assign)35 b(to)g(the)h(b)r(oundary)f(comp)r(onen)n(ts)f FJ(\013;)14 b(:)g(:)g(:)g(;)g(\016)456 1856 y FQ(ob)5 b(jects)27 b FJ(A;)14 b(:)g(:)g(:)g(;)g(D)r FQ(.)36 b(Then:)1269 2032 y FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\))24 b(=)1676 1953 y Fy(M)1688 2131 y FI(i)p FE(2)p FI(I)1802 2032 y FL(h)p FJ(A;)14 b(B)t(;)g(V)2085 2044 y FI(i)2113 2032 y FL(i)19 b(\012)f(h)p FJ(V)2346 1998 y FE(\003)2327 2053 y FI(i)2385 2032 y FJ(;)c(C)q(;)g(D)r FL(i)p FJ(;)1241 2239 y(\034)9 b FQ(\(\006)p FJ(;)14 b(M)1496 2251 y FM(0)1533 2239 y FQ(\))24 b(=)e FL(h)p FJ(A;)14 b(B)t(;)g(C)q(;)g(D)r FL(i)p FJ(;)1246 2394 y(\034)9 b FQ(\(\006)p FJ(;)14 b(M)1510 2360 y FE(0)1533 2394 y FQ(\))24 b(=)1676 2315 y Fy(M)1684 2493 y FI(j)s FE(2)p FI(I)1802 2394 y FL(h)p FJ(D)r(;)14 b(A;)g(V)2089 2406 y FI(j)2125 2394 y FL(i)k(\012)g(h)p FJ(V)2358 2360 y FE(\003)2338 2414 y FI(j)2396 2394 y FJ(;)c(B)t(;)g(C)6 b FL(i)p FJ(:)456 2648 y FQ(Then)29 b(the)h(corresp)r(onding)d(isomorphisms)h FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\))27 b FL(!)f FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)2561 2660 y FM(0)2598 2648 y FQ(\))27 b FL(!)f FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)3030 2618 y FE(0)3053 2648 y FQ(\))30 b(are)e(giv)n(en)456 2747 y(b)n(y)f(Figure)g(5.18)f(b)r(elo)n(w.)762 3632 y @beginspecial 0 @llx 0 @lly 78 @urx 82 @ury 780 @rwi @setspecial %%BeginDocument: figures/ftaustand1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: ftaustand1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Jun 10 12:24:16 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 78 82 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.1800 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -105.0 163.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 16016 m -1000 -1000 l 17898 -1000 l 17898 16016 l cp clip 0.01080 0.01080 sc % Arc 30.000 slw gs n 20340.0 11400.0 4215.0 -145.3 145.3 arcn gs col-1 s gr gr % Arc gs n 13321.9 7855.4 1969.8 141.7 35.5 arcn gs col-1 s gr gr % Arc gs n 13321.9 15019.6 1969.8 -141.7 -35.5 arc gs col-1 s gr gr % Ellipse n 10800 9000 975 375 0 360 DrawEllipse gs col-1 s gr % Ellipse n 10800 13800 975 375 0 360 DrawEllipse gs col-1 s gr % Ellipse n 15900 9000 975 375 0 360 DrawEllipse gs col-1 s gr % Arc gs n 6360.0 11400.0 4215.0 -34.7 34.7 arc gs col-1 s gr gr % Ellipse n 15900 13800 975 375 0 360 DrawEllipse gs col-1 s gr /Symbol ff 750.00 scf sf 10560 15000 m gs 1 -1 sc (d) col-1 sh gr % Polyline 15.000 slw n 10590 11370 m 10590 11371 l 10593 11374 l 10599 11381 l 10607 11393 l 10618 11407 l 10630 11421 l 10641 11435 l 10651 11448 l 10659 11459 l 10667 11468 l 10675 11477 l 10683 11485 l 10692 11495 l 10701 11504 l 10711 11514 l 10722 11524 l 10734 11534 l 10745 11543 l 10757 11552 l 10768 11560 l 10779 11568 l 10790 11575 l 10799 11581 l 10809 11586 l 10819 11592 l 10830 11598 l 10842 11604 l 10854 11609 l 10866 11615 l 10877 11620 l 10889 11626 l 10901 11631 l 10912 11635 l 10923 11640 l 10933 11645 l 10945 11649 l 10957 11654 l 10969 11659 l 10982 11665 l 10995 11670 l 11008 11675 l 11021 11681 l 11033 11686 l 11045 11691 l 11057 11695 l 11068 11700 l 11078 11705 l 11090 11709 l 11101 11714 l 11113 11719 l 11125 11725 l 11138 11730 l 11150 11735 l 11163 11741 l 11175 11746 l 11187 11751 l 11199 11755 l 11210 11760 l 11222 11765 l 11234 11769 l 11247 11774 l 11260 11779 l 11274 11784 l 11289 11789 l 11304 11794 l 11319 11799 l 11333 11803 l 11347 11808 l 11361 11811 l 11375 11815 l 11389 11818 l 11403 11822 l 11418 11825 l 11434 11828 l 11451 11831 l 11468 11834 l 11484 11837 l 11501 11840 l 11517 11843 l 11532 11845 l 11546 11848 l 11560 11850 l 11574 11852 l 11588 11855 l 11602 11857 l 11617 11860 l 11632 11862 l 11648 11865 l 11663 11868 l 11678 11870 l 11693 11873 l 11707 11875 l 11721 11878 l 11735 11880 l 11749 11882 l 11763 11885 l 11778 11887 l 11794 11890 l 11811 11893 l 11828 11895 l 11844 11898 l 11861 11901 l 11877 11904 l 11892 11907 l 11906 11910 l 11920 11913 l 11934 11915 l 11948 11919 l 11962 11922 l 11977 11925 l 11992 11929 l 12008 11933 l 12023 11936 l 12039 11940 l 12054 11943 l 12069 11946 l 12083 11950 l 12098 11953 l 12110 11955 l 12123 11957 l 12136 11960 l 12150 11962 l 12165 11965 l 12180 11967 l 12196 11969 l 12211 11972 l 12227 11974 l 12242 11976 l 12256 11978 l 12270 11979 l 12284 11981 l 12298 11983 l 12313 11984 l 12329 11986 l 12345 11987 l 12362 11989 l 12379 11991 l 12397 11992 l 12414 11994 l 12431 11995 l 12448 11996 l 12463 11998 l 12478 11999 l 12493 12000 l 12507 12001 l 12522 12002 l 12537 12004 l 12553 12005 l 12569 12006 l 12586 12007 l 12603 12008 l 12620 12009 l 12637 12010 l 12653 12011 l 12669 12012 l 12685 12013 l 12699 12013 l 12713 12013 l 12729 12014 l 12745 12014 l 12761 12014 l 12779 12014 l 12797 12015 l 12815 12015 l 12833 12015 l 12851 12015 l 12868 12015 l 12885 12015 l 12901 12015 l 12918 12015 l 12932 12015 l 12946 12015 l 12961 12015 l 12977 12015 l 12993 12015 l 13010 12015 l 13027 12015 l 13044 12015 l 13061 12015 l 13079 12016 l 13096 12016 l 13113 12016 l 13129 12016 l 13146 12017 l 13162 12017 l 13178 12018 l 13194 12018 l 13210 12018 l 13227 12019 l 13244 12020 l 13262 12020 l 13280 12021 l 13299 12022 l 13318 12022 l 13336 12023 l 13354 12023 l 13371 12024 l 13388 12024 l 13403 12025 l 13418 12025 l 13432 12025 l 13445 12025 l 13462 12025 l 13478 12025 l 13494 12024 l 13511 12024 l 13527 12023 l 13543 12022 l 13559 12021 l 13574 12020 l 13588 12018 l 13603 12017 l 13616 12016 l 13630 12015 l 13644 12014 l 13659 12013 l 13674 12011 l 13691 12010 l 13708 12009 l 13725 12008 l 13742 12007 l 13759 12006 l 13776 12005 l 13791 12004 l 13806 12003 l 13820 12003 l 13834 12002 l 13847 12002 l 13861 12001 l 13875 12001 l 13890 12001 l 13904 12000 l 13918 12000 l 13932 12000 l 13945 12000 l 13958 12000 l 13970 12000 l 13983 12000 l 13995 12000 l 14007 12000 l 14021 12000 l 14035 12000 l 14050 12000 l 14066 11999 l 14082 11999 l 14098 11998 l 14115 11998 l 14131 11997 l 14148 11996 l 14165 11995 l 14180 11994 l 14196 11993 l 14213 11991 l 14231 11990 l 14249 11988 l 14269 11986 l 14289 11984 l 14309 11982 l 14328 11980 l 14348 11978 l 14366 11976 l 14384 11974 l 14401 11972 l 14418 11970 l 14434 11968 l 14450 11966 l 14466 11964 l 14482 11962 l 14499 11960 l 14516 11958 l 14533 11955 l 14550 11953 l 14566 11951 l 14581 11949 l 14596 11947 l 14610 11946 l 14624 11944 l 14638 11943 l 14651 11941 l 14664 11940 l 14678 11938 l 14693 11937 l 14708 11935 l 14723 11934 l 14739 11932 l 14755 11930 l 14771 11928 l 14787 11926 l 14803 11924 l 14819 11922 l 14834 11920 l 14850 11918 l 14864 11915 l 14878 11913 l 14893 11910 l 14909 11907 l 14926 11904 l 14942 11901 l 14960 11898 l 14977 11894 l 14995 11890 l 15012 11887 l 15028 11883 l 15045 11879 l 15060 11875 l 15075 11872 l 15089 11868 l 15103 11865 l 15118 11861 l 15132 11857 l 15147 11853 l 15163 11849 l 15178 11844 l 15193 11840 l 15209 11835 l 15224 11830 l 15239 11826 l 15253 11821 l 15267 11817 l 15281 11813 l 15294 11809 l 15308 11805 l 15321 11801 l 15335 11797 l 15349 11793 l 15365 11789 l 15381 11784 l 15397 11779 l 15415 11775 l 15432 11770 l 15449 11765 l 15467 11760 l 15483 11756 l 15500 11751 l 15516 11747 l 15533 11743 l 15549 11738 l 15566 11733 l 15583 11729 l 15601 11723 l 15620 11718 l 15638 11713 l 15657 11707 l 15676 11702 l 15694 11696 l 15710 11690 l 15726 11685 l 15741 11680 l 15755 11675 l 15768 11670 l 15784 11663 l 15800 11656 l 15815 11649 l 15829 11641 l 15843 11634 l 15856 11626 l 15867 11619 l 15877 11613 l 15887 11608 l 15895 11603 l 15905 11597 l 15916 11591 l 15926 11586 l 15936 11580 l 15947 11575 l 15956 11570 l 15965 11565 l 15973 11560 l 15980 11555 l 15988 11549 l 15996 11542 l 16004 11535 l 16012 11528 l 16018 11521 l 16025 11515 l 16030 11510 l 16037 11503 l 16043 11497 l 16050 11489 l 16058 11482 l 16065 11474 l 16073 11465 l 16078 11459 l 16083 11452 l 16090 11444 l 16099 11434 l 16109 11422 l 16119 11410 l 16129 11398 l 16136 11390 l 16139 11386 l 16140 11385 l gs col-1 s gr % Polyline [90] 0 sd n 10590 11400 m 10590 11399 l 10593 11396 l 10599 11389 l 10607 11377 l 10618 11363 l 10630 11349 l 10641 11335 l 10651 11322 l 10659 11311 l 10667 11302 l 10675 11293 l 10683 11285 l 10692 11275 l 10701 11266 l 10711 11256 l 10722 11246 l 10734 11236 l 10745 11227 l 10757 11218 l 10768 11210 l 10779 11202 l 10790 11195 l 10799 11189 l 10809 11184 l 10819 11178 l 10830 11172 l 10842 11166 l 10854 11161 l 10866 11155 l 10877 11150 l 10889 11144 l 10901 11139 l 10912 11135 l 10923 11130 l 10933 11125 l 10945 11121 l 10957 11116 l 10969 11111 l 10982 11105 l 10995 11100 l 11008 11095 l 11021 11089 l 11033 11084 l 11045 11079 l 11057 11075 l 11068 11070 l 11078 11065 l 11090 11061 l 11101 11056 l 11113 11051 l 11125 11045 l 11138 11040 l 11150 11035 l 11163 11029 l 11175 11024 l 11187 11019 l 11199 11015 l 11210 11010 l 11222 11005 l 11234 11001 l 11247 10996 l 11260 10991 l 11274 10986 l 11289 10981 l 11304 10976 l 11319 10971 l 11333 10967 l 11347 10962 l 11361 10959 l 11375 10955 l 11389 10952 l 11403 10948 l 11418 10945 l 11434 10942 l 11451 10939 l 11468 10936 l 11484 10933 l 11501 10930 l 11517 10927 l 11532 10925 l 11546 10922 l 11560 10920 l 11574 10918 l 11588 10915 l 11602 10913 l 11617 10910 l 11632 10908 l 11648 10905 l 11663 10902 l 11678 10900 l 11693 10897 l 11707 10895 l 11721 10892 l 11735 10890 l 11749 10888 l 11763 10885 l 11778 10883 l 11794 10880 l 11811 10877 l 11828 10875 l 11844 10872 l 11861 10869 l 11877 10866 l 11892 10863 l 11906 10860 l 11920 10858 l 11934 10855 l 11948 10851 l 11962 10848 l 11977 10845 l 11992 10841 l 12008 10837 l 12023 10834 l 12039 10830 l 12054 10827 l 12069 10824 l 12083 10820 l 12098 10818 l 12110 10815 l 12123 10813 l 12136 10810 l 12150 10808 l 12165 10805 l 12180 10803 l 12196 10801 l 12211 10798 l 12227 10796 l 12242 10794 l 12256 10792 l 12270 10791 l 12284 10789 l 12298 10788 l 12313 10786 l 12329 10784 l 12345 10783 l 12362 10781 l 12379 10779 l 12397 10778 l 12414 10776 l 12431 10775 l 12448 10774 l 12463 10772 l 12478 10771 l 12493 10770 l 12507 10769 l 12522 10768 l 12537 10766 l 12553 10765 l 12569 10764 l 12586 10763 l 12603 10762 l 12620 10761 l 12637 10760 l 12653 10759 l 12669 10758 l 12685 10758 l 12699 10757 l 12713 10757 l 12729 10756 l 12745 10756 l 12761 10756 l 12779 10756 l 12797 10755 l 12815 10755 l 12833 10755 l 12851 10755 l 12868 10755 l 12885 10755 l 12901 10755 l 12918 10755 l 12932 10755 l 12946 10755 l 12961 10755 l 12977 10755 l 12993 10755 l 13010 10755 l 13027 10755 l 13044 10755 l 13061 10755 l 13079 10754 l 13096 10754 l 13113 10754 l 13129 10754 l 13146 10753 l 13162 10753 l 13178 10753 l 13194 10752 l 13210 10752 l 13227 10751 l 13244 10750 l 13262 10750 l 13280 10749 l 13299 10748 l 13318 10748 l 13336 10747 l 13354 10747 l 13371 10746 l 13388 10746 l 13403 10745 l 13418 10745 l 13432 10745 l 13445 10745 l 13462 10745 l 13478 10745 l 13494 10746 l 13511 10746 l 13527 10747 l 13543 10748 l 13559 10749 l 13574 10750 l 13588 10752 l 13603 10753 l 13616 10754 l 13630 10755 l 13644 10756 l 13659 10757 l 13674 10759 l 13691 10760 l 13708 10761 l 13725 10762 l 13742 10763 l 13759 10764 l 13776 10765 l 13791 10766 l 13806 10767 l 13820 10768 l 13834 10768 l 13847 10768 l 13861 10769 l 13875 10769 l 13890 10769 l 13904 10770 l 13918 10770 l 13932 10770 l 13945 10770 l 13958 10770 l 13970 10770 l 13983 10770 l 13995 10770 l 14007 10770 l 14021 10770 l 14035 10770 l 14050 10770 l 14066 10771 l 14082 10771 l 14098 10772 l 14115 10772 l 14131 10773 l 14148 10774 l 14165 10775 l 14180 10776 l 14196 10777 l 14213 10779 l 14231 10780 l 14249 10782 l 14269 10784 l 14289 10786 l 14309 10788 l 14328 10790 l 14348 10792 l 14366 10794 l 14384 10796 l 14401 10798 l 14418 10800 l 14434 10802 l 14450 10804 l 14466 10806 l 14482 10808 l 14499 10810 l 14516 10812 l 14533 10815 l 14550 10817 l 14566 10819 l 14581 10821 l 14596 10823 l 14610 10824 l 14624 10826 l 14638 10828 l 14651 10829 l 14664 10830 l 14678 10832 l 14693 10833 l 14708 10835 l 14723 10836 l 14739 10838 l 14755 10840 l 14771 10842 l 14787 10844 l 14803 10846 l 14819 10848 l 14834 10850 l 14850 10853 l 14864 10855 l 14878 10857 l 14893 10860 l 14909 10863 l 14926 10866 l 14942 10869 l 14960 10872 l 14977 10876 l 14995 10880 l 15012 10883 l 15028 10887 l 15045 10891 l 15060 10895 l 15075 10898 l 15089 10902 l 15103 10905 l 15118 10909 l 15132 10913 l 15147 10917 l 15163 10921 l 15178 10926 l 15193 10930 l 15209 10935 l 15224 10940 l 15239 10944 l 15253 10949 l 15267 10953 l 15281 10957 l 15294 10961 l 15308 10965 l 15321 10969 l 15335 10973 l 15349 10977 l 15365 10981 l 15381 10986 l 15397 10991 l 15415 10995 l 15432 11000 l 15449 11005 l 15467 11010 l 15483 11014 l 15500 11019 l 15516 11023 l 15533 11028 l 15549 11032 l 15566 11037 l 15583 11041 l 15601 11047 l 15620 11052 l 15638 11057 l 15657 11063 l 15676 11068 l 15694 11074 l 15710 11080 l 15726 11085 l 15741 11090 l 15755 11095 l 15768 11100 l 15781 11106 l 15795 11112 l 15807 11118 l 15820 11124 l 15832 11130 l 15843 11136 l 15854 11143 l 15863 11148 l 15872 11154 l 15880 11159 l 15888 11163 l 15895 11168 l 15905 11173 l 15916 11179 l 15926 11184 l 15936 11190 l 15947 11195 l 15956 11200 l 15965 11205 l 15973 11210 l 15980 11215 l 15988 11221 l 15996 11228 l 16004 11235 l 16012 11242 l 16018 11249 l 16025 11255 l 16030 11260 l 16037 11267 l 16043 11273 l 16050 11281 l 16058 11288 l 16065 11296 l 16073 11305 l 16078 11311 l 16083 11318 l 16090 11326 l 16099 11336 l 16109 11348 l 16119 11360 l 16129 11372 l 16136 11380 l 16139 11384 l 16140 11385 l gs col-1 s gr [] 0 sd /Times-Italic ff 750.00 scf sf 16425 11475 m gs 1 -1 sc (c) col-1 sh gr /Symbol ff 750.00 scf sf 15825 8250 m gs 1 -1 sc (b) col-1 sh gr /Symbol ff 750.00 scf sf 10575 8175 m gs 1 -1 sc (a) col-1 sh gr /Symbol ff 750.00 scf sf 15825 14850 m gs 1 -1 sc (g) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1510 3242 a FI(F)1552 3250 y FG(c)1481 3290 y FL(\000)-18 b(!)1680 3632 y @beginspecial 0 @llx 0 @lly 78 @urx 82 @ury 780 @rwi @setspecial %%BeginDocument: figures/ftaustand3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: ftaustand3.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Jun 10 12:25:03 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 78 82 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.1800 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -228.0 163.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 16016 m -1000 -1000 l 29298 -1000 l 29298 16016 l cp clip 0.01080 0.01080 sc % Arc 30.000 slw gs n 17760.0 11400.0 4215.0 -34.7 34.7 arc gs col-1 s gr gr % Arc gs n 24721.9 7855.4 1969.8 141.7 35.5 arcn gs col-1 s gr gr % Arc gs n 24736.9 15019.6 1969.8 -141.7 -35.5 arc gs col-1 s gr gr % Ellipse n 22200 9000 975 375 0 360 DrawEllipse gs col-1 s gr % Ellipse n 27300 9000 975 375 0 360 DrawEllipse gs col-1 s gr % Arc gs n 31740.0 11400.0 4215.0 -145.3 145.3 arcn gs col-1 s gr gr % Ellipse n 27300 13800 975 375 0 360 DrawEllipse gs col-1 s gr /Symbol ff 750.00 scf sf 27150 14850 m gs 1 -1 sc (g) col-1 sh gr % Ellipse n 22200 13800 975 375 0 360 DrawEllipse gs col-1 s gr /Symbol ff 750.00 scf sf 21975 15000 m gs 1 -1 sc (d) col-1 sh gr /Symbol ff 750.00 scf sf 21975 8175 m gs 1 -1 sc (a) col-1 sh gr /Symbol ff 750.00 scf sf 27150 8250 m gs 1 -1 sc (b) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 2428 3224 a FI(F)2479 3197 y Fx(\000)p FF(1)2470 3250 y FG(c)2497 3238 y Fx(0)2400 3290 y FL(\000)-37 b(\000)-19 b(\000)-37 b(!)2654 3632 y @beginspecial 0 @llx 0 @lly 78 @urx 82 @ury 780 @rwi @setspecial %%BeginDocument: figures/ftaustand2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: ftaustand2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Jun 10 12:24:44 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 78 82 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.1800 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -228.0 163.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 16016 m -1000 -1000 l 29298 -1000 l 29298 16016 l cp clip 0.01080 0.01080 sc % Polyline 30.000 slw n 24900 13350 m 24825 13500 l gs col0 s gr % Arc gs n 24721.9 7855.4 1969.8 141.7 35.5 arcn gs col-1 s gr gr % Arc gs n 24736.9 15019.6 1969.8 -141.7 -35.5 arc gs col-1 s gr gr % Ellipse n 22200 9000 975 375 0 360 DrawEllipse gs col-1 s gr % Ellipse n 27300 9000 975 375 0 360 DrawEllipse gs col-1 s gr % Ellipse n 27300 13800 975 375 0 360 DrawEllipse gs col-1 s gr % Ellipse n 22200 13800 975 375 0 360 DrawEllipse gs col-1 s gr % Arc gs n 17760.0 11400.0 4215.0 -34.7 34.7 arc gs col-1 s gr gr % Arc gs n 31740.0 11400.0 4215.0 -145.3 145.3 arcn gs col-1 s gr gr /Symbol ff 750.00 scf sf 27150 14850 m gs 1 -1 sc (g) col-1 sh gr % Polyline 15.000 slw n 24750 9825 m 24749 9825 l 24744 9828 l 24734 9834 l 24720 9843 l 24704 9852 l 24689 9862 l 24676 9870 l 24665 9878 l 24655 9885 l 24645 9893 l 24637 9899 l 24629 9906 l 24620 9913 l 24611 9922 l 24602 9930 l 24593 9940 l 24584 9949 l 24575 9959 l 24566 9969 l 24558 9978 l 24550 9988 l 24543 9998 l 24535 10007 l 24528 10018 l 24520 10029 l 24512 10041 l 24504 10053 l 24496 10066 l 24488 10079 l 24481 10092 l 24474 10105 l 24467 10117 l 24461 10128 l 24455 10140 l 24449 10152 l 24444 10163 l 24438 10176 l 24432 10189 l 24426 10202 l 24421 10216 l 24415 10230 l 24410 10243 l 24404 10257 l 24399 10270 l 24395 10282 l 24390 10295 l 24385 10308 l 24381 10321 l 24376 10335 l 24371 10350 l 24366 10365 l 24360 10381 l 24355 10398 l 24350 10414 l 24345 10430 l 24341 10445 l 24337 10460 l 24333 10475 l 24329 10488 l 24326 10501 l 24322 10515 l 24319 10529 l 24315 10544 l 24311 10559 l 24308 10575 l 24304 10591 l 24301 10606 l 24297 10621 l 24294 10635 l 24291 10649 l 24288 10662 l 24285 10675 l 24282 10688 l 24279 10701 l 24276 10714 l 24273 10728 l 24270 10742 l 24266 10756 l 24263 10771 l 24260 10785 l 24257 10800 l 24254 10815 l 24252 10829 l 24249 10843 l 24247 10856 l 24245 10870 l 24243 10884 l 24241 10898 l 24240 10914 l 24238 10929 l 24236 10946 l 24235 10963 l 24233 10981 l 24232 10998 l 24230 11016 l 24229 11033 l 24228 11049 l 24227 11065 l 24226 11080 l 24225 11095 l 24224 11110 l 24223 11125 l 24222 11140 l 24221 11155 l 24220 11171 l 24219 11187 l 24218 11204 l 24217 11220 l 24216 11235 l 24215 11250 l 24214 11265 l 24214 11279 l 24213 11292 l 24213 11305 l 24212 11320 l 24212 11335 l 24211 11351 l 24211 11367 l 24211 11383 l 24211 11400 l 24211 11417 l 24211 11433 l 24211 11449 l 24212 11465 l 24212 11480 l 24213 11495 l 24213 11508 l 24214 11521 l 24214 11535 l 24215 11549 l 24216 11564 l 24217 11580 l 24218 11596 l 24219 11612 l 24220 11627 l 24221 11643 l 24222 11658 l 24223 11672 l 24224 11686 l 24225 11700 l 24226 11714 l 24227 11728 l 24228 11742 l 24229 11757 l 24230 11773 l 24232 11788 l 24233 11804 l 24235 11820 l 24236 11836 l 24238 11851 l 24240 11865 l 24241 11879 l 24243 11892 l 24245 11905 l 24247 11920 l 24250 11935 l 24253 11950 l 24256 11966 l 24259 11982 l 24263 11998 l 24266 12014 l 24270 12029 l 24273 12044 l 24277 12057 l 24280 12070 l 24283 12083 l 24285 12094 l 24288 12107 l 24291 12119 l 24294 12132 l 24297 12145 l 24300 12158 l 24302 12171 l 24305 12184 l 24308 12197 l 24310 12210 l 24313 12223 l 24315 12235 l 24317 12248 l 24320 12261 l 24322 12276 l 24325 12291 l 24328 12307 l 24331 12323 l 24334 12340 l 24337 12356 l 24340 12372 l 24343 12387 l 24347 12401 l 24350 12415 l 24354 12429 l 24357 12443 l 24362 12457 l 24366 12471 l 24371 12486 l 24376 12501 l 24381 12515 l 24386 12529 l 24391 12542 l 24396 12555 l 24400 12566 l 24405 12578 l 24410 12588 l 24414 12599 l 24419 12610 l 24425 12621 l 24430 12633 l 24436 12644 l 24441 12656 l 24447 12667 l 24453 12678 l 24459 12688 l 24464 12698 l 24470 12708 l 24476 12717 l 24482 12727 l 24488 12738 l 24495 12749 l 24502 12760 l 24509 12772 l 24516 12783 l 24522 12794 l 24528 12805 l 24533 12814 l 24538 12824 l 24543 12833 l 24548 12845 l 24553 12858 l 24558 12871 l 24562 12883 l 24566 12895 l 24571 12905 l 24575 12914 l 24580 12923 l 24586 12930 l 24592 12937 l 24601 12945 l 24610 12952 l 24620 12959 l 24631 12966 l 24642 12973 l 24653 12980 l 24662 12986 l 24672 12992 l 24684 12999 l 24698 13008 l 24714 13018 l 24731 13029 l 24747 13039 l 24759 13046 l 24764 13049 l 24765 13050 l gs col-1 s gr % Polyline [90] 0 sd n 24690 9825 m 24691 9825 l 24696 9828 l 24706 9834 l 24720 9843 l 24736 9852 l 24751 9862 l 24764 9870 l 24775 9878 l 24785 9885 l 24795 9893 l 24803 9899 l 24811 9906 l 24820 9913 l 24829 9922 l 24838 9930 l 24847 9940 l 24856 9949 l 24865 9959 l 24874 9969 l 24882 9978 l 24890 9988 l 24898 9998 l 24905 10007 l 24912 10018 l 24920 10029 l 24928 10041 l 24936 10053 l 24944 10066 l 24952 10079 l 24959 10092 l 24966 10105 l 24973 10117 l 24979 10128 l 24985 10140 l 24991 10152 l 24996 10163 l 25002 10176 l 25008 10189 l 25014 10202 l 25019 10216 l 25025 10230 l 25030 10243 l 25036 10257 l 25041 10270 l 25045 10282 l 25050 10295 l 25055 10308 l 25059 10321 l 25064 10335 l 25069 10350 l 25074 10365 l 25080 10381 l 25085 10398 l 25090 10414 l 25095 10430 l 25099 10445 l 25103 10460 l 25108 10475 l 25111 10488 l 25114 10501 l 25118 10515 l 25121 10529 l 25125 10544 l 25129 10559 l 25132 10575 l 25136 10591 l 25139 10606 l 25143 10621 l 25146 10635 l 25149 10649 l 25152 10662 l 25155 10675 l 25158 10688 l 25161 10701 l 25164 10714 l 25167 10728 l 25170 10742 l 25174 10756 l 25177 10771 l 25180 10785 l 25183 10800 l 25186 10815 l 25188 10829 l 25191 10843 l 25193 10856 l 25195 10870 l 25197 10884 l 25199 10898 l 25200 10914 l 25202 10929 l 25204 10946 l 25205 10963 l 25207 10981 l 25208 10998 l 25210 11016 l 25211 11033 l 25212 11049 l 25213 11065 l 25214 11080 l 25215 11095 l 25216 11110 l 25217 11125 l 25218 11140 l 25219 11155 l 25220 11171 l 25221 11187 l 25222 11204 l 25223 11220 l 25224 11235 l 25225 11250 l 25226 11265 l 25226 11279 l 25227 11292 l 25228 11305 l 25228 11320 l 25228 11335 l 25229 11351 l 25229 11367 l 25229 11383 l 25229 11400 l 25229 11417 l 25229 11433 l 25229 11449 l 25228 11465 l 25228 11480 l 25228 11495 l 25227 11508 l 25226 11521 l 25226 11535 l 25225 11549 l 25224 11564 l 25223 11580 l 25222 11596 l 25221 11612 l 25220 11627 l 25219 11643 l 25218 11658 l 25217 11672 l 25216 11686 l 25215 11700 l 25214 11714 l 25213 11728 l 25212 11742 l 25211 11757 l 25210 11773 l 25208 11788 l 25207 11804 l 25205 11820 l 25204 11836 l 25202 11851 l 25200 11865 l 25199 11879 l 25197 11892 l 25195 11905 l 25193 11920 l 25190 11935 l 25187 11950 l 25184 11966 l 25181 11982 l 25177 11998 l 25174 12014 l 25170 12029 l 25167 12044 l 25163 12057 l 25160 12070 l 25158 12083 l 25155 12094 l 25152 12107 l 25149 12119 l 25146 12132 l 25143 12145 l 25140 12158 l 25138 12171 l 25135 12184 l 25132 12197 l 25130 12210 l 25127 12223 l 25125 12235 l 25123 12248 l 25120 12261 l 25118 12276 l 25115 12291 l 25112 12307 l 25109 12323 l 25106 12340 l 25103 12356 l 25100 12372 l 25097 12387 l 25093 12401 l 25090 12415 l 25086 12429 l 25083 12443 l 25078 12457 l 25074 12471 l 25069 12486 l 25064 12501 l 25059 12515 l 25054 12529 l 25049 12542 l 25044 12555 l 25040 12566 l 25035 12578 l 25030 12588 l 25026 12599 l 25021 12610 l 25015 12621 l 25010 12633 l 25004 12644 l 24999 12656 l 24993 12667 l 24987 12678 l 24981 12688 l 24976 12698 l 24970 12708 l 24964 12717 l 24958 12727 l 24952 12738 l 24945 12749 l 24938 12760 l 24931 12772 l 24924 12783 l 24918 12794 l 24912 12805 l 24907 12814 l 24902 12824 l 24898 12833 l 24892 12845 l 24887 12858 l 24882 12871 l 24878 12883 l 24874 12895 l 24869 12905 l 24865 12914 l 24860 12923 l 24854 12930 l 24848 12937 l 24839 12945 l 24830 12952 l 24820 12959 l 24809 12966 l 24798 12973 l 24788 12980 l 24778 12986 l 24768 12992 l 24756 12999 l 24742 13008 l 24726 13018 l 24709 13029 l 24693 13039 l 24681 13046 l 24676 13049 l 24675 13050 l gs col-1 s gr [] 0 sd /Times-Italic ff 750.00 scf sf 24450 13725 m gs 1 -1 sc (c) col-1 sh gr /Symbol ff 750.00 scf sf 21975 15000 m gs 1 -1 sc (d) col-1 sh gr /Symbol ff 750.00 scf sf 21975 8175 m gs 1 -1 sc (a) col-1 sh gr /Symbol ff 750.00 scf sf 27150 8250 m gs 1 -1 sc (b) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 3350 3290 a FJ(:)1323 3831 y FP(Figure)32 b(5.17.)40 b FQ(Asso)r(ciativit)n(y)27 b(mo)n(v)n(e.)573 4857 y @beginspecial 0 @llx 0 @lly 69 @urx 70 @ury 690 @rwi @setspecial %%BeginDocument: figures/assmv1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: assmv1.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Jun 10 12:17:09 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 69 70 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2400 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -55.0 104.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8201 m -1000 -1000 l 9546 -1000 l 9546 8201 l cp clip 0.01440 0.01440 sc % Polyline n 5775 7200 m 6375 7200 l % Polyline 30.000 slw n 6949 5100 m 8149 5100 l 8149 5850 l 6949 5850 l cp gs col0 s gr /Symbol ff 600.00 scf sf 7275 5700 m gs 1 -1 sc (Y) col0 sh gr % Polyline n 4200 3000 m 4200 5070 l gs col0 s gr % Polyline gs clippath 5235 3513 m 5325 3081 l 5415 3513 l 5415 2955 l 5235 2955 l cp clip n 5325 3000 m 5325 5100 l gs col0 s gr gr % arrowhead n 5235 3513 m 5325 3081 l 5415 3513 l 5325 3441 l 5235 3513 l cp gs 0.00 setgray ef gr col0 s % Polyline n 4800 3000 m 4800 5070 l gs col0 s gr % Polyline gs clippath 7065 4587 m 6975 5019 l 6885 4587 l 6885 5145 l 7065 5145 l cp clip n 6975 5100 m 6975 3000 l gs col0 s gr gr % arrowhead n 7065 4587 m 6975 5019 l 6885 4587 l 6975 4659 l 7065 4587 l cp gs 0.00 setgray ef gr col0 s % Polyline n 4155 5085 m 5355 5085 l 5355 5835 l 4155 5835 l cp gs col0 s gr % Polyline n 7500 3000 m 7500 5070 l gs col0 s gr /Times-Italic ff 600.00 scf sf 8100 2850 m gs 1 -1 sc (D) col0 sh gr % Polyline n 8100 3000 m 8100 5070 l gs col0 s gr /Symbol ff 600.00 scf sf 4500 5655 m gs 1 -1 sc (F) col0 sh gr /Times-Italic ff 600.00 scf sf 3825 2850 m gs 1 -1 sc (A) col0 sh gr /Times-Italic ff 600.00 scf sf 4425 2850 m gs 1 -1 sc (B) col0 sh gr /Times-Italic ff 600.00 scf sf 5100 2850 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 6975 2850 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 7500 2850 m gs 1 -1 sc (C) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 1217 4566 a FL(!)1369 4857 y @beginspecial 0 @llx 0 @lly 69 @urx 70 @ury 690 @rwi @setspecial %%BeginDocument: figures/assmv2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: assmv2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Jun 10 12:18:08 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 69 70 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2400 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -55.0 104.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8201 m -1000 -1000 l 9546 -1000 l 9546 8201 l cp clip 0.01440 0.01440 sc % Arc 30.000 slw gs n 6150.0 5028.1 828.1 175.0 5.0 arc gs col0 s gr gr % Polyline 0.000 slw n 5400 7200 m 6150 7200 l /Symbol ff 600.00 scf sf 7275 5700 m gs 1 -1 sc (Y) col0 sh gr /Symbol ff 600.00 scf sf 4500 5655 m gs 1 -1 sc (F) col0 sh gr % Polyline 30.000 slw n 4200 3000 m 4200 5070 l gs col0 s gr % Polyline n 4800 3000 m 4800 5070 l gs col0 s gr % Polyline n 7500 3000 m 7500 5070 l gs col0 s gr % Polyline n 4155 5085 m 5355 5085 l 5355 5835 l 4155 5835 l cp gs col0 s gr % Polyline n 8100 3000 m 8100 5070 l gs col0 s gr /Times-Italic ff 600.00 scf sf 8100 2850 m gs 1 -1 sc (D) col0 sh gr % Polyline gs clippath 5937 4110 m 6369 4200 l 5937 4290 l 6495 4290 l 6495 4110 l cp clip n 6450 4200 m 6300 4200 l gs col0 s gr gr % arrowhead n 5937 4110 m 6369 4200 l 5937 4290 l 6009 4200 l 5937 4110 l cp gs 0.00 setgray ef gr col0 s % Polyline n 6949 5100 m 8149 5100 l 8149 5850 l 6949 5850 l cp gs col0 s gr /Times-Italic ff 600.00 scf sf 6075 3975 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 3825 2850 m gs 1 -1 sc (A) col0 sh gr /Times-Italic ff 600.00 scf sf 4425 2850 m gs 1 -1 sc (B) col0 sh gr /Times-Italic ff 600.00 scf sf 7500 2850 m gs 1 -1 sc (C) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 2014 4566 a(!)2166 4487 y Fy(X)2171 4665 y FI(j)s FE(2)p FI(I)2372 4509 y FQ(1)p 2309 4546 168 4 v 2309 4622 a FL(j)p FJ(I)7 b FL(j)p FJ(d)2441 4634 y FI(j)2533 4857 y @beginspecial 0 @llx 0 @lly 87 @urx 70 @ury 870 @rwi @setspecial %%BeginDocument: figures/assmv3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: assmv3.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Jun 10 12:21:25 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 87 70 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2400 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -43.0 104.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8201 m -1000 -1000 l 9985 -1000 l 9985 8201 l cp clip 0.01440 0.01440 sc % Polyline n 5475 7200 m 6150 7200 l % Polyline 30.000 slw gs clippath 4572 3515 m 4651 3080 l 4752 3511 l 4739 2953 l 4559 2957 l cp clip n 5100 3000 m 5100 3003 l 5100 3010 l 5100 3023 l 5099 3043 l 5099 3069 l 5099 3102 l 5098 3139 l 5097 3180 l 5096 3224 l 5095 3268 l 5094 3312 l 5092 3354 l 5090 3394 l 5089 3431 l 5087 3466 l 5085 3498 l 5082 3527 l 5080 3554 l 5077 3579 l 5074 3602 l 5070 3623 l 5067 3643 l 5063 3663 l 5056 3687 l 5050 3710 l 5042 3732 l 5034 3753 l 5025 3772 l 5015 3791 l 5005 3809 l 4994 3825 l 4982 3840 l 4970 3853 l 4958 3865 l 4946 3875 l 4934 3883 l 4922 3889 l 4910 3894 l 4898 3897 l 4886 3899 l 4875 3900 l 4864 3899 l 4852 3897 l 4840 3894 l 4828 3889 l 4816 3883 l 4804 3875 l 4792 3865 l 4780 3853 l 4768 3840 l 4756 3825 l 4745 3809 l 4735 3791 l 4725 3772 l 4716 3753 l 4708 3732 l 4700 3710 l 4694 3687 l 4688 3663 l 4683 3643 l 4680 3623 l 4676 3602 l 4673 3579 l 4670 3554 l 4668 3527 l 4665 3498 l 4663 3466 l 4661 3431 l 4660 3394 l 4658 3354 l 4656 3312 l 4655 3268 l 4654 3224 l 4653 3180 l 4652 3139 l 4651 3102 l 4651 3069 l 4651 3043 l 4650 3000 l gs col0 s gr gr % arrowhead n 4572 3515 m 4651 3080 l 4752 3511 l 4660 3441 l 4572 3515 l cp gs 0.00 setgray ef gr col0 s % Polyline n 3375 3000 m 3375 3002 l 3375 3007 l 3375 3015 l 3375 3028 l 3375 3047 l 3375 3072 l 3375 3102 l 3375 3139 l 3375 3181 l 3375 3228 l 3375 3280 l 3375 3334 l 3375 3392 l 3375 3450 l 3375 3510 l 3375 3569 l 3375 3628 l 3375 3685 l 3375 3741 l 3375 3794 l 3375 3845 l 3375 3894 l 3375 3941 l 3375 3985 l 3375 4027 l 3375 4066 l 3375 4104 l 3375 4140 l 3375 4173 l 3375 4206 l 3375 4237 l 3375 4266 l 3375 4295 l 3375 4323 l 3375 4350 l 3375 4384 l 3375 4417 l 3375 4450 l 3375 4482 l 3375 4513 l 3375 4545 l 3376 4576 l 3376 4608 l 3376 4639 l 3377 4670 l 3378 4701 l 3378 4732 l 3379 4762 l 3380 4793 l 3381 4823 l 3383 4854 l 3384 4883 l 3386 4913 l 3388 4942 l 3390 4971 l 3392 5000 l 3394 5029 l 3397 5057 l 3400 5085 l 3402 5114 l 3406 5142 l 3409 5171 l 3413 5200 l 3416 5226 l 3419 5253 l 3423 5280 l 3427 5308 l 3432 5337 l 3437 5367 l 3442 5397 l 3447 5429 l 3453 5461 l 3460 5493 l 3467 5527 l 3474 5561 l 3482 5595 l 3490 5630 l 3499 5665 l 3508 5700 l 3518 5735 l 3528 5770 l 3539 5805 l 3550 5839 l 3561 5873 l 3573 5907 l 3585 5939 l 3598 5971 l 3611 6003 l 3624 6033 l 3638 6063 l 3652 6092 l 3666 6120 l 3681 6147 l 3697 6174 l 3713 6200 l 3726 6222 l 3741 6243 l 3755 6264 l 3771 6284 l 3787 6305 l 3804 6325 l 3822 6346 l 3841 6366 l 3861 6386 l 3882 6405 l 3904 6425 l 3927 6444 l 3951 6464 l 3977 6483 l 4003 6501 l 4031 6519 l 4060 6537 l 4090 6555 l 4121 6572 l 4153 6589 l 4187 6605 l 4221 6621 l 4257 6636 l 4293 6651 l 4331 6665 l 4369 6679 l 4408 6692 l 4449 6705 l 4490 6716 l 4532 6728 l 4574 6739 l 4618 6749 l 4662 6759 l 4708 6768 l 4754 6776 l 4801 6785 l 4850 6793 l 4900 6800 l 4939 6805 l 4979 6811 l 5020 6816 l 5061 6820 l 5104 6825 l 5148 6829 l 5193 6834 l 5239 6838 l 5286 6841 l 5334 6845 l 5383 6848 l 5433 6852 l 5485 6855 l 5537 6857 l 5590 6860 l 5644 6862 l 5698 6864 l 5754 6866 l 5810 6868 l 5867 6869 l 5924 6870 l 5982 6871 l 6040 6872 l 6098 6872 l 6157 6872 l 6215 6872 l 6274 6872 l 6332 6871 l 6391 6870 l 6448 6869 l 6506 6868 l 6563 6866 l 6619 6864 l 6675 6862 l 6730 6860 l 6785 6857 l 6838 6855 l 6891 6852 l 6943 6848 l 6994 6845 l 7043 6841 l 7092 6838 l 7140 6834 l 7187 6829 l 7233 6825 l 7278 6820 l 7323 6816 l 7366 6811 l 7408 6805 l 7450 6800 l 7501 6793 l 7551 6786 l 7600 6778 l 7648 6769 l 7696 6761 l 7743 6751 l 7789 6742 l 7834 6731 l 7879 6720 l 7923 6709 l 7967 6697 l 8010 6684 l 8052 6671 l 8094 6656 l 8134 6642 l 8174 6626 l 8213 6610 l 8251 6594 l 8288 6576 l 8324 6558 l 8359 6540 l 8392 6521 l 8425 6501 l 8456 6481 l 8486 6460 l 8515 6439 l 8543 6418 l 8569 6396 l 8595 6373 l 8619 6350 l 8641 6327 l 8663 6304 l 8684 6280 l 8703 6255 l 8722 6231 l 8739 6205 l 8755 6180 l 8771 6154 l 8786 6127 l 8800 6100 l 8815 6069 l 8829 6037 l 8842 6004 l 8855 5971 l 8867 5936 l 8878 5900 l 8888 5863 l 8898 5825 l 8907 5786 l 8915 5746 l 8923 5706 l 8929 5665 l 8935 5623 l 8940 5580 l 8944 5537 l 8947 5494 l 8950 5450 l 8951 5407 l 8952 5364 l 8952 5321 l 8951 5278 l 8949 5236 l 8947 5194 l 8943 5154 l 8939 5114 l 8934 5075 l 8929 5037 l 8923 5001 l 8916 4965 l 8908 4931 l 8900 4898 l 8891 4866 l 8882 4835 l 8872 4806 l 8861 4777 l 8850 4750 l 8835 4716 l 8818 4684 l 8801 4654 l 8783 4624 l 8763 4596 l 8742 4570 l 8721 4544 l 8698 4520 l 8675 4496 l 8650 4475 l 8625 4454 l 8600 4435 l 8574 4418 l 8548 4402 l 8522 4387 l 8496 4375 l 8471 4363 l 8445 4353 l 8421 4345 l 8397 4338 l 8373 4332 l 8351 4328 l 8330 4324 l 8309 4323 l 8290 4322 l 8271 4322 l 8254 4323 l 8238 4325 l 8218 4329 l 8200 4334 l 8183 4341 l 8167 4349 l 8152 4358 l 8138 4369 l 8125 4381 l 8113 4395 l 8102 4410 l 8092 4425 l 8083 4442 l 8075 4460 l 8068 4478 l 8062 4497 l 8057 4516 l 8053 4536 l 8049 4555 l 8046 4574 l 8043 4593 l 8041 4612 l 8039 4631 l 8038 4650 l 8036 4671 l 8034 4692 l 8033 4713 l 8032 4735 l 8031 4759 l 8030 4784 l 8029 4811 l 8028 4840 l 8028 4871 l 8027 4904 l 8027 4938 l 8026 4971 l 8026 5003 l 8026 5033 l 8025 5057 l 8025 5076 l 8025 5089 l 8025 5097 l 8025 5100 l gs col0 s gr % Arc gs n 6150.0 5028.1 828.1 175.0 5.0 arc gs col0 s gr gr % Polyline n 6949 5100 m 8149 5100 l 8149 5850 l 6949 5850 l cp gs col0 s gr /Symbol ff 600.00 scf sf 7275 5700 m gs 1 -1 sc (Y) col0 sh gr % Polyline n 4200 3000 m 4200 5070 l gs col0 s gr % Polyline n 7500 3000 m 7500 5070 l gs col0 s gr % Polyline gs clippath 5937 4110 m 6369 4200 l 5937 4290 l 6495 4290 l 6495 4110 l cp clip n 6450 4200 m 6300 4200 l gs col0 s gr gr % arrowhead n 5937 4110 m 6369 4200 l 5937 4290 l 6009 4200 l 5937 4110 l cp gs 0.00 setgray ef gr col0 s % Polyline n 4155 5085 m 5355 5085 l 5355 5835 l 4155 5835 l cp gs col0 s gr /Symbol ff 600.00 scf sf 4500 5655 m gs 1 -1 sc (F) col0 sh gr % Polyline n 5775 3000 m 5775 3003 l 5775 3011 l 5775 3024 l 5774 3043 l 5773 3069 l 5772 3100 l 5771 3136 l 5770 3173 l 5768 3212 l 5766 3251 l 5764 3288 l 5762 3323 l 5759 3355 l 5756 3385 l 5753 3413 l 5750 3438 l 5746 3461 l 5741 3482 l 5736 3501 l 5731 3520 l 5725 3538 l 5718 3554 l 5711 3571 l 5703 3587 l 5695 3603 l 5685 3619 l 5675 3635 l 5663 3651 l 5651 3667 l 5638 3684 l 5624 3701 l 5609 3718 l 5594 3735 l 5578 3752 l 5561 3770 l 5544 3788 l 5526 3807 l 5508 3825 l 5490 3844 l 5471 3863 l 5452 3883 l 5432 3904 l 5413 3925 l 5396 3943 l 5380 3961 l 5362 3980 l 5345 4000 l 5326 4021 l 5308 4042 l 5288 4065 l 5269 4088 l 5248 4113 l 5228 4137 l 5207 4163 l 5186 4189 l 5165 4215 l 5144 4242 l 5124 4269 l 5103 4296 l 5084 4322 l 5064 4349 l 5045 4375 l 5027 4400 l 5010 4425 l 4994 4450 l 4978 4473 l 4963 4497 l 4949 4519 l 4936 4541 l 4924 4562 l 4913 4583 l 4899 4608 l 4887 4633 l 4876 4658 l 4866 4682 l 4857 4707 l 4849 4733 l 4842 4759 l 4835 4786 l 4830 4815 l 4824 4845 l 4819 4875 l 4815 4906 l 4811 4937 l 4808 4967 l 4806 4994 l 4804 5018 l 4802 5038 l 4801 5052 l 4800 5062 l 4800 5068 l 4800 5070 l gs col0 s gr /Times-Italic ff 600.00 scf sf 3000 2850 m gs 1 -1 sc (D) col0 sh gr /Times-Italic ff 600.00 scf sf 6075 3975 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 7500 2850 m gs 1 -1 sc (C) col0 sh gr /Times-Italic ff 600.00 scf sf 5850 2850 m gs 1 -1 sc (B) col0 sh gr /Times-Italic ff 600.00 scf sf 5325 2850 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 4500 2850 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 3825 2850 m gs 1 -1 sc (A) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 3304 4566 a FJ(:)1187 5058 y FP(Figure)32 b(5.18.)40 b FQ(Asso)r(ciativit)n(y)27 b(isomorphism.)p eop %%Page: 117 25 117 120 bop 1028 226 a FM(5.5.)29 b(MODULAR)g(CA)-5 b(TEGORIES)29 b(AND)g(MODULAR)g(FUNCTOR)451 b(117)515 425 y FK(5.5.)46 b(Mo)s(dular)31 b(categories)g(and)i(mo)s(dular)d(functor)i(for)h(zero) f(cen)m(tral)g(c)m(harge)605 575 y FQ(In)27 b(this)f(section,)g(w)n(e)g (will)h(sho)n(w,)e(dev)n(eloping)h(the)g(ideas)g(of)g(the)h(previous)e (section,)h(that)456 674 y(the)g(notion)h(of)f(a)g(mo)r(dular)g (functor)g(\(for)g(arbitrary)f(gen)n(us\))h(is)g(equiv)-5 b(alen)n(t)26 b(to)h(the)f(notion)h(of)456 774 y(a)d(mo)r(dular)g (tensor)g(category)-7 b(.)34 b(Recall)24 b(that)h(for)f(ev)n(ery)g(mo)r (dular)g(category)e(w)n(e)j(ha)n(v)n(e)e(de\014ned)456 874 y(the)28 b(n)n(um)n(b)r(ers)f FJ(p)976 843 y FE(\006)1059 874 y FQ(b)n(y)h(\(3.1.7\).)36 b(In)28 b(this)g(section)f(w)n(e)g (consider)g(the)h(sp)r(ecial)f(case)g(of)g(mo)r(dular)456 973 y(categories)k(with)k FJ(p)1083 943 y FM(+)1138 973 y FJ(=p)1222 943 y FE(\000)1311 973 y FQ(=)e(1.)55 b(\(F)-7 b(or)34 b(the)g(mo)r(dular)f(categories)f(coming)h(from)h(conformal)456 1073 y(\014eld)27 b(theory)g(this)h(iden)n(tit)n(y)g(holds)f(if)h(the)g (Virasoro)d(cen)n(tral)i(c)n(harge)e(of)j(the)g(theory)f(is)g(equal)456 1172 y(to)g(0)g(\(cf.)i(Remark)d(3.1.20\),)g(hence)i(the)g(title)g(of)g (this)g(section.\))605 1324 y FP(Theorem)k FQ(5.5.1)p FP(.)40 b FO(L)l(et)35 b FL(C)40 b FO(b)l(e)35 b(a)h(mo)l(dular)g (tensor)f(c)l(ate)l(gory)h(with)g FJ(p)2810 1293 y FM(+)2865 1324 y FJ(=p)2949 1293 y FE(\000)3038 1324 y FQ(=)d(1)p FO(.)55 b(Then)456 1423 y(ther)l(e)33 b(exists)f(a)h(unique)g FL(C)5 b FO(-extende)l(d)32 b(mo)l(dular)i(functor)e FJ(\034)43 b FO(which)34 b(satis\014es)g(c)l(onditions)40 b FQ(\(i\){)456 1523 y(\(iii\))27 b FO(of)i(The)l(or)l(em)f FQ(5.4.1)p FO(.)36 b(This)29 b(MF)e(is)h(non-de)l(gener)l(ate)f(and)h (satis\014es)f(c)l(onditions)35 b FQ(\(iv\),)26 b(\(v\))456 1623 y FO(of)k(The)l(or)l(em)h FQ(5.4.1)d FO(and)j(c)l(ondition)37 b FQ(\(vi\))30 b FO(b)l(elow.)605 1722 y FQ(\(vi\))g FO(L)l(et)g FJ(S)961 1734 y FM(1)p FI(;)p FM(1)1080 1722 y FO(b)l(e)g(the)g(torus)f(with)h(one)g(hole.)40 b(Identify)1012 1879 y FJ(\034)9 b FQ(\()p FJ(S)1140 1891 y FM(1)p FI(;)p FM(1)1231 1879 y FQ(;)14 b FJ(A)p FQ(\))24 b(=)1473 1800 y Fy(M)1599 1879 y FL(h)p FJ(A;)14 b(V)1778 1891 y FI(i)1806 1879 y FJ(;)g(V)1910 1845 y FE(\003)1891 1900 y FI(i)1948 1879 y FL(i)23 b FQ(=)2091 1800 y Fy(M)2230 1879 y FQ(Hom\()p FJ(A)2497 1845 y FE(\003)2536 1879 y FJ(;)14 b(V)2621 1891 y FI(i)2668 1879 y FL(\012)k FJ(V)2817 1845 y FE(\003)2799 1900 y FI(i)2856 1879 y FQ(\))456 2029 y FO(using)32 b(the)g(p)l(ar)l(ameterization)i(of)f FJ(S)1605 2041 y FM(1)p FI(;)p FM(1)1727 2029 y FO(shown)g(in)f(Figur)l(e)h FQ(5.12)p FO(.)44 b(L)l(et)32 b FJ(s)9 b FQ(:)29 b FJ(S)2863 2041 y FM(1)p FI(;)p FM(1)2980 2029 y FL(!)f FJ(S)3142 2041 y FM(1)p FI(;)p FM(1)3264 2029 y FO(b)l(e)k(as)456 2129 y(de\014ne)l(d)e(in)36 b FQ(\(5.1.5\))o FO(.)j(Then)30 b(the)g(c)l(orr)l(esp)l(onding)930 2283 y FJ(s)969 2295 y FE(\003)1030 2283 y FQ(=)23 b FJ(S)14 b FQ(:)1247 2204 y Fy(M)1387 2283 y FQ(Hom\()p FJ(A)1654 2249 y FE(\003)1692 2283 y FJ(;)g(V)1777 2295 y FI(i)1824 2283 y FL(\012)k FJ(V)1974 2249 y FE(\003)1955 2303 y FI(i)2012 2283 y FQ(\))23 b FL(!)2173 2204 y Fy(M)2312 2283 y FQ(Hom\()p FJ(A)2579 2249 y FE(\003)2618 2283 y FJ(;)14 b(V)2703 2295 y FI(i)2750 2283 y FL(\012)k FJ(V)2899 2249 y FE(\003)2881 2303 y FI(i)2938 2283 y FQ(\))-2514 b(\(5.5.1\))456 2432 y FO(is)30 b(given)g(by)g(The)l(or)l(em)h FQ(3.1.17)p FO(.)605 2532 y(Conversely,)25 b(let)d FL(C)k FO(b)l(e)c(a)g (semisimple)h(ab)l(elian)h(c)l(ate)l(gory,)g(and)e(let)g FJ(\034)31 b FO(b)l(e)22 b(a)g(non-de)l(gener)l(ate)456 2632 y FL(C)5 b FO(-extende)l(d)20 b(MF.)i(Assume)f(for)h(simplicity)h (that)e(the)h(c)l(orr)l(esp)l(onding)g(structur)l(e)e(of)i(a)g (monoidal)456 2731 y(c)l(ate)l(gory)35 b(on)g FL(C)k FQ(\()p FO(se)l(e)c(The)l(or)l(em)h FQ(5.4.1\))d FO(is)i(rigid.)55 b(Then)35 b FL(C)40 b FO(is)35 b(a)g(mo)l(dular)g(tensor)g(c)l(ate)l (gory)456 2831 y(with)30 b FJ(p)678 2801 y FM(+)756 2831 y FQ(=)23 b FJ(p)886 2801 y FE(\000)941 2831 y FO(;)31 b(in)e(p)l(articular,)j(it)d(has)i(only)f(a)g(\014nite)g(numb)l(er)f (of)h(simple)h(obje)l(cts.)605 2982 y FP(Pr)n(oof.)41 b FQ(Assume)21 b(that)g FL(C)k FQ(is)c(a)f(mo)r(dular)h(category)-7 b(.)32 b(By)21 b(Theorem)f(5.4.1,)h(the)g(structure)456 3082 y(of)32 b(a)g(mo)r(dular)f(category)f(on)i FL(C)37 b FQ(de\014nes)32 b(a)g(gen)n(us)g(zero)f(MF.)h(Therefore,)h(w)n(e)e (only)h(need)h(to)456 3181 y(sho)n(w)k(that)i(this)f(MF)h(can)f(b)r(e)h (extended)f(to)g(p)r(ositiv)n(e)g(gen)n(us.)69 b(In)38 b(order)f(to)h(do)g(this,)k(b)n(y)456 3284 y(Theorem)34 b(5.2.9,)h(w)n(e)g(need)g(to)f(de\014ne)h(an)g(isomorphism)f FJ(S)14 b FQ(:)30 b FJ(\034)9 b FQ(\()p FJ(S)2592 3296 y FM(1)p FI(;)p FM(1)2683 3284 y FJ(;)14 b(M)9 b FQ(\))2905 3237 y FE(\030)2877 3284 y FL(\000)-40 b(!)35 b FJ(\034)9 b FQ(\()p FJ(S)3148 3296 y FM(1)p FI(;)p FM(1)3239 3284 y FJ(;)14 b(M)3366 3253 y FE(0)3389 3284 y FQ(\),)456 3383 y(where)34 b FJ(S)754 3395 y FM(1)p FI(;)p FM(1)880 3383 y FQ(is)h(the)h(standard)e(torus)h(and)g FJ(M)t(;)14 b(M)2078 3353 y FE(0)2136 3383 y FQ(are)35 b(the)g(parameterizations)f (sho)n(wn)g(in)456 3483 y(Figure)27 b(5.12,)f(and)h(then)h(c)n(hec)n(k) f(that)h(relations)e(MF8,)i(MF9)f(are)g(satis\014ed.)605 3582 y(Note)h(that)g(b)n(y)f(de\014nition)916 3732 y FJ(\034)9 b FQ(\()p FJ(S)1044 3744 y FM(1)p FI(;)p FM(1)1135 3732 y FJ(;)14 b(M)9 b FQ(;)14 b FJ(A)p FQ(\))23 b(=)f FJ(\034)9 b FQ(\()p FJ(S)1631 3744 y FM(1)p FI(;)p FM(1)1722 3732 y FJ(;)14 b(M)1849 3698 y FE(0)1872 3732 y FQ(;)g FJ(A)p FQ(\))23 b(=)2114 3653 y Fy(M)2165 3830 y FI(i)2240 3732 y FL(h)p FJ(A;)14 b(V)2419 3744 y FI(i)2447 3732 y FJ(;)g(V)2551 3698 y FE(\003)2532 3753 y FI(i)2589 3732 y FL(i)23 b FQ(=)g(Hom\()p FJ(A)2999 3698 y FE(\003)3038 3732 y FJ(;)14 b(H)7 b FQ(\))p FJ(;)456 3962 y FQ(where,)23 b(as)e(b)r(efore,)i FJ(H)30 b FQ(=)1266 3900 y Fy(L)1372 3962 y FJ(V)1420 3974 y FI(i)1456 3962 y FL(\012)8 b FJ(V)1595 3932 y FE(\003)1577 3984 y FI(i)1633 3962 y FQ(.)36 b(Th)n(us,)23 b(de\014ning)f(an)g(isomorphism)f FJ(S)14 b FQ(:)28 b FJ(\034)9 b FQ(\()p FJ(S)3063 3974 y FM(1)p FI(;)p FM(1)3154 3962 y FJ(;)14 b(M)9 b FQ(\))3364 3915 y FE(\030)3336 3962 y FL(\000)-40 b(!)456 4072 y FJ(\034)9 b FQ(\()p FJ(S)584 4084 y FM(1)p FI(;)p FM(1)675 4072 y FJ(;)14 b(M)802 4042 y FE(0)824 4072 y FQ(\))19 b(is)f(the)h(same)f(as)g(de\014ning)g(a)g(functorial)g(system)g(of)g (isomorphisms)f(Hom\()p FJ(A)3233 4042 y FE(\003)3272 4072 y FJ(;)d(H)7 b FQ(\))3468 4025 y FE(\030)3440 4072 y FL(\000)-39 b(!)456 4172 y FQ(Hom\()p FJ(A)723 4142 y FE(\003)761 4172 y FJ(;)14 b(H)7 b FQ(\))31 b(for)e(ev)n(ery)g(ob)5 b(ject)30 b FJ(A)p FQ(.)45 b(By)30 b(Lemma)g(5.3.1,)g(this)h(is)f(the)g (same)g(as)f(de\014ning)i(an)456 4271 y(isomorphism)26 b FJ(S)14 b FQ(:)28 b FJ(H)i FL(!)23 b FJ(H)7 b FQ(.)605 4371 y(Let)30 b(us)f(\014rst)h(sho)n(w)f(that)g(if)i(w)n(e)e(de\014ne)h FJ(S)k FQ(as)29 b(in)h(the)g(statemen)n(t)g(of)f(the)h(theorem,)g(then) 456 4471 y(relations)g(MF8,)j(MF9)f(are)f(satis\014ed.)49 b(Relations)32 b(MF8)f(immediately)i(follo)n(w)e(from)g(Theo-)456 4570 y(rem)c(3.1.17)f(and)h(the)h(assumption)f FJ(p)1647 4540 y FM(+)1725 4570 y FQ(=)c FJ(p)1855 4540 y FE(\000)1911 4570 y FQ(.)605 4670 y(T)-7 b(o)28 b(c)n(hec)n(k)g(relation)g(MF9)g (for)g(a)h(torus)e(with)j(t)n(w)n(o)d(holes,)i(let)g(us)f(rewrite)g(it) h(in)g(terms)g(of)456 4769 y(tensor)d(categories.)2450 b Fq(?!)605 4921 y FP(Lemma)31 b FQ(5.5.2)p FP(.)40 b FO(L)l(et)25 b FL(C)30 b FO(b)l(e)25 b(a)h(semisimple)h(ribb)l(on)f(c)l (ate)l(gory)g(with)g(\014nite)f(numb)l(er)f(of)i(sim-)456 5020 y(ple)k(obje)l(cts,)h(and)f(let)g FJ(S)k FO(b)l(e)c(an)g (isomorphism)1204 5170 y FJ(S)e FQ(=)1370 5091 y Fy(M)1510 5170 y FJ(S)1561 5182 y FI(j)s(i)1628 5170 y FQ(:)1693 5091 y Fy(M)1832 5170 y FJ(V)1880 5182 y FI(i)1927 5170 y FL(\012)18 b FJ(V)2076 5136 y FE(\003)2058 5190 y FI(i)2138 5170 y FL(!)2244 5091 y Fy(M)2383 5170 y FJ(V)2431 5182 y FI(j)2485 5170 y FL(\012)g FJ(V)2635 5136 y FE(\003)2616 5190 y FI(j)2673 5170 y FJ(:)-2240 b FQ(\(5.5.2\))p eop %%Page: 118 26 118 121 bop 456 226 a FM(118)1010 b(5.)29 b(MODULAR)g(FUNCTOR)456 425 y FO(Then)h(r)l(elation)37 b FQ(MF9)29 b FO(for)i FJ(S)j FO(is)c(e)l(quivalent)h(to)e(the)h(fol)t(lowing)i(c)l(ondition)p FQ(:)1336 1315 y @beginspecial 0 @llx 0 @lly 61 @urx 97 @ury 610 @rwi @setspecial %%BeginDocument: figures/g1n2a.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2a.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Jun 10 16:45:04 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 61 97 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2800 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -56.0 121.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8201 m -1000 -1000 l 7919 -1000 l 7919 8201 l cp clip 0.01680 0.01680 sc % Polyline n 3675 7200 m 4275 7200 l % Polyline 30.000 slw n 4684 3810 m 6034 3810 l 6034 4890 l 4684 4890 l cp gs col0 s gr % Polyline n 5775 1515 m 5775 2385 l gs col0 s gr % Polyline gs clippath 5850 3282 m 5760 3714 l 5670 3282 l 5670 3840 l 5850 3840 l cp clip n 5760 2625 m 5760 3795 l gs col0 s gr gr % arrowhead n 5850 3282 m 5760 3714 l 5670 3282 l 5760 3354 l 5850 3282 l cp gs 0.00 setgray ef gr col0 s /Times-Italic ff 450.00 scf sf 5400 4650 m gs 1 -1 sc (kj) col0 sh gr % Polyline gs clippath 5899 6087 m 5809 6519 l 5719 6087 l 5719 6645 l 5899 6645 l cp clip n 5809 4890 m 5809 6600 l gs col0 s gr gr % arrowhead n 5899 6087 m 5809 6519 l 5719 6087 l 5809 6159 l 5899 6087 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 4788 5418 m 4878 4985 l 4968 5418 l 4969 4860 l 4789 4860 l cp clip n 4879 4905 m 4875 6600 l gs col0 s gr gr % arrowhead n 4788 5418 m 4878 4985 l 4968 5418 l 4878 5346 l 4788 5418 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 3810 5538 m 3900 5106 l 3990 5538 l 3990 4980 l 3810 4980 l cp clip n 3900 5025 m 3900 5175 l gs col0 s gr gr % arrowhead n 3810 5538 m 3900 5106 l 3990 5538 l 3900 5466 l 3810 5538 l cp gs 0.00 setgray ef gr col0 s /Times-Italic ff 600.00 scf sf 5089 4500 m gs 1 -1 sc (S) col0 sh gr % Polyline gs clippath 4695 2013 m 4785 1581 l 4875 2013 l 4875 1455 l 4695 1455 l cp clip n 4785 1500 m 4785 3825 l gs col0 s gr gr % arrowhead n 4695 2013 m 4785 1581 l 4875 2013 l 4785 1941 l 4695 2013 l cp gs 0.00 setgray ef gr col0 s /Times-Italic ff 600.00 scf sf 3375 6450 m gs 1 -1 sc (i) col0 sh gr % Polyline n 4890 2895 m 4891 2894 l 4894 2893 l 4899 2891 l 4908 2887 l 4920 2881 l 4936 2873 l 4956 2864 l 4980 2852 l 5010 2838 l 5043 2822 l 5082 2803 l 5124 2783 l 5170 2761 l 5219 2737 l 5271 2712 l 5325 2685 l 5381 2658 l 5438 2630 l 5495 2602 l 5553 2573 l 5610 2545 l 5666 2517 l 5720 2489 l 5774 2462 l 5825 2435 l 5874 2409 l 5920 2384 l 5964 2360 l 6006 2337 l 6045 2315 l 6082 2293 l 6116 2272 l 6148 2252 l 6177 2232 l 6205 2213 l 6231 2194 l 6255 2175 l 6286 2150 l 6314 2124 l 6341 2097 l 6366 2070 l 6390 2041 l 6412 2011 l 6434 1980 l 6455 1947 l 6475 1913 l 6495 1877 l 6514 1840 l 6533 1803 l 6551 1765 l 6568 1728 l 6585 1691 l 6600 1655 l 6614 1622 l 6627 1591 l 6638 1563 l 6648 1539 l 6656 1519 l 6663 1502 l 6668 1489 l 6671 1480 l 6673 1475 l 6674 1471 l 6675 1470 l gs col0 s gr % Polyline n 3900 6600 m 3900 6598 l 3900 6593 l 3900 6585 l 3900 6572 l 3900 6553 l 3900 6528 l 3900 6498 l 3900 6461 l 3900 6418 l 3901 6371 l 3901 6320 l 3901 6265 l 3901 6207 l 3901 6148 l 3902 6088 l 3902 6029 l 3902 5970 l 3902 5912 l 3903 5856 l 3903 5802 l 3904 5750 l 3904 5701 l 3904 5654 l 3905 5609 l 3905 5567 l 3906 5527 l 3906 5488 l 3907 5452 l 3908 5417 l 3908 5384 l 3909 5352 l 3910 5322 l 3911 5292 l 3912 5263 l 3913 5235 l 3914 5200 l 3915 5165 l 3917 5131 l 3918 5097 l 3920 5063 l 3922 5030 l 3924 4997 l 3926 4964 l 3928 4931 l 3930 4899 l 3933 4866 l 3936 4834 l 3938 4803 l 3941 4771 l 3944 4740 l 3947 4710 l 3951 4681 l 3954 4651 l 3957 4623 l 3961 4595 l 3964 4568 l 3968 4542 l 3971 4516 l 3975 4491 l 3979 4466 l 3982 4441 l 3986 4417 l 3990 4393 l 3994 4366 l 3999 4340 l 4003 4313 l 4008 4285 l 4014 4257 l 4019 4228 l 4025 4199 l 4031 4169 l 4038 4139 l 4044 4108 l 4052 4077 l 4059 4046 l 4067 4014 l 4075 3983 l 4084 3952 l 4093 3921 l 4102 3891 l 4111 3861 l 4121 3831 l 4131 3803 l 4141 3775 l 4151 3748 l 4162 3721 l 4172 3695 l 4184 3670 l 4195 3645 l 4207 3620 l 4219 3596 l 4232 3571 l 4246 3546 l 4261 3520 l 4277 3494 l 4295 3467 l 4313 3438 l 4333 3408 l 4355 3376 l 4378 3343 l 4403 3309 l 4429 3273 l 4455 3237 l 4482 3200 l 4509 3165 l 4535 3131 l 4559 3099 l 4580 3071 l 4598 3048 l 4612 3030 l 4623 3016 l 4630 3007 l 4633 3002 l 4635 3000 l gs col0 s gr /Times-Italic ff 600.00 scf sf 4275 2025 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 5925 2025 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 6750 2025 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 4425 6450 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 6075 6450 m gs 1 -1 sc (j) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 1914 910 a(=)2047 1315 y @beginspecial 0 @llx 0 @lly 62 @urx 97 @ury 620 @rwi @setspecial %%BeginDocument: figures/g1n2b.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2b.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Jun 10 16:44:14 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 62 97 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2800 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -25.0 121.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8201 m -1000 -1000 l 6133 -1000 l 6133 8201 l cp clip 0.01680 0.01680 sc % Polyline n 2775 7200 m 3450 7200 l % Polyline 30.000 slw n 5100 6600 m 5100 6597 l 5100 6591 l 5100 6581 l 5100 6564 l 5100 6542 l 5100 6515 l 5100 6483 l 5100 6448 l 5100 6411 l 5100 6372 l 5100 6334 l 5100 6297 l 5100 6261 l 5100 6226 l 5100 6194 l 5100 6163 l 5100 6133 l 5100 6105 l 5100 6078 l 5100 6052 l 5100 6026 l 5100 6001 l 5100 5975 l 5100 5949 l 5100 5923 l 5100 5896 l 5100 5869 l 5099 5840 l 5099 5812 l 5098 5783 l 5097 5753 l 5096 5723 l 5095 5693 l 5093 5662 l 5091 5632 l 5089 5602 l 5086 5572 l 5083 5543 l 5080 5515 l 5076 5488 l 5072 5462 l 5067 5436 l 5062 5412 l 5057 5389 l 5051 5367 l 5044 5345 l 5038 5325 l 5029 5304 l 5020 5283 l 5010 5263 l 4999 5243 l 4987 5223 l 4973 5203 l 4957 5182 l 4940 5161 l 4921 5139 l 4900 5117 l 4878 5094 l 4855 5070 l 4831 5048 l 4808 5026 l 4787 5005 l 4767 4988 l 4752 4974 l 4740 4963 l 4732 4956 l 4727 4952 l 4725 4950 l gs col0 s gr % Polyline n 3000 4950 m 3000 4953 l 3000 4961 l 3001 4974 l 3001 4993 l 3002 5018 l 3004 5049 l 3005 5084 l 3008 5121 l 3010 5159 l 3013 5196 l 3016 5232 l 3020 5266 l 3024 5297 l 3028 5326 l 3033 5352 l 3038 5375 l 3044 5396 l 3051 5415 l 3058 5432 l 3066 5448 l 3075 5463 l 3086 5477 l 3098 5491 l 3112 5504 l 3127 5516 l 3144 5527 l 3164 5538 l 3186 5548 l 3211 5558 l 3238 5568 l 3267 5577 l 3297 5586 l 3328 5595 l 3358 5603 l 3386 5610 l 3409 5616 l 3427 5620 l 3440 5623 l 3447 5624 l 3450 5625 l gs col0 s gr % Polyline n 1830 3825 m 3180 3825 l 3180 4905 l 1830 4905 l cp gs col0 s gr % Polyline gs clippath 1980 2013 m 2070 1581 l 2160 2013 l 2160 1455 l 1980 1455 l cp clip n 2070 1500 m 2070 3825 l gs col0 s gr gr % arrowhead n 1980 2013 m 2070 1581 l 2160 2013 l 2070 1941 l 1980 2013 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 1980 5448 m 2070 5016 l 2160 5448 l 2160 4890 l 1980 4890 l cp clip n 2070 4935 m 2070 6600 l gs col0 s gr gr % arrowhead n 1980 5448 m 2070 5016 l 2160 5448 l 2070 5376 l 1980 5448 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 3015 3312 m 2925 3744 l 2835 3312 l 2835 3870 l 3015 3870 l cp clip n 2925 3825 m 2925 1500 l gs col0 s gr gr % arrowhead n 3015 3312 m 2925 3744 l 2835 3312 l 2925 3384 l 3015 3312 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 5190 6087 m 5100 6519 l 5010 6087 l 5010 6645 l 5190 6645 l cp clip n 5100 6225 m 5100 6600 l gs col0 s gr gr % arrowhead n 5190 6087 m 5100 6519 l 5010 6087 l 5100 6159 l 5190 6087 l cp gs 0.00 setgray ef gr col0 s /Times-Italic ff 600.00 scf sf 2160 4515 m gs 1 -1 sc (S) col0 sh gr % Polyline gs clippath 4560 2013 m 4650 1581 l 4740 2013 l 4740 1455 l 4560 1455 l cp clip n 3750 5700 m 3751 5700 l 3755 5700 l 3765 5700 l 3781 5700 l 3803 5700 l 3827 5700 l 3853 5700 l 3878 5699 l 3902 5699 l 3924 5699 l 3945 5699 l 3965 5698 l 3985 5698 l 4005 5698 l 4021 5697 l 4038 5697 l 4056 5696 l 4075 5695 l 4094 5693 l 4114 5691 l 4135 5688 l 4156 5685 l 4177 5681 l 4198 5676 l 4219 5670 l 4239 5663 l 4259 5655 l 4278 5647 l 4296 5637 l 4313 5627 l 4329 5615 l 4345 5603 l 4357 5591 l 4369 5579 l 4381 5565 l 4393 5550 l 4404 5534 l 4416 5516 l 4427 5496 l 4438 5476 l 4449 5453 l 4460 5429 l 4470 5404 l 4480 5378 l 4489 5351 l 4498 5322 l 4507 5293 l 4515 5264 l 4523 5233 l 4530 5202 l 4537 5171 l 4543 5139 l 4549 5106 l 4555 5073 l 4559 5049 l 4563 5024 l 4566 4999 l 4570 4973 l 4573 4947 l 4577 4919 l 4580 4890 l 4584 4860 l 4587 4830 l 4590 4798 l 4593 4765 l 4596 4732 l 4599 4697 l 4602 4662 l 4605 4626 l 4608 4590 l 4611 4553 l 4613 4515 l 4616 4477 l 4618 4439 l 4620 4401 l 4622 4363 l 4624 4325 l 4626 4287 l 4628 4249 l 4630 4212 l 4631 4174 l 4633 4137 l 4634 4099 l 4635 4062 l 4636 4025 l 4638 3988 l 4638 3954 l 4639 3920 l 4640 3886 l 4641 3851 l 4642 3815 l 4642 3779 l 4643 3742 l 4644 3705 l 4644 3667 l 4645 3628 l 4645 3589 l 4646 3549 l 4646 3508 l 4647 3468 l 4647 3426 l 4648 3385 l 4648 3343 l 4648 3302 l 4649 3260 l 4649 3219 l 4649 3177 l 4649 3136 l 4649 3096 l 4649 3056 l 4650 3016 l 4650 2977 l 4650 2939 l 4650 2902 l 4650 2865 l 4650 2829 l 4650 2793 l 4650 2758 l 4650 2724 l 4650 2691 l 4650 2658 l 4650 2625 l 4650 2589 l 4650 2553 l 4650 2517 l 4650 2481 l 4650 2444 l 4650 2408 l 4650 2370 l 4650 2331 l 4650 2292 l 4650 2250 l 4650 2208 l 4650 2163 l 4650 2117 l 4650 2070 l 4650 2021 l 4650 1971 l 4650 1920 l 4650 1868 l 4650 1818 l 4650 1768 l 4650 1721 l 4650 1677 l 4650 1637 l 4650 1602 l 4650 1572 l 4650 1547 l 4650 1529 l 4650 1500 l gs col0 s gr gr % arrowhead n 4560 2013 m 4650 1581 l 4740 2013 l 4650 1941 l 4560 2013 l cp gs 0.00 setgray ef gr col0 s /Times-Italic ff 450.00 scf sf 2475 4650 m gs 1 -1 sc (ki) col0 sh gr % Polyline n 4425 4875 m 4422 4876 l 4414 4877 l 4401 4879 l 4382 4882 l 4356 4886 l 4325 4892 l 4290 4898 l 4252 4905 l 4213 4912 l 4175 4920 l 4138 4928 l 4104 4936 l 4071 4945 l 4042 4953 l 4015 4962 l 3990 4971 l 3967 4980 l 3947 4989 l 3927 5000 l 3909 5011 l 3893 5023 l 3878 5034 l 3863 5046 l 3849 5060 l 3836 5074 l 3822 5089 l 3810 5106 l 3797 5123 l 3785 5142 l 3773 5162 l 3761 5183 l 3750 5206 l 3740 5229 l 3729 5254 l 3720 5279 l 3711 5305 l 3702 5332 l 3694 5359 l 3686 5386 l 3679 5415 l 3673 5443 l 3667 5472 l 3661 5502 l 3655 5532 l 3650 5563 l 3646 5586 l 3642 5611 l 3639 5636 l 3635 5662 l 3632 5689 l 3628 5718 l 3625 5748 l 3621 5781 l 3618 5815 l 3614 5851 l 3611 5889 l 3607 5929 l 3603 5972 l 3599 6017 l 3595 6064 l 3591 6112 l 3587 6162 l 3583 6213 l 3579 6263 l 3575 6312 l 3572 6360 l 3568 6404 l 3565 6445 l 3563 6481 l 3560 6511 l 3559 6536 l 3557 6556 l 3556 6569 l 3555 6578 l 3555 6583 l 3555 6585 l gs col0 s gr /Times-Italic ff 600.00 scf sf 1650 6450 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 3105 1935 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 1500 1935 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 4950 1950 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 4650 6450 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 3150 6450 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 2700 5550 m gs 1 -1 sc (i) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 456 910 a(\(5.5.3\))456 1437 y FO(for)e(every)h FJ(i;)14 b(j;)g(k)25 b FL(2)f FJ(I)7 b FO(.)605 1599 y FQ(The)28 b(pro)r(of)f(of)g(this)h(lemma)g(will)f(b)r(e)h(giv)n(en)f (after)h(the)g(pro)r(of)f(of)g(the)h(theorem.)605 1699 y(It)g(is)f(easy)g(to)h(c)n(hec)n(k)e(that)i(the)g(op)r(erator)e FJ(S)32 b FQ(de\014ned)c(b)n(y)h(\(3.1.32\))d(satis\014es)h(\(5.5.3\))o (.)605 1798 y(No)n(w,)39 b(let)e(us)g(pro)n(v)n(e)e(uniqueness.)65 b(Assume)37 b(that)g(w)n(e)g(ha)n(v)n(e)f(de\014ned)h(an)g(op)r(erator) e FJ(S)456 1898 y FQ(of)e(the)i(form)e(\(5.5.2\))g(suc)n(h)g(that)i (relations)d(MF8,)j(MF9)f(are)f(satis\014ed.)55 b(Rewrite)33 b(relation)456 1997 y(MF9)i(in)h(the)g(form)f(\(5.5.3\))o(,)j(put)e FJ(j)41 b FQ(=)36 b(0)f(and)g(note)h(that)g FJ(S)2433 2009 y FI(k)q FM(0)2516 1997 y FQ(:)30 b FK(1)36 b FL(!)g FJ(V)2820 2009 y FI(k)2885 1997 y FL(\012)24 b FJ(V)3041 1967 y FE(\003)3022 2021 y FI(k)3114 1997 y FQ(is)36 b(a)f(non-)456 2097 y(zero)g(m)n(ultiple)j(of)f FJ(i)1108 2109 y FI(V)1147 2118 y FG(k)1187 2097 y FQ(.)65 b(This)36 b(immediately)h(implies)h(that)f FJ(S)2487 2109 y FI(k)q(i)2589 2097 y FQ(=)h FJ(a)2736 2109 y FI(k)2777 2097 y FJ(S)2833 2067 y FM(st)2828 2121 y FI(k)q(i)2929 2097 y FQ(for)f(some)f(non-)456 2197 y(zero)f(constan)n(t)h FJ(a)1028 2209 y FI(k)1068 2197 y FQ(,)j(where)d(w)n(e)g(temp)r(orarily)f(denoted)i(b)n(y)f FJ(S)2474 2167 y FM(st)2566 2197 y FQ(the)h(op)r(erator)e(de\014ned)i (b)n(y)456 2296 y(\(3.1.32\))n(.)48 b(Equiv)-5 b(alen)n(tly)e(,)32 b(w)n(e)f(can)g(write)g FJ(S)j FQ(=)29 b FJ(AS)2100 2266 y FM(st)2156 2296 y FQ(,)k(where)d(the)i(op)r(erator)e FJ(A)9 b FQ(:)29 b FJ(H)36 b FL(!)29 b FJ(H)39 b FQ(is)456 2396 y(\\diagonal":)30 b FJ(A)p FL(j)984 2408 y FI(V)1023 2416 y FG(i)1050 2408 y FE(\012)p FI(V)1155 2388 y Fx(\003)1141 2427 y FG(i)1217 2396 y FQ(=)23 b FJ(a)1349 2408 y FI(i)1390 2396 y FQ(id.)35 b(No)n(w,)20 b(let)g(us)g(use)f(the)h(axiom)f(MF8.)34 b(In)20 b(particular,)f(w)n(e)h(ha)n(v)n(e)456 2502 y FJ(T)12 b(S)5 b(T)12 b(S)5 b(T)31 b FQ(=)23 b FJ(S)5 b FQ(.)35 b(Since)22 b FJ(S)27 b FQ(=)c FJ(AS)1467 2471 y FM(st)1523 2502 y FQ(,)g(and)f FJ(A)g FQ(comm)n(utes)g(with)g FJ(T)12 b FQ(,)22 b(w)n(e)f(get)h FJ(T)12 b(S)2849 2471 y FM(st)2904 2502 y FJ(T)g(AS)3083 2471 y FM(st)3139 2502 y FJ(T)34 b FQ(=)22 b FJ(S)3365 2471 y FM(st)3421 2502 y FQ(.)456 2601 y(On)41 b(the)g(other)g(hand,)j(the)e(op)r(erator) d FJ(S)1803 2571 y FM(st)1901 2601 y FQ(itself)i(satis\014es)g(the)g (axiom)g(MF8,)j(and)d(th)n(us,)456 2701 y FJ(T)12 b(S)573 2671 y FM(st)628 2701 y FJ(T)g(S)745 2671 y FM(st)800 2701 y FJ(T)34 b FQ(=)23 b FJ(S)1027 2671 y FM(st)1083 2701 y FQ(.)37 b(This)27 b(implies)h FJ(A)23 b FQ(=)g(id)p FJ(;)14 b(S)28 b FQ(=)22 b FJ(S)2115 2671 y FM(st)2172 2701 y FQ(.)605 2800 y(The)27 b(pro)r(of)f(of)g(the)h(con)n(v)n(erse)e (statemen)n(t|that)i(a)f(MF)h(de\014nes)g(a)f(structure)g(of)g(a)h(mo)r (d-)456 2900 y(ular)d(category|is)f(trivial.)36 b(Indeed,)26 b(the)f(iden)n(tit)n(y)h FJ(\034)9 b FQ(\(\006\))24 b(=)2391 2838 y Fy(L)2497 2900 y FQ(End)13 b FJ(V)2707 2912 y FI(i)2761 2900 y FQ(for)25 b(\006)g(b)r(eing)g(a)g(torus)456 3000 y(without)g(punctures)h(implies)g(that)f FL(C)30 b FQ(has)25 b(only)g(\014nitely)h(man)n(y)f(simple)h(ob)5 b(jects)25 b(\(since)g FJ(\034)9 b FQ(\(\006\))456 3099 y(is)32 b(\014nite)h(dimensional\).)51 b(Th)n(us,)33 b(w)n(e)f(only)g(ha)n(v)n(e)g(to)g(c)n(hec)n(k)f(that)i(the)g(matrix)i (~)-45 b FJ(s)p FQ(,)33 b(de\014ned)g(in)456 3199 y(\(3.1.1\))o(,)k(is) e(non-degenerate.)57 b(But)35 b(the)h(iden)n(tit)n(y)f FJ(S)40 b FQ(=)35 b FJ(AS)2419 3169 y FM(st)2510 3199 y FQ(and)g(the)g(in)n(v)n(ertibilit)n(y)g(of)g FJ(S)456 3299 y FQ(imply)28 b(that)f FJ(S)924 3268 y FM(st)1008 3299 y FQ(is)h(in)n(v)n(ertible.)p 3384 3299 4 57 v 3388 3246 50 4 v 3388 3299 V 3437 3299 4 57 v 605 3479 a FP(Pr)n(oof)j(of)h (Lemma)f FQ(5.5.2)p FP(.)40 b FQ(Consider)24 b(the)h(diagram)e(in)j (Figure)e(5.15.)35 b(Let)25 b FJ(m)3157 3491 y FM(1)3219 3479 y FQ(b)r(e)g(the)456 3579 y(graph)30 b(in)i(the)g(upp)r(er)g(left) g(corner;)g(for)f(con)n(v)n(enience,)h(replace)e(the)i(graph)f FJ(m)g FQ(in)h(the)g(lo)n(w)n(er)456 3678 y(righ)n(t)e(corner)f(b)n(y)i FJ(m)1109 3690 y FM(2)1175 3678 y FQ(=)d FJ(F)1321 3690 y FI(c)1351 3698 y FF(4)1388 3678 y FQ(\()p FJ(m)p FQ(\).)47 b(Then)31 b(the)h(v)n(ector)d(spaces)h FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(m)2719 3690 y FM(1)2757 3678 y FQ(\))31 b(and)g FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(m)3232 3690 y FM(2)3270 3678 y FQ(\))31 b(are)456 3778 y(giv)n(en)26 b(b)n(y)1223 3946 y FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(m)1470 3958 y FM(1)1508 3946 y FQ(\))23 b(=)1651 3867 y Fy(M)1677 4044 y FI(i;j)1777 3946 y FL(h)p FJ(V)1876 3912 y FE(\003)1857 3967 y FI(j)1914 3946 y FJ(;)14 b(A;)g(V)2098 3958 y FI(i)2126 3946 y FL(i)19 b(\012)f(h)p FJ(V)2359 3912 y FE(\003)2340 3967 y FI(i)2397 3946 y FJ(;)c(B)t(;)g(V)2586 3958 y FI(j)2621 3946 y FL(i)p FJ(;)1223 4184 y(\034)9 b FQ(\(\006)p FJ(;)14 b(m)1470 4196 y FM(2)1508 4184 y FQ(\))23 b(=)1651 4105 y Fy(M)1696 4284 y FI(k)1777 4184 y FL(h)p FJ(A;)14 b(V)1956 4196 y FI(k)1997 4184 y FJ(;)g(V)2101 4150 y FE(\003)2082 4205 y FI(k)2139 4184 y FJ(;)g(B)t FL(i)p FJ(;)456 4096 y FQ(\(5.5.4\))456 4415 y(where)26 b FJ(A;)14 b(B)31 b FQ(are)26 b(the)h(ob)5 b(jects)26 b(assigned)g(to)g(the)i(b)r(oundary)e(comp)r(onen)n(ts)g FJ(\013;)14 b(\014)31 b FQ(resp)r(ectiv)n(ely)456 4514 y(\(see)c(\(5.4.4\))o(\).)605 4614 y(Then)i(relation)f(MF9)g(can)g(b)r (e)h(written)g(as)f(follo)n(ws:)38 b(for)28 b(ev)n(ery)g(\010)19 b FL(\012)f FQ(\011)25 b FL(2)g(h)p FJ(V)3078 4584 y FE(\003)3059 4636 y FI(j)3116 4614 y FJ(;)14 b(A;)g(V)3300 4626 y FI(i)3328 4614 y FL(i)20 b(\012)456 4717 y(h)p FJ(V)555 4687 y FE(\003)536 4739 y FI(i)593 4717 y FJ(;)14 b(B)t(;)g(V)782 4729 y FI(j)817 4717 y FL(i)p FQ(,)33 b(w)n(e)e(ha)n(v)n(e)f FJ(f)9 b FQ(\(\010)21 b FL(\012)f FQ(\011\))30 b(=)f FJ(g)s FQ(\(\010)20 b FL(\012)h FQ(\011\),)32 b(where)f FJ(f)40 b FQ(is)31 b(the)h(isomorphism)e(giv)n(en)h(b)n(y)456 4817 y(the)26 b(comp)r(osition)f(of)g(mo)n(v)n(es)g(forming)g(the)h (left)g(side)g(and)f(the)i(b)r(ottom)f(of)f(the)h(comm)n(utativ)n(e)456 4917 y(diagram,)34 b(and)g FJ(g)s FQ(|b)n(y)f(the)h(mo)n(v)n(es)f(on)h (the)g(top)g(and)g(the)h(righ)n(t)e(side.)56 b(W)-7 b(e)34 b(represen)n(t)f(this)456 5016 y(iden)n(tit)n(y)28 b(pictorially)-7 b(,)27 b(using)h(Example)f(5.4.2,)g(Eq.)h(\(5.2.9\))o(,)g(and)g(the)g (graphical)f(calculus)h(of)456 5116 y(Section)f(2.3.)605 5216 y(A)h(simple)g(manipulation)f(with)h(\014gures)f(sho)n(ws)f(that:) p eop %%Page: 119 27 119 122 bop 1028 226 a FM(5.5.)29 b(MODULAR)g(CA)-5 b(TEGORIES)29 b(AND)g(MODULAR)g(FUNCTOR)451 b(119)541 997 y FJ(f)9 b FQ(\(\010)19 b FL(\012)f FQ(\011\))23 b(=)992 1401 y @beginspecial 0 @llx 0 @lly 94 @urx 97 @ury 940 @rwi @setspecial %%BeginDocument: figures/g1n2rel2c.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2rel2c.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Wed Jun 9 12:27:12 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 94 97 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2200 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -44.0 100.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /reencdict 12 dict def /ReEncode { reencdict begin /newcodesandnames exch def /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName newfontname put newcodesandnames aload pop 128 1 255 { newfont /Encoding get exch /.notdef put } for newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat newfontname newfont definefont pop end } def /isovec [ 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde 8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis 8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron 8#220 /dotlessi 8#230 /oe 8#231 /OE 8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling 8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis 8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot 8#255 /endash 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus 8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph 8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine 8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf 8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute 8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring 8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute 8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute 8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve 8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply 8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex 8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave 8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring 8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute 8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute 8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve 8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide 8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex 8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def /Times-Italic /Times-Italic-iso isovec ReEncode /Times-Roman /Times-Roman-iso isovec ReEncode /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8550 m -1000 -1000 l 11444 -1000 l 11444 8550 l cp clip 0.01320 0.01320 sc /Symbol ff 600.00 scf sf 8175 5625 m gs 1 -1 sc (Y) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 6585 3840 m gs 1 -1 sc (S) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 6900 3975 m gs 1 -1 sc (ki) col0 sh gr % Polyline 30.000 slw n 6255 3150 m 7605 3150 l 7605 4230 l 6255 4230 l cp gs col0 s gr % Polyline n 4155 5085 m 5355 5085 l 5355 5835 l 4155 5835 l cp gs col0 s gr /Symbol ff 600.00 scf sf 4500 5655 m gs 1 -1 sc (F) col0 sh gr /Symbol ff 600.00 scf sf 8081 4305 m gs 1 -1 sc (q) col0 sh gr /Times-Roman-iso ff 450.00 scf sf 8366 4050 m gs 1 -1 sc (-1) col0 sh gr % Ellipse n 8410 4055 455 455 0 360 DrawEllipse gs col0 s gr % Polyline gs clippath 6405 843 m 6495 411 l 6585 843 l 6585 285 l 6405 285 l cp clip n 6495 330 m 6495 3150 l gs col0 s gr gr % arrowhead n 6405 843 m 6495 411 l 6585 843 l 6495 771 l 6405 843 l cp gs 0.00 setgray ef gr col0 s % Polyline n 4800 330 m 4800 5070 l gs col0 s gr % Polyline n 8400 4515 m 8400 5010 l gs col0 s gr % Polyline gs clippath 10044 5061 m 9996 5499 l 9864 5079 l 9920 5634 l 10099 5616 l cp clip n 9990 5430 m 10005 5580 l gs col0 s gr gr % arrowhead n 10044 5061 m 9996 5499 l 9864 5079 l 9961 5141 l 10044 5061 l cp gs 0.00 setgray ef gr col0 s % Polyline n 7849 5025 m 9049 5025 l 9049 5775 l 7849 5775 l cp gs col0 s gr % Polyline gs clippath 3330 6138 m 3420 5706 l 3510 6138 l 3510 5580 l 3330 5580 l cp clip n 3420 5625 m 3420 5775 l gs col0 s gr gr % arrowhead n 3330 6138 m 3420 5706 l 3510 6138 l 3420 6066 l 3330 6138 l cp gs 0.00 setgray ef gr col0 s /Times-Italic-iso ff 600.00 scf sf 8850 3315 m gs 1 -1 sc (B) col0 sh gr % Polyline gs clippath 7759 4561 m 7946 4960 l 7615 4669 l 7950 5115 l 8094 5007 l cp clip n 7410 4245 m 7995 5025 l gs col0 s gr gr % arrowhead n 7759 4561 m 7946 4960 l 7615 4669 l 7730 4672 l 7759 4561 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 6054 4447 m 6470 4301 l 6146 4601 l 6625 4314 l 6532 4160 l cp clip n 6540 4260 m 5190 5070 l gs col0 s gr gr % arrowhead n 6054 4447 m 6470 4301 l 6146 4601 l 6162 4487 l 6054 4447 l cp gs 0.00 setgray ef gr col0 s % Polyline n 8520 3645 m 8520 3643 l 8521 3640 l 8523 3633 l 8526 3623 l 8530 3608 l 8535 3589 l 8541 3566 l 8548 3538 l 8557 3506 l 8566 3471 l 8576 3433 l 8587 3393 l 8598 3351 l 8609 3308 l 8620 3266 l 8630 3223 l 8641 3182 l 8651 3143 l 8660 3105 l 8669 3069 l 8678 3035 l 8685 3002 l 8692 2972 l 8699 2943 l 8705 2916 l 8710 2890 l 8715 2865 l 8720 2836 l 8725 2808 l 8730 2781 l 8734 2754 l 8738 2727 l 8741 2702 l 8744 2676 l 8747 2652 l 8749 2627 l 8752 2603 l 8754 2579 l 8756 2555 l 8758 2532 l 8760 2508 l 8762 2484 l 8765 2460 l 8767 2435 l 8770 2410 l 8772 2385 l 8775 2359 l 8779 2332 l 8782 2305 l 8786 2278 l 8790 2250 l 8794 2224 l 8798 2197 l 8801 2170 l 8805 2143 l 8809 2115 l 8812 2086 l 8816 2057 l 8819 2028 l 8822 1998 l 8825 1968 l 8828 1937 l 8831 1907 l 8834 1876 l 8837 1846 l 8840 1815 l 8844 1785 l 8848 1756 l 8852 1726 l 8857 1697 l 8863 1669 l 8869 1642 l 8875 1615 l 8883 1589 l 8891 1563 l 8900 1539 l 8910 1515 l 8922 1490 l 8935 1466 l 8950 1441 l 8966 1417 l 8985 1392 l 9006 1366 l 9028 1339 l 9052 1312 l 9078 1284 l 9105 1255 l 9133 1227 l 9161 1198 l 9189 1171 l 9215 1145 l 9240 1121 l 9262 1099 l 9282 1081 l 9298 1065 l 9310 1054 l 9319 1045 l 9325 1039 l 9329 1036 l 9330 1035 l gs col0 s gr % Polyline gs clippath 7445 2629 m 7325 3054 l 7266 2617 l 7227 3174 l 7407 3186 l cp clip n 7320 3135 m 7322 3106 l 7324 3087 l 7326 3063 l 7328 3034 l 7331 3001 l 7335 2964 l 7339 2924 l 7343 2882 l 7348 2840 l 7354 2798 l 7360 2756 l 7367 2716 l 7374 2678 l 7383 2643 l 7392 2609 l 7402 2579 l 7413 2550 l 7425 2523 l 7439 2499 l 7455 2475 l 7470 2455 l 7486 2436 l 7504 2418 l 7522 2399 l 7542 2381 l 7564 2363 l 7586 2345 l 7609 2328 l 7633 2310 l 7658 2293 l 7683 2276 l 7709 2258 l 7736 2242 l 7763 2225 l 7789 2208 l 7816 2192 l 7843 2175 l 7870 2159 l 7896 2144 l 7922 2128 l 7948 2114 l 7973 2099 l 7998 2085 l 8022 2072 l 8046 2059 l 8069 2047 l 8092 2036 l 8115 2025 l 8142 2014 l 8168 2003 l 8196 1994 l 8225 1985 l 8255 1977 l 8287 1970 l 8321 1963 l 8356 1956 l 8393 1950 l 8431 1944 l 8469 1938 l 8507 1932 l 8544 1927 l 8579 1923 l 8612 1919 l 8642 1915 l 8667 1912 l 8688 1910 l 8704 1908 l 8716 1907 l gs col0 s gr gr % arrowhead n 7445 2629 m 7325 3054 l 7266 2617 l 7350 2695 l 7445 2629 l cp gs 0.00 setgray ef gr col0 s % Polyline n 8985 1845 m 8987 1844 l 8991 1842 l 8998 1837 l 9009 1831 l 9024 1822 l 9044 1810 l 9067 1796 l 9094 1779 l 9124 1761 l 9156 1741 l 9190 1721 l 9224 1700 l 9257 1678 l 9289 1657 l 9320 1637 l 9349 1617 l 9375 1598 l 9399 1580 l 9420 1563 l 9438 1546 l 9454 1531 l 9468 1515 l 9480 1500 l 9493 1479 l 9504 1459 l 9512 1438 l 9519 1417 l 9524 1395 l 9527 1374 l 9530 1353 l 9531 1331 l 9532 1310 l 9532 1288 l 9532 1267 l 9531 1245 l 9530 1223 l 9528 1201 l 9525 1179 l 9522 1156 l 9517 1133 l 9510 1110 l 9503 1091 l 9495 1071 l 9485 1051 l 9474 1031 l 9461 1011 l 9446 990 l 9431 969 l 9414 947 l 9397 926 l 9379 904 l 9361 882 l 9343 860 l 9326 839 l 9308 817 l 9292 796 l 9276 775 l 9262 755 l 9248 735 l 9237 715 l 9226 696 l 9217 678 l 9210 660 l 9203 639 l 9197 617 l 9193 595 l 9191 573 l 9189 549 l 9190 524 l 9191 498 l 9193 471 l 9195 445 l 9198 419 l 9201 396 l 9203 375 l 9206 358 l 9208 346 l 9209 337 l 9210 332 l 9210 330 l gs col0 s gr % Polyline n 9525 930 m 9527 928 l 9531 924 l 9538 917 l 9548 907 l 9562 892 l 9580 875 l 9600 854 l 9623 831 l 9646 807 l 9670 782 l 9694 757 l 9717 733 l 9738 709 l 9757 688 l 9775 668 l 9790 649 l 9803 632 l 9815 616 l 9825 600 l 9836 581 l 9845 561 l 9853 541 l 9861 519 l 9867 495 l 9873 470 l 9879 444 l 9884 417 l 9888 392 l 9892 369 l 9895 349 l 9897 334 l 9899 324 l 9900 318 l 9900 315 l gs col0 s gr % Polyline n 4335 5055 m 4334 5053 l 4332 5047 l 4329 5038 l 4323 5023 l 4316 5004 l 4307 4980 l 4296 4953 l 4284 4922 l 4270 4890 l 4256 4858 l 4242 4827 l 4227 4798 l 4211 4771 l 4196 4747 l 4180 4727 l 4164 4710 l 4147 4697 l 4129 4687 l 4110 4680 l 4094 4677 l 4077 4675 l 4058 4674 l 4038 4673 l 4017 4673 l 3994 4674 l 3970 4675 l 3946 4676 l 3920 4677 l 3893 4679 l 3866 4681 l 3839 4683 l 3811 4686 l 3784 4689 l 3756 4693 l 3729 4698 l 3703 4704 l 3678 4712 l 3654 4721 l 3631 4732 l 3609 4744 l 3589 4759 l 3571 4776 l 3554 4796 l 3539 4819 l 3525 4845 l 3515 4867 l 3507 4891 l 3499 4916 l 3491 4944 l 3485 4973 l 3478 5004 l 3472 5037 l 3467 5071 l 3462 5107 l 3457 5144 l 3453 5182 l 3449 5221 l 3445 5261 l 3442 5302 l 3438 5343 l 3435 5386 l 3432 5428 l 3430 5470 l 3427 5513 l 3425 5556 l 3423 5598 l 3421 5640 l 3420 5682 l 3419 5724 l 3418 5765 l 3418 5805 l 3418 5844 l 3418 5883 l 3420 5922 l 3421 5959 l 3424 5996 l 3427 6033 l 3430 6069 l 3435 6105 l 3441 6141 l 3447 6176 l 3454 6212 l 3461 6248 l 3469 6284 l 3477 6321 l 3485 6357 l 3494 6395 l 3502 6432 l 3511 6470 l 3520 6508 l 3529 6546 l 3538 6585 l 3547 6623 l 3557 6662 l 3567 6701 l 3577 6739 l 3587 6777 l 3598 6815 l 3609 6853 l 3621 6890 l 3633 6926 l 3647 6962 l 3661 6997 l 3676 7030 l 3692 7063 l 3709 7094 l 3728 7125 l 3747 7153 l 3769 7181 l 3791 7207 l 3816 7231 l 3842 7254 l 3870 7275 l 3897 7292 l 3925 7309 l 3954 7324 l 3984 7337 l 4015 7350 l 4047 7361 l 4079 7372 l 4113 7381 l 4146 7389 l 4181 7397 l 4215 7403 l 4251 7409 l 4286 7414 l 4322 7419 l 4358 7423 l 4395 7426 l 4432 7429 l 4469 7432 l 4507 7435 l 4545 7437 l 4584 7439 l 4624 7442 l 4664 7444 l 4704 7446 l 4746 7448 l 4788 7450 l 4832 7452 l 4876 7455 l 4921 7458 l 4968 7460 l 5016 7463 l 5066 7466 l 5117 7469 l 5170 7473 l 5224 7476 l 5281 7479 l 5339 7482 l 5400 7485 l 5442 7487 l 5486 7489 l 5531 7490 l 5577 7492 l 5624 7493 l 5672 7494 l 5722 7496 l 5773 7497 l 5825 7498 l 5878 7499 l 5933 7500 l 5989 7501 l 6046 7502 l 6104 7503 l 6163 7504 l 6224 7505 l 6285 7506 l 6347 7507 l 6410 7508 l 6473 7509 l 6538 7509 l 6603 7510 l 6668 7511 l 6734 7512 l 6800 7513 l 6867 7513 l 6933 7514 l 7000 7515 l 7067 7515 l 7133 7516 l 7200 7516 l 7266 7516 l 7331 7517 l 7396 7517 l 7461 7517 l 7525 7517 l 7588 7517 l 7650 7517 l 7712 7517 l 7772 7516 l 7831 7516 l 7889 7515 l 7947 7514 l 8002 7513 l 8057 7512 l 8110 7510 l 8162 7509 l 8212 7507 l 8261 7505 l 8309 7503 l 8355 7501 l 8400 7498 l 8443 7495 l 8485 7492 l 8526 7489 l 8565 7485 l 8627 7478 l 8685 7471 l 8741 7464 l 8793 7455 l 8842 7446 l 8889 7437 l 8933 7428 l 8975 7418 l 9015 7408 l 9053 7397 l 9089 7386 l 9124 7376 l 9157 7364 l 9189 7353 l 9220 7342 l 9250 7330 l 9279 7318 l 9307 7306 l 9336 7293 l 9363 7281 l 9391 7268 l 9418 7255 l 9445 7242 l 9471 7228 l 9498 7214 l 9524 7200 l 9551 7185 l 9577 7170 l 9602 7154 l 9627 7137 l 9652 7120 l 9676 7103 l 9699 7084 l 9720 7065 l 9743 7042 l 9763 7018 l 9782 6993 l 9799 6968 l 9814 6941 l 9828 6913 l 9840 6885 l 9851 6856 l 9861 6826 l 9870 6796 l 9878 6765 l 9885 6734 l 9892 6702 l 9898 6670 l 9903 6638 l 9908 6605 l 9913 6573 l 9918 6540 l 9923 6508 l 9927 6475 l 9932 6442 l 9937 6410 l 9942 6377 l 9947 6345 l 9952 6313 l 9957 6280 l 9962 6248 l 9966 6215 l 9971 6183 l 9975 6150 l 9978 6119 l 9981 6087 l 9983 6056 l 9985 6023 l 9987 5990 l 9988 5957 l 9989 5923 l 9990 5888 l 9990 5853 l 9990 5818 l 9990 5782 l 9990 5746 l 9990 5710 l 9989 5674 l 9989 5637 l 9988 5601 l 9987 5564 l 9986 5528 l 9985 5492 l 9984 5456 l 9982 5421 l 9980 5386 l 9978 5352 l 9976 5319 l 9974 5287 l 9971 5255 l 9968 5224 l 9964 5194 l 9960 5165 l 9956 5138 l 9951 5111 l 9945 5085 l 9937 5052 l 9927 5021 l 9917 4991 l 9906 4962 l 9894 4934 l 9881 4907 l 9868 4881 l 9854 4856 l 9840 4831 l 9825 4807 l 9810 4783 l 9795 4760 l 9780 4737 l 9764 4714 l 9748 4692 l 9732 4671 l 9716 4650 l 9700 4630 l 9684 4611 l 9668 4592 l 9651 4575 l 9635 4558 l 9618 4543 l 9600 4530 l 9580 4517 l 9560 4507 l 9538 4497 l 9516 4489 l 9493 4482 l 9469 4476 l 9445 4471 l 9420 4466 l 9394 4462 l 9369 4459 l 9343 4456 l 9317 4454 l 9291 4452 l 9266 4451 l 9241 4451 l 9217 4452 l 9194 4453 l 9171 4456 l 9149 4461 l 9129 4467 l 9109 4475 l 9090 4485 l 9073 4496 l 9057 4510 l 9042 4527 l 9026 4546 l 9010 4569 l 8993 4594 l 8977 4623 l 8960 4654 l 8942 4688 l 8925 4724 l 8907 4760 l 8889 4798 l 8873 4835 l 8857 4870 l 8842 4904 l 8829 4934 l 8818 4960 l 8808 4981 l 8801 4998 l 8796 5011 l 8793 5019 l 8791 5023 l 8790 5025 l gs col0 s gr /Times-Italic-iso ff 600.00 scf sf 10275 5490 m gs 1 -1 sc (j) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 6000 1365 m gs 1 -1 sc (k) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 7800 1875 m gs 1 -1 sc (k) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 7200 4860 m gs 1 -1 sc (i) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 5850 5175 m gs 1 -1 sc (i) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 4215 3285 m gs 1 -1 sc (A) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 1799 997 a FJ(;)97 b(g)s FQ(\(\010)18 b FL(\012)g FQ(\011\))23 b(=)2362 1384 y @beginspecial 0 @llx 0 @lly 114 @urx 93 @ury 1140 @rwi @setspecial %%BeginDocument: figures/g1n2rel2d.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2rel2d.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Wed Jun 9 16:43:52 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 114 93 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2200 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -44.0 100.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /reencdict 12 dict def /ReEncode { reencdict begin /newcodesandnames exch def /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName newfontname put newcodesandnames aload pop 128 1 255 { newfont /Encoding get exch /.notdef put } for newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat newfontname newfont definefont pop end } def /isovec [ 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde 8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis 8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron 8#220 /dotlessi 8#230 /oe 8#231 /OE 8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling 8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis 8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot 8#255 /endash 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus 8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph 8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine 8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf 8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute 8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring 8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute 8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute 8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve 8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply 8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex 8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave 8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring 8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute 8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute 8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve 8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide 8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex 8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def /Times-Italic /Times-Italic-iso isovec ReEncode /Times-Roman /Times-Roman-iso isovec ReEncode /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8540 m -1000 -1000 l 12928 -1000 l 12928 8540 l cp clip 0.01320 0.01320 sc /Symbol ff 600.00 scf sf 8250 5625 m gs 1 -1 sc (Y) col0 sh gr % Polyline 30.000 slw n 4155 5085 m 5355 5085 l 5355 5835 l 4155 5835 l cp gs col0 s gr /Symbol ff 600.00 scf sf 4500 5640 m gs 1 -1 sc (F) col0 sh gr /Symbol ff 600.00 scf sf 8081 4305 m gs 1 -1 sc (q) col0 sh gr /Times-Roman-iso ff 450.00 scf sf 8366 4050 m gs 1 -1 sc (-1) col0 sh gr % Ellipse n 8410 4055 455 455 0 360 DrawEllipse gs col0 s gr /Times-Italic-iso ff 600.00 scf sf 10245 4140 m gs 1 -1 sc (S) col0 sh gr /Times-Italic-iso ff 450.00 scf sf 10575 4275 m gs 1 -1 sc (kj) col0 sh gr % Polyline n 9840 3450 m 11190 3450 l 11190 4530 l 9840 4530 l cp gs col0 s gr % Polyline n 4815 585 m 4800 5070 l gs col0 s gr % Polyline n 8400 4515 m 8400 5010 l gs col0 s gr % Polyline gs clippath 10080 1188 m 10170 756 l 10260 1188 l 10260 630 l 10080 630 l cp clip n 10170 675 m 10170 3495 l gs col0 s gr gr % arrowhead n 10080 1188 m 10170 756 l 10260 1188 l 10170 1116 l 10080 1188 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 11100 2937 m 11010 3369 l 10920 2937 l 10920 3495 l 11100 3495 l cp clip n 11010 630 m 11010 3450 l gs col0 s gr gr % arrowhead n 11100 2937 m 11010 3369 l 10920 2937 l 11010 3009 l 11100 2937 l cp gs 0.00 setgray ef gr col0 s % Polyline n 7849 5025 m 9049 5025 l 9049 5775 l 7849 5775 l cp gs col0 s gr % Polyline gs clippath 9537 4648 m 9973 4587 l 9597 4817 l 10123 4630 l 10062 4460 l cp clip n 10050 4560 m 8790 5010 l gs col0 s gr gr % arrowhead n 9537 4648 m 9973 4587 l 9597 4817 l 9635 4708 l 9537 4648 l cp gs 0.00 setgray ef gr col0 s /Times-Italic-iso ff 600.00 scf sf 11100 5550 m gs 1 -1 sc (j) col0 sh gr % Polyline n 10305 1965 m 10935 1740 l gs col0 s gr % Polyline gs clippath 7008 7597 m 6576 7507 l 7008 7417 l 6450 7417 l 6450 7597 l cp clip n 6667 7507 m 6495 7507 l gs col0 s gr gr % arrowhead n 7008 7597 m 6576 7507 l 7008 7417 l 6936 7507 l 7008 7597 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 6207 4095 m 6639 4185 l 6207 4275 l 6765 4275 l 6765 4095 l cp clip n 6600 4185 m 6720 4185 l gs col0 s gr gr % arrowhead n 6207 4095 m 6639 4185 l 6207 4275 l 6279 4185 l 6207 4095 l cp gs 0.00 setgray ef gr col0 s % Polyline n 5100 5070 m 5101 5068 l 5102 5063 l 5104 5055 l 5107 5042 l 5111 5025 l 5117 5003 l 5125 4976 l 5133 4944 l 5143 4910 l 5153 4872 l 5165 4833 l 5177 4794 l 5190 4755 l 5204 4717 l 5217 4680 l 5232 4645 l 5247 4613 l 5262 4583 l 5278 4556 l 5295 4532 l 5314 4509 l 5333 4489 l 5355 4470 l 5375 4455 l 5396 4441 l 5419 4427 l 5443 4414 l 5467 4401 l 5493 4389 l 5519 4378 l 5547 4367 l 5574 4356 l 5603 4345 l 5632 4335 l 5661 4325 l 5691 4316 l 5721 4306 l 5752 4297 l 5782 4288 l 5813 4279 l 5845 4270 l 5876 4262 l 5908 4253 l 5940 4245 l 5973 4238 l 6006 4230 l 6039 4223 l 6073 4217 l 6108 4210 l 6144 4205 l 6180 4200 l 6211 4196 l 6242 4193 l 6275 4191 l 6308 4188 l 6343 4186 l 6378 4185 l 6414 4183 l 6452 4182 l 6490 4181 l 6528 4180 l 6568 4180 l 6608 4179 l 6649 4179 l 6690 4179 l 6731 4178 l 6773 4179 l 6814 4179 l 6856 4179 l 6897 4179 l 6939 4180 l 6979 4181 l 7019 4182 l 7059 4183 l 7098 4184 l 7135 4186 l 7172 4188 l 7208 4190 l 7243 4192 l 7276 4195 l 7308 4198 l 7339 4201 l 7369 4205 l 7398 4210 l 7425 4215 l 7462 4223 l 7496 4232 l 7529 4242 l 7560 4254 l 7589 4265 l 7617 4278 l 7643 4292 l 7669 4306 l 7694 4320 l 7718 4335 l 7741 4351 l 7763 4366 l 7786 4382 l 7807 4398 l 7829 4414 l 7850 4430 l 7870 4446 l 7890 4462 l 7910 4479 l 7929 4495 l 7947 4511 l 7964 4527 l 7980 4543 l 7995 4560 l 8011 4581 l 8024 4603 l 8036 4626 l 8046 4652 l 8055 4680 l 8063 4710 l 8069 4743 l 8075 4777 l 8080 4813 l 8085 4849 l 8089 4883 l 8092 4916 l 8094 4946 l 8096 4971 l 8098 4992 l 8099 5007 l 8099 5017 l 8100 5022 l 8100 5025 l gs col0 s gr % Polyline n 4335 5055 m 4334 5053 l 4332 5047 l 4329 5038 l 4323 5023 l 4316 5004 l 4307 4980 l 4296 4953 l 4284 4922 l 4270 4890 l 4256 4858 l 4242 4827 l 4227 4798 l 4211 4771 l 4196 4747 l 4180 4727 l 4164 4710 l 4147 4697 l 4129 4687 l 4110 4680 l 4094 4677 l 4077 4675 l 4058 4674 l 4038 4673 l 4017 4673 l 3994 4674 l 3970 4675 l 3946 4676 l 3920 4677 l 3893 4679 l 3866 4681 l 3839 4683 l 3811 4686 l 3784 4689 l 3756 4693 l 3729 4698 l 3703 4704 l 3678 4712 l 3654 4721 l 3631 4732 l 3609 4744 l 3589 4759 l 3571 4776 l 3554 4796 l 3539 4819 l 3525 4845 l 3515 4867 l 3507 4891 l 3499 4916 l 3491 4944 l 3485 4973 l 3478 5004 l 3472 5037 l 3467 5071 l 3462 5107 l 3457 5144 l 3453 5182 l 3449 5221 l 3445 5261 l 3442 5302 l 3438 5343 l 3435 5386 l 3432 5428 l 3430 5470 l 3427 5513 l 3425 5556 l 3423 5598 l 3421 5640 l 3420 5682 l 3419 5724 l 3418 5765 l 3418 5805 l 3418 5844 l 3418 5883 l 3420 5922 l 3421 5959 l 3424 5996 l 3427 6033 l 3430 6069 l 3435 6105 l 3441 6141 l 3447 6176 l 3454 6212 l 3461 6248 l 3469 6284 l 3477 6321 l 3485 6357 l 3494 6395 l 3502 6432 l 3511 6470 l 3520 6508 l 3529 6546 l 3538 6585 l 3547 6623 l 3557 6662 l 3567 6701 l 3577 6739 l 3587 6777 l 3598 6815 l 3609 6853 l 3621 6890 l 3633 6926 l 3647 6962 l 3661 6997 l 3676 7030 l 3692 7063 l 3709 7094 l 3728 7125 l 3747 7153 l 3769 7181 l 3791 7207 l 3816 7231 l 3842 7254 l 3870 7275 l 3897 7292 l 3925 7309 l 3954 7324 l 3985 7337 l 4017 7350 l 4050 7361 l 4084 7372 l 4119 7381 l 4155 7389 l 4191 7397 l 4229 7404 l 4267 7410 l 4306 7415 l 4345 7420 l 4385 7424 l 4426 7427 l 4466 7431 l 4508 7434 l 4549 7436 l 4591 7439 l 4633 7441 l 4676 7443 l 4718 7445 l 4761 7448 l 4805 7450 l 4848 7452 l 4892 7454 l 4936 7457 l 4980 7459 l 5025 7462 l 5070 7465 l 5115 7468 l 5161 7471 l 5207 7474 l 5254 7477 l 5302 7480 l 5351 7482 l 5400 7485 l 5442 7487 l 5484 7488 l 5527 7490 l 5571 7491 l 5615 7492 l 5660 7493 l 5706 7494 l 5752 7495 l 5800 7496 l 5847 7496 l 5896 7497 l 5944 7497 l 5994 7498 l 6044 7498 l 6094 7498 l 6145 7498 l 6196 7498 l 6247 7499 l 6299 7499 l 6351 7499 l 6403 7498 l 6455 7498 l 6508 7498 l 6560 7498 l 6613 7497 l 6665 7497 l 6718 7497 l 6770 7496 l 6822 7495 l 6874 7494 l 6926 7493 l 6977 7492 l 7029 7491 l 7080 7489 l 7130 7488 l 7181 7486 l 7231 7484 l 7280 7482 l 7330 7479 l 7378 7477 l 7427 7474 l 7475 7471 l 7523 7467 l 7571 7463 l 7618 7459 l 7665 7455 l 7714 7450 l 7763 7445 l 7812 7439 l 7860 7433 l 7909 7427 l 7958 7421 l 8007 7414 l 8056 7407 l 8105 7400 l 8155 7393 l 8204 7385 l 8254 7378 l 8304 7370 l 8354 7362 l 8404 7354 l 8455 7346 l 8505 7338 l 8555 7330 l 8606 7322 l 8656 7313 l 8706 7305 l 8756 7296 l 8806 7287 l 8856 7278 l 8906 7269 l 8955 7260 l 9003 7251 l 9052 7242 l 9100 7232 l 9147 7223 l 9193 7213 l 9239 7203 l 9285 7193 l 9329 7183 l 9373 7172 l 9415 7161 l 9457 7150 l 9498 7139 l 9538 7128 l 9576 7116 l 9614 7104 l 9650 7091 l 9686 7078 l 9720 7065 l 9762 7047 l 9803 7029 l 9842 7010 l 9879 6990 l 9914 6970 l 9948 6950 l 9981 6929 l 10012 6907 l 10042 6886 l 10071 6864 l 10100 6842 l 10127 6819 l 10153 6796 l 10179 6773 l 10204 6750 l 10229 6727 l 10253 6703 l 10277 6680 l 10300 6656 l 10323 6632 l 10346 6608 l 10369 6583 l 10392 6559 l 10414 6534 l 10436 6509 l 10458 6484 l 10480 6459 l 10502 6433 l 10523 6407 l 10543 6380 l 10564 6353 l 10583 6326 l 10602 6298 l 10620 6270 l 10637 6241 l 10653 6211 l 10668 6181 l 10682 6150 l 10695 6118 l 10707 6085 l 10718 6051 l 10729 6016 l 10739 5981 l 10748 5945 l 10757 5909 l 10766 5872 l 10774 5834 l 10781 5797 l 10788 5759 l 10795 5720 l 10802 5682 l 10808 5644 l 10815 5606 l 10821 5568 l 10827 5530 l 10833 5493 l 10840 5457 l 10846 5421 l 10852 5386 l 10858 5352 l 10864 5319 l 10870 5286 l 10876 5255 l 10882 5225 l 10888 5196 l 10894 5168 l 10900 5141 l 10905 5115 l 10912 5077 l 10919 5041 l 10925 5005 l 10930 4971 l 10934 4936 l 10939 4901 l 10942 4866 l 10946 4831 l 10949 4795 l 10952 4760 l 10954 4725 l 10957 4691 l 10959 4660 l 10960 4632 l 10962 4607 l 10963 4587 l 10964 4571 l 10964 4559 l 10965 4551 l 10965 4547 l 10965 4545 l gs col0 s gr % Polyline n 11130 1680 m 11132 1679 l 11138 1678 l 11147 1676 l 11161 1673 l 11179 1668 l 11201 1663 l 11226 1657 l 11253 1650 l 11280 1642 l 11308 1635 l 11334 1627 l 11359 1619 l 11383 1611 l 11404 1603 l 11424 1594 l 11442 1585 l 11460 1575 l 11476 1565 l 11491 1555 l 11507 1544 l 11523 1534 l 11539 1523 l 11555 1512 l 11571 1502 l 11587 1491 l 11603 1480 l 11619 1469 l 11635 1457 l 11651 1445 l 11666 1432 l 11682 1419 l 11696 1404 l 11710 1388 l 11724 1370 l 11737 1350 l 11749 1329 l 11760 1305 l 11768 1285 l 11776 1264 l 11783 1240 l 11791 1214 l 11798 1185 l 11805 1154 l 11812 1120 l 11819 1083 l 11826 1044 l 11833 1002 l 11840 959 l 11847 916 l 11854 871 l 11860 828 l 11866 786 l 11872 747 l 11877 711 l 11882 679 l 11886 651 l 11889 629 l 11891 612 l 11893 599 l 11894 591 l 11895 587 l 11895 585 l gs col0 s gr % Polyline n 8445 3555 m 8445 3553 l 8445 3548 l 8445 3540 l 8446 3527 l 8446 3509 l 8447 3486 l 8448 3459 l 8449 3427 l 8451 3391 l 8452 3353 l 8454 3313 l 8456 3273 l 8459 3232 l 8461 3193 l 8464 3155 l 8468 3118 l 8471 3084 l 8475 3053 l 8480 3023 l 8485 2996 l 8491 2971 l 8498 2947 l 8505 2925 l 8514 2902 l 8524 2879 l 8534 2857 l 8545 2836 l 8555 2816 l 8566 2796 l 8577 2777 l 8589 2758 l 8600 2740 l 8611 2722 l 8623 2704 l 8635 2687 l 8648 2669 l 8662 2652 l 8676 2634 l 8692 2616 l 8709 2598 l 8727 2580 l 8747 2561 l 8769 2542 l 8794 2524 l 8820 2505 l 8841 2491 l 8863 2477 l 8887 2464 l 8912 2450 l 8939 2436 l 8967 2421 l 8997 2407 l 9028 2392 l 9060 2377 l 9093 2363 l 9127 2348 l 9162 2332 l 9197 2317 l 9233 2302 l 9269 2287 l 9305 2272 l 9340 2257 l 9376 2242 l 9410 2228 l 9445 2214 l 9478 2200 l 9510 2187 l 9541 2174 l 9571 2162 l 9599 2150 l 9626 2138 l 9652 2128 l 9676 2118 l 9699 2109 l 9720 2100 l 9753 2087 l 9783 2076 l 9812 2066 l 9839 2058 l 9865 2050 l 9891 2044 l 9917 2038 l 9942 2032 l 9966 2027 l 9989 2023 l 10009 2019 l 10027 2016 l 10041 2014 l 10052 2012 l 10059 2011 l 10063 2010 l 10065 2010 l gs col0 s gr /Times-Italic-iso ff 600.00 scf sf 8790 3315 m gs 1 -1 sc (B) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 4215 3285 m gs 1 -1 sc (A) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 11250 2700 m gs 1 -1 sc (k) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 9600 1575 m gs 1 -1 sc (k) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 9600 5325 m gs 1 -1 sc (j) col0 sh gr /Times-Italic-iso ff 600.00 scf sf 5775 4875 m gs 1 -1 sc (i) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 3335 997 a FJ(:)605 1531 y FQ(The)28 b(iden)n(tit)n(y)f FJ(f)9 b FQ(\(\010)19 b FL(\012)f FQ(\011\))23 b(=)f FJ(g)s FQ(\(\010)d FL(\012)f FQ(\011\))27 b FL(8)p FQ(\010)g(is)g (equiv)-5 b(alen)n(t)28 b(to:)1189 2394 y @beginspecial 0 @llx 0 @lly 66 @urx 83 @ury 660 @rwi @setspecial %%BeginDocument: figures/g1n2rel2e.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2rel2e.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Wed Jun 9 12:48:48 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 66 83 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2400 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -86.0 87.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7033 m -1000 -1000 l 11519 -1000 l 11519 7033 l cp clip 0.01440 0.01440 sc /Symbol ff 600.00 scf sf 8175 5625 m gs 1 -1 sc (Y) col0 sh gr /Times-Italic ff 600.00 scf sf 6585 3840 m gs 1 -1 sc (S) col0 sh gr /Times-Italic ff 450.00 scf sf 6900 3975 m gs 1 -1 sc (ki) col0 sh gr % Polyline 30.000 slw n 6255 3150 m 7605 3150 l 7605 4230 l 6255 4230 l cp gs col0 s gr % Polyline gs clippath 6405 843 m 6495 411 l 6585 843 l 6585 285 l 6405 285 l cp clip n 6495 330 m 6495 3150 l gs col0 s gr gr % arrowhead n 6405 843 m 6495 411 l 6585 843 l 6495 771 l 6405 843 l cp gs 0.00 setgray ef gr col0 s % Polyline n 8400 4500 m 8400 5010 l gs col0 s gr % Polyline gs clippath 10044 5061 m 9996 5499 l 9864 5079 l 9920 5634 l 10099 5616 l cp clip n 9990 5430 m 10005 5580 l gs col0 s gr gr % arrowhead n 10044 5061 m 9996 5499 l 9864 5079 l 9961 5141 l 10044 5061 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 7759 4561 m 7946 4960 l 7615 4669 l 7950 5115 l 8094 5007 l cp clip n 7410 4245 m 7995 5025 l gs col0 s gr gr % arrowhead n 7759 4561 m 7946 4960 l 7615 4669 l 7730 4672 l 7759 4561 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 6435 4713 m 6525 4281 l 6615 4713 l 6615 4155 l 6435 4155 l cp clip n 6525 4200 m 6525 6000 l gs col0 s gr gr % arrowhead n 6435 4713 m 6525 4281 l 6615 4713 l 6525 4641 l 6435 4713 l cp gs 0.00 setgray ef gr col0 s % Polyline n 7849 5025 m 9049 5025 l 9049 5775 l 7849 5775 l cp gs col0 s gr % Polyline gs clippath 7445 2629 m 7325 3054 l 7266 2617 l 7227 3174 l 7407 3186 l cp clip n 7320 3135 m 7322 3106 l 7324 3087 l 7326 3063 l 7328 3034 l 7331 3001 l 7335 2964 l 7339 2924 l 7343 2882 l 7348 2840 l 7354 2798 l 7360 2756 l 7367 2716 l 7374 2678 l 7383 2643 l 7392 2609 l 7402 2579 l 7413 2550 l 7425 2523 l 7439 2499 l 7455 2475 l 7470 2455 l 7486 2436 l 7504 2418 l 7522 2399 l 7542 2381 l 7564 2363 l 7586 2345 l 7609 2328 l 7633 2310 l 7658 2293 l 7683 2276 l 7709 2258 l 7736 2242 l 7763 2225 l 7789 2208 l 7816 2192 l 7843 2175 l 7870 2159 l 7896 2144 l 7922 2128 l 7948 2114 l 7973 2099 l 7998 2085 l 8022 2072 l 8046 2059 l 8069 2047 l 8092 2036 l 8115 2025 l 8142 2014 l 8168 2003 l 8196 1994 l 8225 1985 l 8255 1977 l 8287 1970 l 8321 1963 l 8356 1956 l 8393 1950 l 8431 1944 l 8469 1938 l 8507 1932 l 8544 1927 l 8579 1923 l 8612 1919 l 8642 1915 l 8667 1912 l 8688 1910 l 8704 1908 l 8716 1907 l gs col0 s gr gr % arrowhead n 7445 2629 m 7325 3054 l 7266 2617 l 7350 2695 l 7445 2629 l cp gs 0.00 setgray ef gr col0 s /Times-Italic ff 600.00 scf sf 6075 5325 m gs 1 -1 sc (i) col0 sh gr % Polyline n 8985 1845 m 8987 1844 l 8991 1842 l 8998 1837 l 9009 1831 l 9024 1822 l 9044 1810 l 9067 1796 l 9094 1779 l 9124 1761 l 9156 1741 l 9190 1721 l 9224 1700 l 9257 1678 l 9289 1657 l 9320 1637 l 9349 1617 l 9375 1598 l 9399 1580 l 9420 1563 l 9438 1546 l 9454 1531 l 9468 1515 l 9480 1500 l 9493 1479 l 9504 1459 l 9512 1438 l 9519 1417 l 9524 1395 l 9527 1374 l 9530 1353 l 9531 1331 l 9532 1310 l 9532 1288 l 9532 1267 l 9531 1245 l 9530 1223 l 9528 1201 l 9525 1179 l 9522 1156 l 9517 1133 l 9510 1110 l 9503 1091 l 9495 1071 l 9485 1051 l 9474 1031 l 9461 1011 l 9446 990 l 9431 969 l 9414 947 l 9397 926 l 9379 904 l 9361 882 l 9343 860 l 9326 839 l 9308 817 l 9292 796 l 9276 775 l 9262 755 l 9248 735 l 9237 715 l 9226 696 l 9217 678 l 9210 660 l 9203 639 l 9197 617 l 9193 595 l 9191 573 l 9189 549 l 9190 524 l 9191 498 l 9193 471 l 9195 445 l 9198 419 l 9201 396 l 9203 375 l 9206 358 l 9208 346 l 9209 337 l 9210 332 l 9210 330 l gs col0 s gr % Polyline n 9525 930 m 9527 928 l 9531 924 l 9538 917 l 9548 907 l 9562 892 l 9580 875 l 9600 854 l 9623 831 l 9646 807 l 9670 782 l 9694 757 l 9717 733 l 9738 709 l 9757 688 l 9775 668 l 9790 649 l 9803 632 l 9815 616 l 9825 600 l 9836 581 l 9845 561 l 9853 541 l 9861 519 l 9867 495 l 9873 470 l 9879 444 l 9884 417 l 9888 392 l 9892 369 l 9895 349 l 9897 334 l 9899 324 l 9900 318 l 9900 315 l gs col0 s gr % Polyline n 9975 6000 m 9975 5998 l 9975 5995 l 9975 5988 l 9975 5978 l 9976 5963 l 9976 5944 l 9977 5920 l 9977 5892 l 9978 5859 l 9978 5822 l 9979 5782 l 9979 5739 l 9979 5693 l 9980 5646 l 9980 5599 l 9980 5552 l 9979 5505 l 9979 5459 l 9978 5415 l 9977 5372 l 9975 5332 l 9973 5294 l 9971 5258 l 9968 5225 l 9965 5193 l 9961 5164 l 9956 5136 l 9951 5110 l 9945 5085 l 9937 5055 l 9927 5026 l 9917 4998 l 9906 4970 l 9894 4944 l 9881 4917 l 9868 4891 l 9854 4866 l 9840 4841 l 9825 4816 l 9810 4791 l 9795 4767 l 9780 4743 l 9764 4719 l 9748 4696 l 9732 4674 l 9716 4652 l 9700 4631 l 9684 4611 l 9668 4593 l 9651 4575 l 9635 4558 l 9618 4543 l 9600 4530 l 9580 4517 l 9560 4507 l 9538 4497 l 9516 4489 l 9493 4482 l 9469 4476 l 9445 4471 l 9420 4466 l 9394 4462 l 9369 4459 l 9343 4456 l 9317 4454 l 9291 4452 l 9266 4451 l 9241 4451 l 9217 4452 l 9194 4453 l 9171 4456 l 9149 4461 l 9129 4467 l 9109 4475 l 9090 4485 l 9073 4496 l 9057 4510 l 9042 4527 l 9026 4546 l 9010 4569 l 8993 4594 l 8977 4623 l 8960 4654 l 8942 4688 l 8925 4724 l 8907 4760 l 8889 4798 l 8873 4835 l 8857 4870 l 8842 4904 l 8829 4934 l 8818 4960 l 8808 4981 l 8801 4998 l 8796 5011 l 8793 5019 l 8791 5023 l 8790 5025 l gs col0 s gr % Polyline n 8400 4500 m 8400 4498 l 8401 4494 l 8402 4487 l 8403 4476 l 8405 4461 l 8407 4440 l 8411 4415 l 8414 4385 l 8419 4351 l 8424 4313 l 8429 4272 l 8434 4228 l 8440 4183 l 8446 4137 l 8452 4090 l 8458 4045 l 8464 4000 l 8470 3957 l 8476 3915 l 8482 3875 l 8488 3838 l 8493 3802 l 8498 3768 l 8504 3735 l 8509 3704 l 8514 3674 l 8520 3645 l 8526 3616 l 8532 3587 l 8538 3558 l 8544 3529 l 8551 3501 l 8558 3472 l 8565 3443 l 8572 3415 l 8580 3386 l 8588 3358 l 8596 3329 l 8604 3301 l 8612 3272 l 8620 3244 l 8628 3215 l 8636 3187 l 8644 3159 l 8651 3131 l 8659 3103 l 8666 3076 l 8673 3048 l 8680 3021 l 8687 2994 l 8693 2968 l 8699 2942 l 8705 2916 l 8710 2890 l 8715 2865 l 8720 2836 l 8725 2808 l 8730 2781 l 8734 2754 l 8738 2727 l 8741 2702 l 8744 2676 l 8747 2652 l 8749 2627 l 8752 2603 l 8754 2579 l 8756 2555 l 8758 2532 l 8760 2508 l 8762 2484 l 8765 2460 l 8767 2435 l 8770 2410 l 8772 2385 l 8775 2359 l 8779 2332 l 8782 2305 l 8786 2278 l 8790 2250 l 8794 2224 l 8798 2197 l 8801 2170 l 8805 2143 l 8809 2115 l 8812 2086 l 8816 2057 l 8819 2028 l 8822 1998 l 8825 1968 l 8828 1937 l 8831 1907 l 8834 1876 l 8837 1846 l 8840 1815 l 8844 1785 l 8848 1756 l 8852 1726 l 8857 1697 l 8863 1669 l 8869 1642 l 8875 1615 l 8883 1589 l 8891 1563 l 8900 1539 l 8910 1515 l 8922 1490 l 8935 1466 l 8950 1441 l 8966 1417 l 8985 1392 l 9006 1366 l 9028 1339 l 9052 1312 l 9078 1284 l 9105 1255 l 9133 1227 l 9161 1198 l 9189 1171 l 9215 1145 l 9240 1121 l 9262 1099 l 9282 1081 l 9298 1065 l 9310 1054 l 9319 1045 l 9325 1039 l 9329 1036 l 9330 1035 l gs col0 s gr /Times-Italic ff 600.00 scf sf 6000 1365 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 7800 1875 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 7200 4860 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 8850 3315 m gs 1 -1 sc (B) col0 sh gr /Times-Italic ff 600.00 scf sf 10350 5325 m gs 1 -1 sc (j) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 1829 2001 a FJ(:)1808 2048 y FQ(=)1942 2398 y @beginspecial 0 @llx 0 @lly 84 @urx 84 @ury 840 @rwi @setspecial %%BeginDocument: figures/g1n2rel2f.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2rel2f.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Wed Jun 9 12:50:57 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 84 84 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2400 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -88.0 87.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7033 m -1000 -1000 l 12928 -1000 l 12928 7033 l cp clip 0.01440 0.01440 sc /Symbol ff 600.00 scf sf 8250 5625 m gs 1 -1 sc (Y) col0 sh gr /Times-Italic ff 600.00 scf sf 10245 4140 m gs 1 -1 sc (S) col0 sh gr /Times-Italic ff 450.00 scf sf 10575 4275 m gs 1 -1 sc (kj) col0 sh gr % Polyline 30.000 slw n 9840 3450 m 11190 3450 l 11190 4530 l 9840 4530 l cp gs col0 s gr % Polyline n 8400 4575 m 8400 5010 l gs col0 s gr % Polyline gs clippath 10080 813 m 10170 381 l 10260 813 l 10260 255 l 10080 255 l cp clip n 10170 300 m 10170 3450 l gs col0 s gr gr % arrowhead n 10080 813 m 10170 381 l 10260 813 l 10170 741 l 10080 813 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 9537 4648 m 9973 4587 l 9597 4817 l 10123 4630 l 10062 4460 l cp clip n 10050 4560 m 8790 5010 l gs col0 s gr gr % arrowhead n 9537 4648 m 9973 4587 l 9597 4817 l 9635 4708 l 9537 4648 l cp gs 0.00 setgray ef gr col0 s % Polyline n 10275 1875 m 10800 1725 l gs col0 s gr % Polyline gs clippath 11100 5487 m 11010 5919 l 10920 5487 l 10920 6045 l 11100 6045 l cp clip n 11010 4530 m 11010 6000 l gs col0 s gr gr % arrowhead n 11100 5487 m 11010 5919 l 10920 5487 l 11010 5559 l 11100 5487 l cp gs 0.00 setgray ef gr col0 s % Polyline n 7849 5025 m 9049 5025 l 9049 5775 l 7849 5775 l cp gs col0 s gr % Polyline gs clippath 11115 2937 m 11025 3369 l 10935 2937 l 10935 3495 l 11115 3495 l cp clip n 11025 300 m 11025 3450 l gs col0 s gr gr % arrowhead n 11115 2937 m 11025 3369 l 10935 2937 l 11025 3009 l 11115 2937 l cp gs 0.00 setgray ef gr col0 s /Times-Italic ff 600.00 scf sf 6150 5325 m gs 1 -1 sc (i) col0 sh gr % Polyline gs clippath 6435 5868 m 6525 5436 l 6615 5868 l 6615 5310 l 6435 5310 l cp clip n 6525 5775 m 6525 5355 l gs col0 s gr gr % arrowhead n 6435 5868 m 6525 5436 l 6615 5868 l 6525 5796 l 6435 5868 l cp gs 0.00 setgray ef gr col0 s % Polyline n 8400 4575 m 8400 4573 l 8401 4568 l 8402 4558 l 8403 4544 l 8405 4523 l 8407 4497 l 8411 4465 l 8414 4427 l 8419 4386 l 8423 4340 l 8429 4292 l 8434 4243 l 8440 4193 l 8446 4144 l 8452 4095 l 8458 4048 l 8464 4002 l 8470 3958 l 8476 3916 l 8482 3876 l 8489 3837 l 8496 3800 l 8502 3764 l 8509 3729 l 8517 3695 l 8524 3662 l 8533 3629 l 8541 3596 l 8550 3563 l 8559 3531 l 8568 3500 l 8578 3468 l 8588 3435 l 8599 3402 l 8610 3369 l 8622 3335 l 8634 3300 l 8647 3265 l 8660 3230 l 8674 3194 l 8689 3158 l 8704 3122 l 8719 3086 l 8735 3050 l 8751 3014 l 8768 2978 l 8785 2943 l 8802 2908 l 8819 2874 l 8836 2841 l 8853 2809 l 8871 2777 l 8888 2747 l 8905 2717 l 8922 2688 l 8940 2661 l 8957 2634 l 8974 2609 l 8991 2584 l 9008 2560 l 9025 2538 l 9046 2510 l 9068 2484 l 9090 2458 l 9112 2433 l 9135 2409 l 9159 2386 l 9183 2363 l 9207 2340 l 9232 2318 l 9257 2297 l 9282 2277 l 9307 2257 l 9332 2238 l 9357 2221 l 9382 2204 l 9406 2188 l 9430 2173 l 9453 2158 l 9476 2145 l 9498 2133 l 9519 2122 l 9539 2111 l 9558 2101 l 9577 2092 l 9595 2083 l 9613 2075 l 9637 2064 l 9660 2054 l 9683 2044 l 9706 2035 l 9730 2026 l 9754 2017 l 9780 2009 l 9806 2000 l 9833 1991 l 9861 1983 l 9888 1975 l 9914 1967 l 9936 1961 l 9953 1956 l 9965 1953 l 9972 1951 l 9975 1950 l gs col0 s gr % Polyline n 11175 1650 m 11176 1650 l 11179 1649 l 11188 1646 l 11202 1642 l 11222 1636 l 11246 1629 l 11273 1620 l 11300 1612 l 11326 1603 l 11350 1594 l 11372 1586 l 11392 1578 l 11411 1570 l 11429 1561 l 11446 1552 l 11463 1543 l 11476 1534 l 11490 1526 l 11503 1516 l 11518 1506 l 11532 1494 l 11547 1481 l 11561 1468 l 11577 1453 l 11592 1436 l 11607 1419 l 11621 1400 l 11636 1380 l 11650 1358 l 11663 1336 l 11676 1313 l 11689 1289 l 11701 1264 l 11712 1238 l 11722 1211 l 11733 1183 l 11740 1161 l 11746 1139 l 11753 1115 l 11760 1090 l 11766 1064 l 11773 1035 l 11780 1004 l 11787 971 l 11793 935 l 11801 897 l 11808 855 l 11816 812 l 11823 765 l 11831 717 l 11839 667 l 11847 616 l 11855 566 l 11863 517 l 11870 471 l 11876 429 l 11881 392 l 11886 362 l 11890 338 l 11892 320 l 11894 309 l 11895 303 l 11895 300 l gs col0 s gr % Polyline n 6525 6000 m 6525 5997 l 6525 5992 l 6525 5981 l 6525 5965 l 6525 5943 l 6526 5915 l 6526 5883 l 6527 5846 l 6527 5806 l 6528 5765 l 6528 5723 l 6529 5682 l 6530 5641 l 6531 5603 l 6532 5566 l 6533 5532 l 6535 5499 l 6536 5469 l 6538 5441 l 6539 5415 l 6541 5390 l 6543 5366 l 6545 5343 l 6547 5321 l 6550 5300 l 6553 5275 l 6557 5251 l 6561 5226 l 6565 5202 l 6570 5178 l 6575 5154 l 6581 5129 l 6587 5105 l 6593 5080 l 6600 5056 l 6607 5032 l 6614 5008 l 6622 4985 l 6630 4962 l 6638 4940 l 6647 4918 l 6655 4897 l 6664 4877 l 6673 4857 l 6682 4838 l 6691 4819 l 6700 4800 l 6710 4781 l 6719 4762 l 6730 4743 l 6741 4724 l 6753 4704 l 6765 4684 l 6779 4664 l 6793 4644 l 6808 4624 l 6824 4603 l 6841 4584 l 6858 4564 l 6876 4545 l 6895 4527 l 6914 4510 l 6934 4493 l 6954 4477 l 6975 4463 l 6996 4449 l 7017 4436 l 7040 4424 l 7063 4413 l 7084 4403 l 7107 4394 l 7131 4385 l 7156 4377 l 7182 4369 l 7209 4361 l 7237 4355 l 7265 4348 l 7295 4343 l 7325 4338 l 7355 4333 l 7385 4329 l 7415 4326 l 7445 4324 l 7475 4322 l 7503 4321 l 7531 4321 l 7558 4321 l 7584 4322 l 7608 4323 l 7632 4325 l 7654 4328 l 7675 4331 l 7695 4335 l 7718 4340 l 7739 4346 l 7760 4353 l 7780 4361 l 7799 4370 l 7817 4380 l 7834 4391 l 7851 4403 l 7866 4416 l 7881 4430 l 7895 4444 l 7907 4459 l 7919 4475 l 7930 4491 l 7940 4507 l 7949 4523 l 7958 4540 l 7966 4556 l 7973 4573 l 7980 4590 l 7987 4607 l 7993 4625 l 8000 4644 l 8007 4665 l 8013 4687 l 8020 4710 l 8028 4736 l 8035 4765 l 8043 4795 l 8052 4828 l 8060 4861 l 8069 4895 l 8076 4927 l 8084 4957 l 8090 4982 l 8094 5001 l 8097 5014 l 8099 5022 l 8100 5025 l gs col0 s gr /Times-Italic ff 600.00 scf sf 9600 1575 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 9600 5325 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 11325 5325 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 11250 2700 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 8400 2700 m gs 1 -1 sc (B) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 2688 2048 a FJ(:)605 2523 y FQ(W)-7 b(e)28 b(manipulate)g(this)f(as)g(follo)n(ws:)1015 3391 y @beginspecial 0 @llx 0 @lly 112 @urx 84 @ury 1120 @rwi @setspecial %%BeginDocument: figures/g1n2rel2e2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2rel2e2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Wed Jun 9 17:14:28 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 112 84 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2400 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -35.0 87.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7033 m -1000 -1000 l 11144 -1000 l 11144 7033 l cp clip 0.01440 0.01440 sc % Polyline 30.000 slw n 6225 1950 m 6222 1950 l 6214 1951 l 6202 1952 l 6183 1954 l 6159 1956 l 6130 1960 l 6099 1964 l 6066 1970 l 6033 1976 l 6002 1983 l 5972 1991 l 5944 2000 l 5919 2010 l 5896 2021 l 5874 2033 l 5854 2047 l 5835 2063 l 5817 2080 l 5800 2100 l 5789 2114 l 5777 2129 l 5766 2146 l 5755 2163 l 5743 2182 l 5732 2202 l 5720 2223 l 5709 2246 l 5697 2271 l 5685 2297 l 5673 2324 l 5661 2353 l 5649 2383 l 5637 2414 l 5625 2447 l 5613 2481 l 5601 2516 l 5589 2552 l 5577 2589 l 5565 2626 l 5553 2665 l 5541 2704 l 5530 2743 l 5518 2784 l 5507 2824 l 5495 2866 l 5484 2908 l 5473 2950 l 5461 2993 l 5450 3038 l 5441 3071 l 5433 3106 l 5424 3141 l 5415 3177 l 5405 3214 l 5396 3252 l 5386 3290 l 5376 3330 l 5366 3370 l 5356 3411 l 5345 3453 l 5334 3495 l 5323 3538 l 5312 3582 l 5300 3626 l 5288 3670 l 5276 3714 l 5263 3759 l 5251 3804 l 5238 3849 l 5225 3893 l 5212 3937 l 5199 3981 l 5185 4024 l 5172 4067 l 5158 4109 l 5144 4150 l 5131 4190 l 5117 4229 l 5103 4267 l 5089 4304 l 5076 4340 l 5062 4375 l 5048 4409 l 5034 4441 l 5020 4473 l 5006 4503 l 4991 4532 l 4977 4560 l 4963 4588 l 4944 4620 l 4925 4651 l 4906 4681 l 4886 4710 l 4866 4738 l 4844 4765 l 4823 4791 l 4800 4815 l 4777 4839 l 4753 4862 l 4729 4884 l 4704 4905 l 4678 4925 l 4652 4944 l 4626 4961 l 4599 4978 l 4571 4994 l 4544 5009 l 4516 5022 l 4489 5035 l 4461 5047 l 4433 5057 l 4405 5067 l 4378 5076 l 4351 5085 l 4323 5092 l 4296 5099 l 4269 5105 l 4243 5111 l 4216 5116 l 4189 5121 l 4163 5125 l 4134 5129 l 4105 5134 l 4075 5137 l 4045 5141 l 4014 5144 l 3983 5147 l 3951 5149 l 3918 5151 l 3885 5153 l 3852 5154 l 3817 5155 l 3783 5155 l 3748 5155 l 3713 5154 l 3678 5152 l 3644 5150 l 3609 5148 l 3575 5145 l 3541 5141 l 3508 5137 l 3475 5132 l 3443 5126 l 3411 5120 l 3381 5114 l 3351 5107 l 3322 5099 l 3294 5091 l 3266 5082 l 3239 5072 l 3213 5063 l 3186 5052 l 3160 5040 l 3135 5028 l 3109 5015 l 3083 5001 l 3058 4986 l 3033 4971 l 3007 4954 l 2982 4936 l 2957 4917 l 2932 4898 l 2908 4877 l 2884 4855 l 2860 4833 l 2837 4810 l 2814 4786 l 2792 4761 l 2771 4736 l 2751 4711 l 2732 4685 l 2713 4659 l 2696 4632 l 2679 4605 l 2663 4579 l 2649 4551 l 2635 4524 l 2622 4497 l 2610 4469 l 2598 4441 l 2588 4413 l 2578 4385 l 2569 4358 l 2561 4329 l 2553 4300 l 2546 4271 l 2539 4240 l 2533 4208 l 2527 4176 l 2522 4143 l 2518 4109 l 2514 4074 l 2510 4039 l 2507 4003 l 2505 3967 l 2504 3930 l 2503 3893 l 2502 3856 l 2503 3819 l 2504 3782 l 2505 3745 l 2507 3708 l 2510 3672 l 2513 3636 l 2516 3600 l 2521 3566 l 2525 3532 l 2530 3498 l 2536 3465 l 2542 3432 l 2548 3400 l 2555 3369 l 2563 3338 l 2571 3304 l 2580 3271 l 2589 3238 l 2599 3205 l 2610 3172 l 2621 3138 l 2633 3105 l 2646 3071 l 2659 3038 l 2673 3004 l 2687 2971 l 2702 2937 l 2718 2904 l 2733 2872 l 2750 2840 l 2766 2809 l 2783 2779 l 2800 2749 l 2817 2721 l 2834 2694 l 2851 2668 l 2868 2643 l 2885 2619 l 2902 2597 l 2919 2575 l 2935 2556 l 2952 2537 l 2968 2519 l 2984 2503 l 3000 2488 l 3017 2472 l 3034 2458 l 3052 2444 l 3069 2432 l 3087 2421 l 3105 2410 l 3123 2401 l 3141 2393 l 3160 2386 l 3178 2380 l 3196 2376 l 3215 2373 l 3233 2371 l 3250 2370 l 3268 2371 l 3285 2373 l 3301 2376 l 3317 2380 l 3332 2386 l 3347 2393 l 3361 2401 l 3374 2410 l 3386 2421 l 3398 2432 l 3409 2444 l 3419 2458 l 3429 2472 l 3438 2488 l 3446 2504 l 3453 2522 l 3461 2541 l 3467 2562 l 3473 2585 l 3479 2610 l 3484 2638 l 3488 2667 l 3493 2700 l 3497 2735 l 3500 2773 l 3504 2814 l 3507 2858 l 3510 2903 l 3513 2950 l 3515 2998 l 3517 3046 l 3519 3092 l 3520 3136 l 3522 3176 l 3523 3211 l 3524 3241 l 3524 3264 l 3525 3280 l 3525 3291 l 3525 3297 l 3525 3300 l gs col0 s gr % Polyline n 9675 4800 m 9675 4798 l 9675 4793 l 9675 4784 l 9675 4771 l 9675 4752 l 9674 4728 l 9674 4698 l 9674 4664 l 9674 4625 l 9673 4583 l 9673 4539 l 9672 4493 l 9671 4447 l 9671 4401 l 9670 4356 l 9669 4312 l 9668 4270 l 9667 4229 l 9666 4190 l 9665 4153 l 9664 4117 l 9663 4083 l 9661 4050 l 9660 4017 l 9658 3986 l 9656 3955 l 9654 3924 l 9652 3893 l 9650 3863 l 9648 3833 l 9645 3804 l 9643 3774 l 9640 3744 l 9637 3713 l 9634 3682 l 9631 3650 l 9628 3617 l 9624 3584 l 9620 3550 l 9616 3516 l 9612 3482 l 9607 3447 l 9603 3413 l 9598 3378 l 9593 3343 l 9588 3308 l 9583 3273 l 9577 3239 l 9572 3205 l 9566 3172 l 9561 3139 l 9555 3107 l 9549 3075 l 9543 3045 l 9537 3015 l 9531 2986 l 9525 2957 l 9519 2930 l 9513 2902 l 9506 2876 l 9500 2850 l 9492 2819 l 9484 2787 l 9475 2757 l 9466 2726 l 9457 2695 l 9447 2665 l 9437 2634 l 9426 2604 l 9415 2573 l 9404 2543 l 9392 2513 l 9380 2484 l 9368 2455 l 9356 2426 l 9343 2399 l 9330 2372 l 9317 2346 l 9304 2320 l 9291 2296 l 9278 2273 l 9265 2250 l 9252 2229 l 9239 2208 l 9226 2188 l 9213 2169 l 9200 2150 l 9186 2130 l 9171 2111 l 9155 2091 l 9139 2072 l 9123 2053 l 9105 2034 l 9087 2015 l 9068 1997 l 9048 1978 l 9028 1960 l 9006 1942 l 8984 1925 l 8962 1908 l 8939 1891 l 8915 1875 l 8891 1860 l 8867 1846 l 8842 1832 l 8817 1819 l 8792 1806 l 8766 1795 l 8741 1783 l 8714 1773 l 8688 1763 l 8665 1755 l 8643 1747 l 8619 1739 l 8595 1732 l 8570 1725 l 8544 1717 l 8517 1710 l 8489 1703 l 8461 1696 l 8431 1690 l 8401 1683 l 8369 1677 l 8337 1671 l 8305 1664 l 8272 1659 l 8238 1653 l 8205 1648 l 8171 1643 l 8137 1638 l 8103 1633 l 8069 1629 l 8036 1625 l 8002 1621 l 7969 1617 l 7936 1614 l 7904 1611 l 7871 1608 l 7839 1605 l 7807 1602 l 7775 1600 l 7745 1598 l 7714 1596 l 7684 1594 l 7652 1592 l 7620 1591 l 7587 1589 l 7552 1588 l 7516 1587 l 7478 1586 l 7439 1585 l 7397 1583 l 7354 1583 l 7309 1582 l 7261 1581 l 7212 1580 l 7161 1579 l 7109 1579 l 7057 1578 l 7005 1577 l 6954 1577 l 6905 1577 l 6860 1576 l 6818 1576 l 6781 1576 l 6750 1575 l 6725 1575 l 6705 1575 l 6691 1575 l 6682 1575 l 6677 1575 l 6675 1575 l gs col0 s gr % Polyline n 6150 1575 m 6148 1575 l 6142 1575 l 6132 1575 l 6118 1576 l 6097 1576 l 6071 1577 l 6041 1577 l 6006 1578 l 5969 1579 l 5929 1581 l 5889 1582 l 5849 1584 l 5810 1585 l 5772 1587 l 5736 1589 l 5701 1592 l 5668 1594 l 5636 1597 l 5606 1600 l 5576 1603 l 5548 1607 l 5520 1611 l 5493 1615 l 5465 1620 l 5438 1625 l 5412 1630 l 5385 1636 l 5358 1641 l 5331 1648 l 5303 1655 l 5275 1662 l 5246 1670 l 5216 1679 l 5187 1688 l 5156 1698 l 5126 1708 l 5095 1719 l 5064 1730 l 5034 1742 l 5003 1755 l 4973 1768 l 4944 1781 l 4915 1795 l 4887 1809 l 4860 1824 l 4833 1839 l 4808 1854 l 4783 1869 l 4760 1884 l 4737 1900 l 4716 1917 l 4695 1933 l 4675 1950 l 4654 1969 l 4634 1988 l 4615 2009 l 4595 2030 l 4577 2052 l 4559 2075 l 4541 2099 l 4524 2124 l 4507 2149 l 4491 2176 l 4475 2203 l 4460 2231 l 4446 2259 l 4432 2287 l 4419 2316 l 4407 2344 l 4396 2373 l 4385 2401 l 4375 2429 l 4366 2456 l 4358 2483 l 4350 2510 l 4343 2536 l 4336 2562 l 4330 2587 l 4325 2613 l 4320 2638 l 4315 2663 l 4311 2688 l 4307 2714 l 4303 2741 l 4300 2768 l 4297 2797 l 4294 2827 l 4292 2859 l 4289 2893 l 4287 2928 l 4285 2965 l 4284 3004 l 4282 3043 l 4281 3082 l 4279 3121 l 4278 3158 l 4277 3192 l 4277 3222 l 4276 3248 l 4276 3268 l 4275 3283 l 4275 3292 l 4275 3298 l 4275 3300 l gs col0 s gr /Symbol ff 600.00 scf sf 3600 3900 m gs 1 -1 sc (Y) col0 sh gr % Polyline gs clippath 6405 843 m 6495 411 l 6585 843 l 6585 285 l 6405 285 l cp clip n 6495 330 m 6495 3150 l gs col0 s gr gr % arrowhead n 6405 843 m 6495 411 l 6585 843 l 6495 771 l 6405 843 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 7515 2637 m 7425 3069 l 7335 2637 l 7335 3195 l 7515 3195 l cp clip n 7425 2175 m 7425 3150 l gs col0 s gr gr % arrowhead n 7515 2637 m 7425 3069 l 7335 2637 l 7425 2709 l 7515 2637 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 6435 4713 m 6525 4281 l 6615 4713 l 6615 4155 l 6435 4155 l cp clip n 6525 4200 m 6525 6000 l gs col0 s gr gr % arrowhead n 6435 4713 m 6525 4281 l 6615 4713 l 6525 4641 l 6435 4713 l cp gs 0.00 setgray ef gr col0 s % Polyline n 3825 300 m 3825 3300 l gs col0 s gr % Polyline gs clippath 7515 4362 m 7425 4794 l 7335 4362 l 7335 4920 l 7515 4920 l cp clip n 7425 4650 m 7425 4875 l gs col0 s gr gr % arrowhead n 7515 4362 m 7425 4794 l 7335 4362 l 7425 4434 l 7515 4362 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 9585 4713 m 9675 4281 l 9765 4713 l 9765 4155 l 9585 4155 l cp clip n 9675 4200 m 9675 6000 l gs col0 s gr gr % arrowhead n 9585 4713 m 9675 4281 l 9765 4713 l 9675 4641 l 9585 4713 l cp gs 0.00 setgray ef gr col0 s /Times-Italic ff 600.00 scf sf 6585 3840 m gs 1 -1 sc (S) col0 sh gr % Polyline n 7425 375 m 7425 1350 l gs col0 s gr /Times-Italic ff 600.00 scf sf 8025 5325 m gs 1 -1 sc (i) col0 sh gr % Polyline n 7425 4200 m 7425 4203 l 7425 4208 l 7425 4219 l 7426 4235 l 7426 4257 l 7427 4286 l 7428 4322 l 7430 4362 l 7431 4408 l 7433 4456 l 7436 4508 l 7438 4560 l 7441 4613 l 7444 4664 l 7448 4715 l 7452 4763 l 7456 4809 l 7460 4852 l 7465 4892 l 7470 4930 l 7475 4965 l 7481 4998 l 7487 5029 l 7494 5057 l 7502 5083 l 7510 5108 l 7518 5132 l 7528 5154 l 7538 5175 l 7550 5198 l 7563 5220 l 7578 5242 l 7593 5262 l 7609 5281 l 7627 5300 l 7646 5318 l 7666 5334 l 7687 5350 l 7709 5365 l 7732 5379 l 7755 5391 l 7780 5403 l 7805 5413 l 7830 5422 l 7856 5430 l 7882 5437 l 7908 5443 l 7934 5447 l 7960 5450 l 7986 5453 l 8012 5454 l 8037 5454 l 8062 5454 l 8087 5452 l 8113 5450 l 8138 5447 l 8163 5443 l 8189 5438 l 8215 5433 l 8241 5426 l 8268 5419 l 8296 5411 l 8323 5401 l 8351 5391 l 8379 5380 l 8406 5368 l 8434 5355 l 8461 5342 l 8488 5327 l 8514 5313 l 8540 5297 l 8564 5281 l 8588 5265 l 8610 5248 l 8632 5231 l 8652 5214 l 8671 5197 l 8690 5179 l 8707 5161 l 8722 5143 l 8738 5125 l 8751 5108 l 8763 5090 l 8775 5071 l 8786 5052 l 8797 5032 l 8807 5011 l 8817 4990 l 8826 4967 l 8835 4943 l 8843 4918 l 8850 4893 l 8857 4866 l 8864 4838 l 8870 4810 l 8876 4780 l 8881 4750 l 8886 4720 l 8890 4688 l 8893 4657 l 8897 4624 l 8900 4592 l 8902 4559 l 8905 4525 l 8907 4491 l 8908 4457 l 8910 4422 l 8911 4386 l 8913 4350 l 8913 4321 l 8914 4291 l 8915 4261 l 8916 4230 l 8917 4198 l 8917 4165 l 8918 4131 l 8918 4096 l 8919 4060 l 8919 4024 l 8919 3986 l 8919 3948 l 8919 3910 l 8919 3870 l 8919 3830 l 8919 3790 l 8919 3750 l 8918 3709 l 8917 3668 l 8917 3628 l 8916 3587 l 8915 3547 l 8914 3507 l 8912 3468 l 8911 3429 l 8909 3391 l 8908 3353 l 8906 3316 l 8904 3280 l 8902 3245 l 8900 3211 l 8898 3177 l 8895 3144 l 8893 3112 l 8890 3081 l 8888 3050 l 8884 3011 l 8880 2973 l 8875 2935 l 8870 2898 l 8865 2861 l 8860 2824 l 8854 2787 l 8847 2751 l 8841 2716 l 8833 2680 l 8826 2645 l 8818 2611 l 8809 2578 l 8800 2545 l 8791 2514 l 8782 2483 l 8772 2454 l 8762 2426 l 8751 2399 l 8741 2373 l 8730 2349 l 8719 2326 l 8708 2304 l 8697 2284 l 8686 2264 l 8674 2246 l 8662 2229 l 8650 2213 l 8637 2196 l 8623 2180 l 8608 2164 l 8593 2150 l 8576 2136 l 8559 2122 l 8541 2109 l 8521 2097 l 8501 2085 l 8479 2074 l 8457 2063 l 8433 2053 l 8408 2044 l 8382 2035 l 8355 2027 l 8328 2020 l 8299 2013 l 8270 2007 l 8241 2001 l 8210 1996 l 8179 1992 l 8147 1988 l 8115 1984 l 8082 1981 l 8048 1978 l 8013 1975 l 7986 1973 l 7959 1971 l 7932 1970 l 7903 1968 l 7872 1967 l 7841 1965 l 7807 1964 l 7772 1963 l 7735 1962 l 7696 1961 l 7655 1960 l 7611 1959 l 7565 1958 l 7517 1957 l 7466 1956 l 7413 1956 l 7358 1955 l 7301 1954 l 7242 1954 l 7183 1953 l 7124 1953 l 7066 1952 l 7009 1952 l 6954 1951 l 6903 1951 l 6856 1951 l 6814 1951 l 6777 1950 l 6746 1950 l 6722 1950 l 6703 1950 l 6690 1950 l 6682 1950 l 6677 1950 l 6675 1950 l gs col0 s gr /Times-Italic ff 450.00 scf sf 6900 3975 m gs 1 -1 sc (ki) col0 sh gr % Polyline n 6255 3150 m 7605 3150 l 7605 4230 l 6255 4230 l cp gs col0 s gr % Polyline n 3274 3300 m 4474 3300 l 4474 4050 l 3274 4050 l cp gs col0 s gr /Times-Italic ff 600.00 scf sf 6075 5325 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 6000 1125 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 7725 1125 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 4050 1125 m gs 1 -1 sc (B) col0 sh gr /Times-Italic ff 600.00 scf sf 9975 5325 m gs 1 -1 sc (j) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 2039 2994 a FJ(:)2018 3041 y FQ(=)2152 3391 y @beginspecial 0 @llx 0 @lly 78 @urx 84 @ury 780 @rwi @setspecial %%BeginDocument: figures/g1n2rel2f2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2rel2f2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Wed Jun 9 17:17:56 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 78 84 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2400 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -88.0 87.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7033 m -1000 -1000 l 12526 -1000 l 12526 7033 l cp clip 0.01440 0.01440 sc /Symbol ff 600.00 scf sf 8250 5625 m gs 1 -1 sc (Y) col0 sh gr /Times-Italic ff 600.00 scf sf 10245 4140 m gs 1 -1 sc (S) col0 sh gr /Times-Italic ff 450.00 scf sf 10575 4275 m gs 1 -1 sc (kj) col0 sh gr % Polyline 30.000 slw n 9840 3450 m 11190 3450 l 11190 4530 l 9840 4530 l cp gs col0 s gr % Polyline n 8400 300 m 8400 5010 l gs col0 s gr % Polyline gs clippath 10080 813 m 10170 381 l 10260 813 l 10260 255 l 10080 255 l cp clip n 10170 300 m 10170 3450 l gs col0 s gr gr % arrowhead n 10080 813 m 10170 381 l 10260 813 l 10170 741 l 10080 813 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 9537 4648 m 9973 4587 l 9597 4817 l 10123 4630 l 10062 4460 l cp clip n 10050 4560 m 8790 5010 l gs col0 s gr gr % arrowhead n 9537 4648 m 9973 4587 l 9597 4817 l 9635 4708 l 9537 4648 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 11100 5487 m 11010 5919 l 10920 5487 l 10920 6045 l 11100 6045 l cp clip n 11010 4530 m 11010 6000 l gs col0 s gr gr % arrowhead n 11100 5487 m 11010 5919 l 10920 5487 l 11010 5559 l 11100 5487 l cp gs 0.00 setgray ef gr col0 s % Polyline n 7849 5025 m 9049 5025 l 9049 5775 l 7849 5775 l cp gs col0 s gr % Polyline gs clippath 11115 2937 m 11025 3369 l 10935 2937 l 10935 3495 l 11115 3495 l cp clip n 11025 300 m 11025 3450 l gs col0 s gr gr % arrowhead n 11115 2937 m 11025 3369 l 10935 2937 l 11025 3009 l 11115 2937 l cp gs 0.00 setgray ef gr col0 s /Times-Italic ff 600.00 scf sf 8625 1050 m gs 1 -1 sc (B) col0 sh gr % Polyline gs clippath 6435 5868 m 6525 5436 l 6615 5868 l 6615 5310 l 6435 5310 l cp clip n 6525 5775 m 6525 5355 l gs col0 s gr gr % arrowhead n 6435 5868 m 6525 5436 l 6615 5868 l 6525 5796 l 6435 5868 l cp gs 0.00 setgray ef gr col0 s % Polyline n 6525 6000 m 6525 5997 l 6525 5992 l 6525 5981 l 6525 5965 l 6525 5943 l 6526 5915 l 6526 5883 l 6527 5846 l 6527 5806 l 6528 5765 l 6528 5723 l 6529 5682 l 6530 5641 l 6531 5603 l 6532 5566 l 6533 5532 l 6535 5499 l 6536 5469 l 6538 5441 l 6539 5415 l 6541 5390 l 6543 5366 l 6545 5343 l 6547 5321 l 6550 5300 l 6553 5275 l 6557 5251 l 6561 5226 l 6565 5202 l 6570 5178 l 6575 5154 l 6581 5129 l 6587 5105 l 6593 5080 l 6600 5056 l 6607 5032 l 6614 5008 l 6622 4985 l 6630 4962 l 6638 4940 l 6647 4918 l 6655 4897 l 6664 4877 l 6673 4857 l 6682 4838 l 6691 4819 l 6700 4800 l 6710 4781 l 6719 4762 l 6730 4743 l 6741 4724 l 6753 4704 l 6765 4684 l 6779 4664 l 6793 4644 l 6808 4624 l 6824 4603 l 6841 4584 l 6858 4564 l 6876 4545 l 6895 4527 l 6914 4510 l 6934 4493 l 6954 4477 l 6975 4463 l 6996 4449 l 7017 4436 l 7040 4424 l 7063 4413 l 7084 4403 l 7107 4394 l 7131 4385 l 7156 4377 l 7182 4369 l 7209 4361 l 7237 4355 l 7265 4348 l 7295 4343 l 7325 4338 l 7355 4333 l 7385 4329 l 7415 4326 l 7445 4324 l 7475 4322 l 7503 4321 l 7531 4321 l 7558 4321 l 7584 4322 l 7608 4323 l 7632 4325 l 7654 4328 l 7675 4331 l 7695 4335 l 7718 4340 l 7739 4346 l 7760 4353 l 7780 4361 l 7799 4370 l 7817 4380 l 7834 4391 l 7851 4403 l 7866 4416 l 7881 4430 l 7895 4444 l 7907 4459 l 7919 4475 l 7930 4491 l 7940 4507 l 7949 4523 l 7958 4540 l 7966 4556 l 7973 4573 l 7980 4590 l 7987 4607 l 7993 4625 l 8000 4644 l 8007 4665 l 8013 4687 l 8020 4710 l 8028 4736 l 8035 4765 l 8043 4795 l 8052 4828 l 8060 4861 l 8069 4895 l 8076 4927 l 8084 4957 l 8090 4982 l 8094 5001 l 8097 5014 l 8099 5022 l 8100 5025 l gs col0 s gr /Times-Italic ff 600.00 scf sf 9600 5325 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 11325 5325 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 6150 5325 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 9600 1050 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 11250 1050 m gs 1 -1 sc (k) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 2848 3041 a FJ(;)605 3516 y FQ(and)g(then)i(cancel)e (\011,)g(to)g(get:)1151 4379 y @beginspecial 0 @llx 0 @lly 96 @urx 83 @ury 960 @rwi @setspecial %%BeginDocument: figures/g1n2rel2e3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2rel2e3.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Wed Jun 9 17:37:31 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 96 83 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2400 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -51.0 87.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7033 m -1000 -1000 l 11144 -1000 l 11144 7033 l cp clip 0.01440 0.01440 sc % Polyline 30.000 slw n 6150 1575 m 6147 1575 l 6140 1575 l 6128 1575 l 6110 1575 l 6086 1575 l 6056 1575 l 6020 1574 l 5981 1574 l 5940 1574 l 5898 1573 l 5856 1573 l 5815 1572 l 5775 1572 l 5738 1571 l 5703 1571 l 5670 1570 l 5638 1569 l 5609 1568 l 5580 1567 l 5553 1566 l 5527 1565 l 5501 1564 l 5475 1563 l 5451 1561 l 5427 1560 l 5403 1558 l 5379 1556 l 5354 1553 l 5329 1550 l 5304 1547 l 5279 1543 l 5253 1538 l 5228 1533 l 5203 1526 l 5178 1519 l 5153 1512 l 5129 1503 l 5106 1493 l 5083 1483 l 5061 1471 l 5040 1459 l 5021 1445 l 5002 1431 l 4984 1416 l 4968 1400 l 4952 1383 l 4938 1365 l 4925 1345 l 4913 1325 l 4903 1306 l 4893 1286 l 4885 1265 l 4877 1241 l 4869 1217 l 4862 1190 l 4856 1161 l 4850 1129 l 4845 1095 l 4840 1059 l 4835 1019 l 4831 977 l 4827 932 l 4823 885 l 4819 835 l 4816 784 l 4813 732 l 4811 680 l 4808 630 l 4806 581 l 4805 536 l 4803 496 l 4802 461 l 4801 432 l 4801 410 l 4800 394 l 4800 383 l 4800 378 l 4800 375 l gs col0 s gr % Polyline n 9675 4800 m 9675 4798 l 9675 4793 l 9675 4784 l 9675 4771 l 9675 4752 l 9674 4728 l 9674 4698 l 9674 4664 l 9674 4625 l 9673 4583 l 9673 4539 l 9672 4493 l 9671 4447 l 9671 4401 l 9670 4356 l 9669 4312 l 9668 4270 l 9667 4229 l 9666 4190 l 9665 4153 l 9664 4117 l 9663 4083 l 9661 4050 l 9660 4017 l 9658 3986 l 9656 3955 l 9654 3924 l 9652 3893 l 9650 3863 l 9648 3833 l 9645 3804 l 9643 3774 l 9640 3744 l 9637 3713 l 9634 3682 l 9631 3650 l 9628 3617 l 9624 3584 l 9620 3550 l 9616 3516 l 9612 3482 l 9607 3447 l 9603 3413 l 9598 3378 l 9593 3343 l 9588 3308 l 9583 3273 l 9577 3239 l 9572 3205 l 9566 3172 l 9561 3139 l 9555 3107 l 9549 3075 l 9543 3045 l 9537 3015 l 9531 2986 l 9525 2957 l 9519 2930 l 9513 2902 l 9506 2876 l 9500 2850 l 9492 2819 l 9484 2787 l 9475 2757 l 9466 2726 l 9457 2695 l 9447 2665 l 9437 2634 l 9426 2604 l 9415 2573 l 9404 2543 l 9392 2513 l 9380 2484 l 9368 2455 l 9356 2426 l 9343 2399 l 9330 2372 l 9317 2346 l 9304 2320 l 9291 2296 l 9278 2273 l 9265 2250 l 9252 2229 l 9239 2208 l 9226 2188 l 9213 2169 l 9200 2150 l 9186 2130 l 9171 2111 l 9155 2091 l 9139 2072 l 9123 2053 l 9105 2034 l 9087 2015 l 9068 1997 l 9048 1978 l 9028 1960 l 9006 1942 l 8984 1925 l 8962 1908 l 8939 1891 l 8915 1875 l 8891 1860 l 8867 1846 l 8842 1832 l 8817 1819 l 8792 1806 l 8766 1795 l 8741 1783 l 8714 1773 l 8688 1763 l 8665 1755 l 8643 1747 l 8619 1739 l 8595 1732 l 8570 1725 l 8544 1717 l 8517 1710 l 8489 1703 l 8461 1696 l 8431 1690 l 8401 1683 l 8369 1677 l 8337 1671 l 8305 1664 l 8272 1659 l 8238 1653 l 8205 1648 l 8171 1643 l 8137 1638 l 8103 1633 l 8069 1629 l 8036 1625 l 8002 1621 l 7969 1617 l 7936 1614 l 7904 1611 l 7871 1608 l 7839 1605 l 7807 1602 l 7775 1600 l 7745 1598 l 7714 1596 l 7684 1594 l 7652 1592 l 7620 1591 l 7587 1589 l 7552 1588 l 7516 1587 l 7478 1586 l 7439 1585 l 7397 1583 l 7354 1583 l 7309 1582 l 7261 1581 l 7212 1580 l 7161 1579 l 7109 1579 l 7057 1578 l 7005 1577 l 6954 1577 l 6905 1577 l 6860 1576 l 6818 1576 l 6781 1576 l 6750 1575 l 6725 1575 l 6705 1575 l 6691 1575 l 6682 1575 l 6677 1575 l 6675 1575 l gs col0 s gr % Polyline n 6225 1950 m 6223 1950 l 6218 1950 l 6209 1950 l 6196 1950 l 6178 1950 l 6156 1950 l 6129 1950 l 6100 1950 l 6068 1950 l 6035 1950 l 6001 1950 l 5967 1950 l 5934 1950 l 5901 1950 l 5870 1950 l 5838 1950 l 5807 1950 l 5776 1950 l 5745 1950 l 5714 1950 l 5681 1950 l 5648 1950 l 5613 1950 l 5585 1950 l 5557 1950 l 5528 1950 l 5498 1950 l 5466 1950 l 5434 1949 l 5401 1949 l 5366 1948 l 5331 1947 l 5295 1946 l 5258 1944 l 5220 1943 l 5182 1941 l 5144 1938 l 5105 1936 l 5066 1933 l 5027 1929 l 4989 1925 l 4951 1921 l 4913 1916 l 4876 1911 l 4840 1906 l 4805 1900 l 4771 1893 l 4737 1887 l 4705 1879 l 4675 1872 l 4645 1863 l 4616 1855 l 4589 1845 l 4563 1835 l 4538 1825 l 4510 1812 l 4483 1799 l 4458 1784 l 4433 1768 l 4409 1752 l 4387 1734 l 4364 1715 l 4343 1695 l 4323 1674 l 4303 1652 l 4284 1629 l 4266 1606 l 4249 1581 l 4233 1556 l 4218 1530 l 4204 1504 l 4190 1478 l 4178 1451 l 4167 1424 l 4157 1397 l 4147 1370 l 4138 1344 l 4130 1317 l 4123 1291 l 4117 1265 l 4111 1239 l 4105 1213 l 4100 1188 l 4095 1162 l 4091 1136 l 4087 1109 l 4083 1082 l 4080 1054 l 4076 1025 l 4074 995 l 4071 963 l 4068 929 l 4066 893 l 4064 856 l 4062 816 l 4060 775 l 4059 732 l 4057 689 l 4056 645 l 4055 601 l 4053 559 l 4053 520 l 4052 484 l 4051 453 l 4051 427 l 4050 407 l 4050 392 l 4050 383 l 4050 377 l 4050 375 l gs col0 s gr % Polyline n 6255 3150 m 7605 3150 l 7605 4230 l 6255 4230 l cp gs col0 s gr % Polyline gs clippath 6405 843 m 6495 411 l 6585 843 l 6585 285 l 6405 285 l cp clip n 6495 330 m 6495 3150 l gs col0 s gr gr % arrowhead n 6405 843 m 6495 411 l 6585 843 l 6495 771 l 6405 843 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 7515 2637 m 7425 3069 l 7335 2637 l 7335 3195 l 7515 3195 l cp clip n 7425 2175 m 7425 3150 l gs col0 s gr gr % arrowhead n 7515 2637 m 7425 3069 l 7335 2637 l 7425 2709 l 7515 2637 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 6435 4713 m 6525 4281 l 6615 4713 l 6615 4155 l 6435 4155 l cp clip n 6525 4200 m 6525 6000 l gs col0 s gr gr % arrowhead n 6435 4713 m 6525 4281 l 6615 4713 l 6525 4641 l 6435 4713 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 7515 4362 m 7425 4794 l 7335 4362 l 7335 4920 l 7515 4920 l cp clip n 7425 4650 m 7425 4875 l gs col0 s gr gr % arrowhead n 7515 4362 m 7425 4794 l 7335 4362 l 7425 4434 l 7515 4362 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 9585 4713 m 9675 4281 l 9765 4713 l 9765 4155 l 9585 4155 l cp clip n 9675 4200 m 9675 6000 l gs col0 s gr gr % arrowhead n 9585 4713 m 9675 4281 l 9765 4713 l 9675 4641 l 9585 4713 l cp gs 0.00 setgray ef gr col0 s % Polyline n 7425 375 m 7425 1350 l gs col0 s gr /Times-Italic ff 450.00 scf sf 6900 3975 m gs 1 -1 sc (ki) col0 sh gr % Polyline n 7425 4200 m 7425 4203 l 7425 4208 l 7425 4219 l 7426 4235 l 7426 4257 l 7427 4286 l 7428 4322 l 7430 4362 l 7431 4408 l 7433 4456 l 7436 4508 l 7438 4560 l 7441 4613 l 7444 4664 l 7448 4715 l 7452 4763 l 7456 4809 l 7460 4852 l 7465 4892 l 7470 4930 l 7475 4965 l 7481 4998 l 7487 5029 l 7494 5057 l 7502 5083 l 7510 5108 l 7518 5132 l 7528 5154 l 7538 5175 l 7550 5198 l 7563 5220 l 7578 5242 l 7593 5262 l 7609 5281 l 7627 5300 l 7646 5318 l 7666 5334 l 7687 5350 l 7709 5365 l 7732 5379 l 7755 5391 l 7780 5403 l 7805 5413 l 7830 5422 l 7856 5430 l 7882 5437 l 7908 5443 l 7934 5447 l 7960 5450 l 7986 5453 l 8012 5454 l 8037 5454 l 8062 5454 l 8087 5452 l 8113 5450 l 8138 5447 l 8163 5443 l 8189 5438 l 8215 5433 l 8241 5426 l 8268 5419 l 8296 5411 l 8323 5401 l 8351 5391 l 8379 5380 l 8406 5368 l 8434 5355 l 8461 5342 l 8488 5327 l 8514 5313 l 8540 5297 l 8564 5281 l 8588 5265 l 8610 5248 l 8632 5231 l 8652 5214 l 8671 5197 l 8690 5179 l 8707 5161 l 8722 5143 l 8738 5125 l 8751 5108 l 8763 5090 l 8775 5071 l 8786 5052 l 8797 5032 l 8807 5011 l 8817 4990 l 8826 4967 l 8835 4943 l 8843 4918 l 8850 4893 l 8857 4866 l 8864 4838 l 8870 4810 l 8876 4780 l 8881 4750 l 8886 4720 l 8890 4688 l 8893 4657 l 8897 4624 l 8900 4592 l 8902 4559 l 8905 4525 l 8907 4491 l 8908 4457 l 8910 4422 l 8911 4386 l 8913 4350 l 8913 4321 l 8914 4291 l 8915 4261 l 8916 4230 l 8917 4198 l 8917 4165 l 8918 4131 l 8918 4096 l 8919 4060 l 8919 4024 l 8919 3986 l 8919 3948 l 8919 3910 l 8919 3870 l 8919 3830 l 8919 3790 l 8919 3750 l 8918 3709 l 8917 3668 l 8917 3628 l 8916 3587 l 8915 3547 l 8914 3507 l 8912 3468 l 8911 3429 l 8909 3391 l 8908 3353 l 8906 3316 l 8904 3280 l 8902 3245 l 8900 3211 l 8898 3177 l 8895 3144 l 8893 3112 l 8890 3081 l 8888 3050 l 8884 3011 l 8880 2973 l 8875 2935 l 8870 2898 l 8865 2861 l 8860 2824 l 8854 2787 l 8847 2751 l 8841 2716 l 8833 2680 l 8826 2645 l 8818 2611 l 8809 2578 l 8800 2545 l 8791 2514 l 8782 2483 l 8772 2454 l 8762 2426 l 8751 2399 l 8741 2373 l 8730 2349 l 8719 2326 l 8708 2304 l 8697 2284 l 8686 2264 l 8674 2246 l 8662 2229 l 8650 2213 l 8637 2196 l 8623 2180 l 8608 2164 l 8593 2150 l 8576 2136 l 8559 2122 l 8541 2109 l 8521 2097 l 8501 2085 l 8479 2074 l 8457 2063 l 8433 2053 l 8408 2044 l 8382 2035 l 8355 2027 l 8328 2020 l 8299 2013 l 8270 2007 l 8241 2001 l 8210 1996 l 8179 1992 l 8147 1988 l 8115 1984 l 8082 1981 l 8048 1978 l 8013 1975 l 7986 1973 l 7959 1971 l 7932 1970 l 7903 1968 l 7872 1967 l 7841 1965 l 7807 1964 l 7772 1963 l 7735 1962 l 7696 1961 l 7655 1960 l 7611 1959 l 7565 1958 l 7517 1957 l 7466 1956 l 7413 1956 l 7358 1955 l 7301 1954 l 7242 1954 l 7183 1953 l 7124 1953 l 7066 1952 l 7009 1952 l 6954 1951 l 6903 1951 l 6856 1951 l 6814 1951 l 6777 1950 l 6746 1950 l 6722 1950 l 6703 1950 l 6690 1950 l 6682 1950 l 6677 1950 l 6675 1950 l gs col0 s gr /Times-Italic ff 600.00 scf sf 5175 1125 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 6585 3840 m gs 1 -1 sc (S) col0 sh gr /Times-Italic ff 600.00 scf sf 6075 5325 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 6000 1125 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 7725 1125 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 9975 5325 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 8025 5325 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 3600 1125 m gs 1 -1 sc (i) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 2041 3986 a FJ(:)2021 4033 y FQ(=)2154 4383 y @beginspecial 0 @llx 0 @lly 63 @urx 84 @ury 630 @rwi @setspecial %%BeginDocument: figures/g1n2rel2f3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: g1n2rel2f3.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Wed Jun 9 17:51:21 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 63 84 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2400 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -103.0 87.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7033 m -1000 -1000 l 12526 -1000 l 12526 7033 l cp clip 0.01440 0.01440 sc % Polyline 30.000 slw n 8475 5025 m 8475 5028 l 8476 5035 l 8476 5048 l 8477 5065 l 8479 5085 l 8481 5108 l 8484 5132 l 8487 5155 l 8490 5177 l 8494 5199 l 8499 5219 l 8504 5239 l 8510 5259 l 8517 5279 l 8525 5300 l 8532 5316 l 8539 5332 l 8547 5350 l 8555 5368 l 8565 5386 l 8576 5406 l 8587 5425 l 8600 5446 l 8614 5466 l 8628 5487 l 8644 5507 l 8661 5528 l 8678 5548 l 8696 5567 l 8715 5585 l 8734 5603 l 8754 5620 l 8775 5635 l 8796 5650 l 8817 5664 l 8840 5676 l 8863 5688 l 8884 5697 l 8907 5706 l 8931 5714 l 8956 5722 l 8982 5728 l 9009 5734 l 9038 5739 l 9067 5744 l 9097 5747 l 9128 5750 l 9159 5752 l 9191 5752 l 9223 5752 l 9255 5752 l 9286 5750 l 9317 5747 l 9348 5744 l 9377 5740 l 9406 5735 l 9434 5729 l 9461 5723 l 9487 5716 l 9513 5708 l 9538 5700 l 9564 5690 l 9590 5680 l 9615 5668 l 9640 5655 l 9665 5642 l 9690 5627 l 9714 5612 l 9738 5596 l 9761 5579 l 9784 5561 l 9806 5543 l 9827 5525 l 9847 5506 l 9866 5488 l 9884 5469 l 9900 5451 l 9916 5433 l 9930 5416 l 9943 5399 l 9954 5382 l 9965 5366 l 9975 5350 l 9986 5331 l 9995 5312 l 10004 5294 l 10011 5274 l 10018 5254 l 10024 5233 l 10029 5210 l 10033 5186 l 10037 5160 l 10040 5134 l 10043 5108 l 10046 5084 l 10047 5063 l 10049 5046 l 10049 5035 l 10050 5028 l 10050 5025 l gs col0 s gr % Polyline n 9840 3450 m 11190 3450 l 11190 4530 l 9840 4530 l cp gs col0 s gr % Polyline gs clippath 10080 813 m 10170 381 l 10260 813 l 10260 255 l 10080 255 l cp clip n 10170 300 m 10170 3450 l gs col0 s gr gr % arrowhead n 10080 813 m 10170 381 l 10260 813 l 10170 741 l 10080 813 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 9960 5013 m 10050 4581 l 10140 5013 l 10140 4455 l 9960 4455 l cp clip n 10050 4500 m 10050 5100 l gs col0 s gr gr % arrowhead n 9960 5013 m 10050 4581 l 10140 5013 l 10050 4941 l 9960 5013 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 11100 5487 m 11010 5919 l 10920 5487 l 10920 6045 l 11100 6045 l cp clip n 11010 4530 m 11010 6000 l gs col0 s gr gr % arrowhead n 11100 5487 m 11010 5919 l 10920 5487 l 11010 5559 l 11100 5487 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 11115 2937 m 11025 3369 l 10935 2937 l 10935 3495 l 11115 3495 l cp clip n 11025 300 m 11025 3450 l gs col0 s gr gr % arrowhead n 11115 2937 m 11025 3369 l 10935 2937 l 11025 3009 l 11115 2937 l cp gs 0.00 setgray ef gr col0 s % Polyline n 8475 300 m 8475 5100 l gs col0 s gr /Times-Italic ff 600.00 scf sf 10245 4140 m gs 1 -1 sc (S) col0 sh gr % Polyline n 7200 300 m 7200 6000 l gs col0 s gr /Times-Italic ff 600.00 scf sf 7350 1050 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 450.00 scf sf 10575 4275 m gs 1 -1 sc (kj) col0 sh gr /Times-Italic ff 600.00 scf sf 9600 5325 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 11325 5325 m gs 1 -1 sc (j) col0 sh gr /Times-Italic ff 600.00 scf sf 9600 1050 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 11250 1050 m gs 1 -1 sc (k) col0 sh gr /Times-Italic ff 600.00 scf sf 7350 5325 m gs 1 -1 sc (i) col0 sh gr /Times-Italic ff 600.00 scf sf 8775 1050 m gs 1 -1 sc (j) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 2725 4033 a FJ(:)605 4509 y FQ(F)-7 b(rom)27 b(this)h(it)g(is)g(easy)e(to)i(get)f(the)h(statemen)n(t)g(of)f(the)h (lemma.)p 3384 4509 4 57 v 3388 4456 50 4 v 3388 4509 V 3437 4509 4 57 v 605 4693 a FP(Cor)n(ollar)-6 b(y)33 b FQ(5.5.3)p FP(.)39 b FO(L)l(et)30 b FL(C)k FO(b)l(e)c(an)f(MTC)i (with)g FJ(p)2215 4663 y FM(+)2293 4693 y FQ(=)22 b FJ(p)2422 4663 y FE(\000)2478 4693 y FO(.)39 b(Denote)993 4852 y FJ(\034)9 b FQ(\()p FJ(g)s FQ(;)14 b FJ(W)1228 4864 y FM(1)1266 4852 y FJ(;)g(:)g(:)g(:)g(;)g(W)1529 4864 y FI(n)1574 4852 y FQ(\))23 b(=)g(Hom)1890 4864 y FE(C)1933 4852 y FQ(\()p FK(1)p FJ(;)14 b(H)2126 4818 y FE(\012)p FI(g)2235 4852 y FL(\012)k FJ(W)2396 4864 y FM(1)2452 4852 y FL(\012)g(\001)c(\001)g(\001)k(\012)g FJ(W)2811 4864 y FI(m)2875 4852 y FQ(\))456 5016 y FO(wher)l(e)33 b FJ(H)j FQ(=)891 4954 y Fy(L)997 5016 y FJ(V)1045 5028 y FI(i)1094 5016 y FL(\012)20 b FJ(V)1246 4986 y FE(\003)1227 5038 y FI(i)1284 5016 y FO(.)48 b(Then)34 b(we)f(have)h(an)f(action)h (of)f(the)g(pur)l(e)g(mapping)h(class)g(gr)l(oup)456 5116 y FQ(\000)508 5086 y FE(0)508 5136 y FI(g)r(;n)642 5116 y FO(on)h(this)g(sp)l(ac)l(e.)55 b(In)35 b(p)l(articular,)j(for)e FJ(g)f FQ(=)d(1)p FJ(;)14 b(n)32 b FQ(=)g(1)j FO(this)g(action)h(c)l (oincides)h(with)e(the)456 5216 y(one)30 b(de\014ne)l(d)g(in)g(The)l (or)l(em)g FQ(3.1.17)p FO(.)p eop %%Page: 120 28 120 123 bop 456 226 a FM(120)1010 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FQ(Indeed,)g(let)f FJ(\034)9 b FQ(\(\006\))29 b(b)r(e)g(the)f(mo) r(dular)g(functor)g(corresp)r(onding)e(to)i FL(C)5 b FQ(;)28 b(then)h(it)f(is)g(easy)g(to)456 525 y(see,)d(using)g(the)g (gluing)f(axiom,)h(that)h(if)f(\006)g(is)g(a)g(surface)f(of)h(gen)n(us) f FJ(g)k FQ(then)e FJ(\034)9 b FQ(\(\006;)14 b FJ(W)3066 537 y FM(1)3104 525 y FJ(;)g(:)g(:)g(:)g(;)g(W)3367 537 y FI(n)3412 525 y FQ(\))456 624 y(is)27 b(\(not)h(canonically\))f (isomorphic)f(to)h(the)h(space)f FJ(\034)9 b FQ(\()p FJ(g)s FQ(;)14 b FJ(W)2304 636 y FM(1)2342 624 y FJ(;)g(:)g(:)g(:)g(;)g (W)2605 636 y FI(n)2650 624 y FQ(\))28 b(de\014ned)g(ab)r(o)n(v)n(e.) 605 783 y FP(Remark)k FQ(5.5.4)p FP(.)39 b FQ(In)28 b(fact,)g (Corollary)d(5.5.3)h(also)h(holds)g(for)g(mo)r(dular)g(categories)e (with)456 883 y FJ(p)498 853 y FM(+)552 883 y FJ(=p)636 853 y FE(\000)726 883 y FL(6)p FQ(=)34 b(1)g(if)g(w)n(e)g(replace)f (the)i(w)n(ord)e(\\action")g(b)n(y)h(\\pro)5 b(jectiv)n(e)33 b(action".)55 b(This)35 b(will)f(b)r(e)456 983 y(discussed)27 b(in)h(Section)f(5.7.)605 1142 y FP(Exer)n(cise)32 b FQ(5.5.5)p FP(.)40 b FQ(Pro)n(v)n(e)33 b(the)k(follo)n(wing)e(form)n (ula)g(for)h(the)g(dimension)h(of)f(the)g(space)456 1241 y FJ(\034)9 b FQ(\()p FJ(g)s FQ(\))28 b(for)f FJ(g)f FL(\025)c FQ(1)28 b(\()p FJ(n)23 b FQ(=)f(0\):)1481 1459 y(dim)14 b FJ(\034)9 b FQ(\()p FJ(g)s FQ(\))24 b(=)1897 1380 y Fy(X)1906 1559 y FI(i)p FE(2)p FI(I)2031 1342 y Fy(\022)2131 1403 y FQ(1)p 2102 1440 100 4 v 2102 1516 a FJ(s)2141 1488 y FM(2)2141 1539 y(0)p FI(i)2211 1342 y Fy(\023)2272 1359 y FI(g)r FE(\000)p FM(1)2410 1459 y FJ(:)-1977 b FQ(\(5.5.5\))456 1731 y FO(Hint:)47 b FQ(Pro)n(v)n(e)31 b(that)j(dim)14 b FJ(\034)9 b FQ(\()p FJ(g)s FQ(\))33 b(=)g(tr\()p FJ(a)1692 1701 y FI(g)r FE(\000)p FM(1)1815 1731 y FQ(\),)j(where)d FJ(a)2196 1743 y FI(ij)2287 1731 y FQ(=)f(dim)14 b FJ(\034)9 b FQ(\()p FJ(g)37 b FQ(=)32 b(1;)14 b FJ(V)2914 1743 y FI(i)2942 1731 y FJ(;)g(V)3046 1701 y FE(\003)3027 1752 y FI(j)3084 1731 y FQ(\))p FJ(;)g(i;)g(j)37 b FL(2)c FJ(I)7 b FQ(.)456 1834 y(Then)26 b(pro)n(v)n(e)e(that)j FJ(a)c FQ(=)1227 1772 y Fy(P)1314 1859 y FI(k)1369 1834 y FJ(N)1436 1846 y FI(k)1476 1834 y FJ(N)1543 1846 y FI(k)1579 1830 y Fx(\003)1619 1834 y FQ(,)j(where)g FJ(N)1974 1846 y FI(k)2041 1834 y FQ(is)g(de\014ned)g(as)g(in)g(Prop)r(osition)f (3.1.12,)g(and)456 1934 y(use)i(the)h(V)-7 b(erlinde)28 b(form)n(ula)e(to)i(diagonalize)e FJ(a)p FQ(.)1432 2151 y FK(5.6.)46 b(T)-8 b(o)m(w)m(ers)33 b(of)e(group)s(oids)605 2301 y FQ(Lo)r(oking)26 b(at)h(the)g(previous)f(t)n(w)n(o)g(sections,)g (one)h(is)g(tempted)h(to)e(sa)n(y)g(that)h(there)g(is)g(some)456 2400 y(\\univ)n(ersal")32 b(set)j(of)f(relations)g(whic)n(h)h(m)n(ust)f (hold)h(in)g(an)n(y)f(w)n(eakly)f(ribb)r(on)i(category)-7 b(,)35 b(and)456 2500 y(these)29 b(relations)f(happ)r(en)h(to)h (coincide)e(with)i(the)g(relations)e(for)h(the)g(mapping)g(class)g (group.)456 2599 y(In)d(this)h(section)g(w)n(e)f(sk)n(etc)n(h)g(the)h (appropriate)e(language)g(in)i(whic)n(h)g(one)f(can)g(form)n(ulate)g (this)456 2699 y(and)j(other)g(related)h(results.)42 b(Therefore,)29 b(w)n(e)h(do)f(not)h(really)f(pro)n(v)n(e)f(an)n(y)h (new)h(results)f(here,)456 2799 y(and)e(w)n(e)g(allo)n(w)g(ourselv)n (es)e(to)j(b)r(e)g(somewhat)f(informal.)605 2898 y(Let)33 b(us)f(start)g(b)n(y)g(considering)g(our)f(main)i(example:)46 b(the)33 b FO(T)-6 b(eichm)q(\177)-43 b(ul)t(ler)36 b(tower)42 b FL(T)7 b FJ(eich)p FQ(.)456 2998 y(By)20 b(de\014nition,)i FL(T)7 b FJ(eich)20 b FQ(is)g(a)g(category)f(with)i(ob)5 b(jects)19 b(all)i(extended)f(surfaces,)h(and)f(morphisms)456 3098 y(isotop)n(y)33 b(classes)g(of)h(homeomorphisms)f(of)h(extended)h (surfaces)e(\(see)i(De\014nition)g(5.1.7\(i\)\).)456 3197 y(This)30 b(category)f(is)i(a)f(group)r(oid,)g(i.e.,)i(an)n(y)e (morphism)g(in)h FL(T)7 b FJ(eich)30 b FQ(is)h(in)n(v)n(ertible.)45 b(It)31 b(also)f(has)456 3297 y(some)23 b(additional)g(structures)g (whic)n(h)g(pla)n(y)n(ed)g(an)g(imp)r(ortan)n(t)h(role)f(in)g(the)i (previous)d(sections:)456 3396 y(the)40 b(disjoin)n(t)g(union)g(and)g (gluing)g(of)g(surfaces.)73 b(The)40 b(general)f(de\014nition)h(of)g(a) g(to)n(w)n(er)f(of)456 3496 y(group)r(oids)26 b(will)i(b)r(e)g(mo)r (deled)f(on)h(this)g(example,)f(so)g(let)h(us)f(study)h(it)g(in)g(more) f(detail.)605 3596 y(T)-7 b(emp)r(orarily)g(,)26 b(let)i(us)g(denote)f FL(T)7 b FJ(eich)28 b FQ(b)n(y)f FL(T)21 b FQ(.)37 b(Belo)n(w)27 b(w)n(e)g(list)h(its)g(prop)r(erties.)605 3695 y(\(a\))g FL(T)49 b FQ(is)27 b(a)g(group)r(oid.)605 3795 y(\(b\))32 b(The)g(disjoin)n(t)f(union)g(of)h(surfaces)e FL(t)9 b FQ(:)30 b FL(T)42 b(\002)20 b(T)51 b(!)29 b(T)53 b FQ(and)31 b(the)h(empt)n(y)g(surface)e FL(;)f(2)456 3895 y FQ(Ob)13 b FL(T)49 b FQ(pro)n(vide)27 b FL(T)49 b FQ(with)28 b(the)g(structure)f(of)g(a)g(symmetric)h(tensor)e(category)-7 b(.)605 3994 y(\(c\))34 b(There)f(is)g(a)g(functor)h FJ(A)9 b FQ(:)30 b FL(T)54 b(!)33 b(S)6 b FJ(ets)p FQ(:)49 b(for)33 b(a)g(surface)f(\006,)j FJ(A)p FQ(\(\006\))f(=)e FJ(\031)2995 4006 y FM(0)3033 3994 y FQ(\()p FJ(@)5 b FQ(\006\))34 b(is)f(the)456 4094 y(set)26 b(of)f(its)i(b)r(oundary)e (comp)r(onen)n(ts.)36 b(Here)25 b FL(S)6 b FJ(ets)26 b FQ(is)g(the)g(group)r(oid)f(with)i(ob)5 b(jects)25 b(\014nite)i(sets,)456 4193 y(and)j(morphisms)f(bijections.)45 b(Note)30 b(that)h FJ(A)p FQ(\(\006)1995 4205 y FM(1)2053 4193 y FL(t)20 b FQ(\006)2188 4205 y FM(2)2225 4193 y FQ(\))28 b(=)f FJ(A)p FQ(\(\006)2531 4205 y FM(1)2569 4193 y FQ(\))20 b FL(t)h FJ(A)p FQ(\(\006)2851 4205 y FM(2)2889 4193 y FQ(\))30 b(and)g FJ(A)p FQ(\()p FL(;)p FQ(\))e(=)f FL(;)456 4293 y FQ(\(canonical)f(isomorphisms\).)36 b(In)28 b(other)f(w)n(ords,)f FJ(A)i FQ(is)g(a)f(tensor)f(functor.)605 4393 y(\(d\))j(There)e(is)h(a)g(gluing)g(op)r(eration:)36 b(for)28 b(ev)n(ery)f(surface)g(\006)d FL(2)g FQ(Ob)13 b FL(T)50 b FQ(and)28 b(an)g(unordered)456 4492 y(pair)21 b FJ(\013;)14 b(\014)27 b FL(2)d FJ(A)p FQ(\(\006\),)g(w)n(e)d(ha)n(v)n (e)f(the)i(surface)f FJ(G)1874 4504 y FI(\013;\014)1982 4492 y FQ(\(\006\))j(=)e FL(t)2272 4504 y FI(\013;\014)2380 4492 y FQ(\(\006\))h(obtained)e(b)n(y)h(iden)n(ti\014cation)456 4592 y(of)g(the)g(b)r(oundary)f(comp)r(onen)n(ts)h FJ(\013;)14 b(\014)27 b FQ(\(cf.)22 b(De\014nition)h(5.1.12\(iv\)\).)34 b(The)22 b(gluing)g(satis\014es)f(the)456 4692 y(follo)n(wing)26 b(prop)r(erties:)612 4817 y FK(Compatibilit)m(y)j(with)j FJ(A)p FK(:)41 b FJ(A)p FQ(\()p FJ(G)1727 4829 y FI(\013;\014)1835 4817 y FQ(\(\006\)\))24 b(=)f FJ(A)p FQ(\(\006\))c FL(n)f(f)p FJ(\013;)c(\014)t FL(g)p FQ(.)612 4917 y FK(Compatibilit)m(y)29 b(with)j FL(t)p FK(:)41 b FQ(if)34 b FJ(\013;)14 b(\014)37 b FL(2)32 b FJ(A)p FQ(\(\006)2058 4929 y FM(1)2096 4917 y FQ(\),)j(there)e(is)g(a)g(canonical)f(functorial)g(iso-)711 5016 y(morphism)27 b FJ(G)1164 5028 y FI(\013;\014)1272 5016 y FQ(\(\006)1364 5028 y FM(1)1420 5016 y FL(t)19 b FQ(\006)1554 5028 y FM(2)1591 5016 y FQ(\))k(=)g(\()p FJ(G)1831 5028 y FI(\013;\014)1939 5016 y FQ(\006)1999 5028 y FM(1)2037 5016 y FQ(\))18 b FL(t)h FQ(\006)2221 5028 y FM(2)2286 5016 y FQ(.)612 5116 y FK(Asso)s(ciativit)m(y:)40 b FQ(if)31 b FJ(\013;)14 b(\014)t(;)g(\015)5 b(;)14 b(\016)31 b FL(2)d FJ(A)p FQ(\(\006\))j(are)f(distinct,)i(then)e(there)h(exists)f (a)g(canonical)711 5216 y(functorial)d(isomorphism)g FJ(G)1638 5228 y FI(\013;\014)1746 5216 y FJ(G)1811 5228 y FI(\015)t(;\016)1906 5216 y FQ(\(\006\))c(=)g FJ(G)2206 5228 y FI(\015)t(;\016)2301 5216 y FJ(G)2366 5228 y FI(\013;\014)2474 5216 y FQ(\(\006\).)p eop %%Page: 121 29 121 124 bop 1470 226 a FM(5.6.)29 b(TO)n(WERS)g(OF)g(GR)n(OUPOIDS)893 b(121)612 425 y FK(F)-8 b(unctorialit)m(y:)41 b FQ(for)18 b(eac)n(h)g(morphism)g FJ(f)f FQ(:)28 b(\006)23 b FL(!)g FQ(\006)2248 395 y FE(0)2271 425 y FQ(,)e(w)n(e)d(ha)n(v)n(e)f(an)h (isomorphism)f FJ(G)3257 437 y FI(f)3310 425 y FQ(:)28 b FJ(G)3426 437 y FI(\013;\014)3533 425 y FQ(\(\006\))c FL(!)711 525 y FJ(G)776 537 y FI(\013)819 521 y Fx(0)842 537 y FI(;\014)903 521 y Fx(0)929 525 y FQ(\(\006)1021 495 y FE(0)1045 525 y FQ(\),)37 b(where)e FJ(\013)1438 495 y FE(0)1497 525 y FQ(=)h FJ(A)p FQ(\()p FJ(f)9 b FQ(\)\()p FJ(\013)p FQ(\),)38 b FJ(\014)2003 495 y FE(0)2063 525 y FL(2)e FJ(A)p FQ(\()p FJ(f)9 b FQ(\)\()p FJ(\014)t FQ(\))37 b(are)d(the)i(corresp)r(onding)d(ele-)711 624 y(men)n(ts)28 b(in)g FJ(A)p FQ(\(\006)1205 594 y FE(0)1228 624 y FQ(\).)38 b(These)27 b(isomorphisms)f(satisfy)h FJ(G)2403 636 y FI(f)2435 644 y FF(1)2468 636 y FI(f)2500 644 y FF(2)2560 624 y FQ(=)c FJ(G)2713 636 y FI(f)2745 644 y FF(1)2782 624 y FJ(G)2847 636 y FI(f)2879 644 y FF(2)2944 624 y FQ(and)28 b FJ(G)3171 636 y FM(id)3253 624 y FQ(=)23 b(id.)605 787 y FP(Definition)32 b FQ(5.6.1)p FP(.)40 b FQ(A)29 b FO(tower)j(of)g(gr)l(oup)l(oids)e FQ(\(or)f(just)h(a)f FO(tower)p FQ(\))g(is)h(the)f(follo)n(wing)f(col-) 456 886 y(lection)f(of)h(data:)605 986 y(\(i\))g(A)g(group)r(oid)f FL(T)21 b FQ(;)605 1086 y(\(ii\))41 b(A)f(\\disjoin)n(t)f(union")g (bifunctor)h FL(t)9 b FQ(:)32 b FL(T)48 b(\002)26 b(T)65 b(!)43 b(T)61 b FQ(and)39 b(an)h(ob)5 b(ject)39 b FL(;)k(2)h FQ(Ob)13 b FL(T)456 1185 y FQ(satisfying)27 b(the)g(axioms)g(of)h(a)f (symmetric)g(tensor)g(category;)605 1285 y(\(iii\))h(A)g(\\b)r(oundary) f(functor":)36 b(a)27 b(tensor)g(functor)h FJ(A)9 b FQ(:)28 b FL(T)44 b(!)23 b(S)6 b FJ(ets)p FQ(;)605 1385 y(\(iv\))32 b(A)g(\\gluing)f(op)r(eration":)43 b(for)31 b(ev)n(ery)f(\006)g FL(2)g FQ(Ob)14 b FL(T)53 b FQ(and)31 b(an)g(unordered)g(pair)g FJ(\013;)14 b(\014)34 b FL(2)456 1484 y FJ(A)p FQ(\(\006\),)25 b(w)n(e)f(ha)n(v)n(e)f(an)g(ob)5 b(ject)24 b FJ(G)1421 1496 y FI(\013;\014)1529 1484 y FQ(\(\006\))g FL(2)f(T)f FQ(.)35 b(The)24 b(gluing)g(should)g(b)r(e)g(asso)r(ciativ)n(e,)f (functorial)456 1584 y(and)k(compatible)g(with)h FL(t)g FQ(and)g FJ(A)g FQ(\(see)f(\(d\))i(ab)r(o)n(v)n(e\).)605 1746 y FP(Example)i FQ(5.6.2)p FP(.)40 b FL(S)6 b FJ(ets)27 b FQ(and)h FL(T)7 b FJ(eich)27 b FQ(are)g(to)n(w)n(ers)f(of)h(group)r (oids.)605 1909 y FP(Remark)32 b FQ(5.6.3)p FP(.)39 b FQ(Sometimes)30 b(it)f(is)g(useful)h(to)f(w)n(eak)n(en)f(the)i(ab)r(o)n (v)n(e)e(de\014nition)h(b)n(y)g(con-)456 2008 y(sidering)h(to)n(w)n (ers)g(in)i(whic)n(h)g(the)f(gluing)g(op)r(eration)g FJ(G)2215 2020 y FI(\013;\014)2355 2008 y FQ(is)g(de\014ned)h(not)f (for)g(all)h(but)g(only)456 2108 y(for)27 b(some)g(pairs)g FJ(\013;)14 b(\014)t FQ(.)38 b(In)28 b(this)g(case,)f(the)h(iden)n (tities)g FJ(G)2228 2120 y FI(\013;\014)2336 2108 y FL(t)23 b FQ(=)g FL(t)p FQ(\()p FJ(G)2654 2120 y FI(\013;\014)2781 2108 y FL(\002)18 b FQ(Id)q(\),)28 b FJ(G)3089 2120 y FI(\013;\014)3197 2108 y FJ(G)3262 2120 y FI(\015)t(;\016)3380 2108 y FQ(=)456 2208 y FJ(G)521 2220 y FI(\015)t(;\016)615 2208 y FJ(G)680 2220 y FI(\013;\014)815 2208 y FQ(in)e(the)h (de\014nition)f(ab)r(o)n(v)n(e)f(should)h(b)r(e)g(understo)r(o)r(d)g (in)h(the)f(follo)n(wing)f(w)n(a)n(y:)35 b(if)27 b(one)456 2307 y(side)g(is)h(de\014ned,)g(then)g(the)g(other)f(one)g(is)g(also)g (de\014ned)h(and)f(they)h(are)f(equal.)605 2470 y(An)g(example)g(of)f (suc)n(h)h(a)f(\\partial")f(to)n(w)n(er)h(is)g(giv)n(en)g(b)n(y)h(the)g (the)g FO(T)-6 b(eichm)q(\177)-43 b(ul)t(ler)31 b(tower)e(in)456 2569 y(genus)k(zer)l(o)5 b FQ(,)35 b FL(T)7 b FJ(eich)1103 2581 y FM(0)1140 2569 y FQ(,)34 b(in)e(whic)n(h)h(ob)5 b(jects)32 b(are)g(extended)g(surfaces)g(of)g(gen)n(us)g(zero)g(and)g (the)456 2669 y(functor)26 b FJ(G)808 2681 y FI(\013;\014)943 2669 y FQ(is)g(de\014ned)h(only)f(if)h FJ(\013;)14 b(\014)31 b FQ(b)r(elong)26 b(to)h(di\013eren)n(t)g(connected)f(comp)r(onen)n(ts) g(of)g(\006.)605 2831 y FP(Remark)32 b FQ(5.6.4)p FP(.)39 b FQ(One)j(can)g(giv)n(e)g(a)f(de\014nition)i(of)f(what)h(it)f(means)g (for)g(a)g(to)n(w)n(er)f(of)456 2931 y(group)r(oids)36 b(to)i(b)r(e)g(presen)n(ted)f(b)n(y)g(generators)f(and)h(relations)g (\(but)h(since)g(this)g(is)f(a)h(little)456 3031 y(b)r(oring,)c(w)n(e)f (don't)g(do)g(it)h(here\).)54 b(Then)34 b(the)g(results)f(of)g(Section) g(5.2)g(\(and)g([)p FK(BK)p FQ(]\))h(can)f(b)r(e)456 3130 y(reform)n(ulated)23 b(as)h(giving)g(the)h(generators)d(and)j (relations)e(presen)n(tation)h(of)h(the)g(T)-7 b(eic)n(hm)r(\177)-44 b(uller)456 3230 y(to)n(w)n(er)28 b FL(T)7 b FJ(eich)p FQ(.)42 b(One)30 b(notes)f(that)h(this)g(presen)n(tation)e(is)i(m)n(uc) n(h)f(simpler)g(than)h(the)g(presen)n(ta-)456 3329 y(tions)d(for)g (individual)h(mapping)g(class)f(groups)f(\000\(\006\).)38 b(The)28 b(idea)f(of)h(using)g(the)g(T)-7 b(eic)n(hm)r(\177)-44 b(uller)456 3429 y(to)n(w)n(er)29 b(with)i(the)g(gluing)f(op)r(eration) g(for)g(the)h(study)g(of)g(mapping)f(class)g(groups)g(b)r(elongs)g(to) 456 3529 y(Grothendiec)n(k)c([)p FK(G)q FQ(].)37 b(More)26 b(results)h(in)h(this)g(direction)f(can)g(b)r(e)h(found)g(in)g([)p FK(HLS)p FQ(].)605 3691 y(Before)33 b(giving)f(more)h(examples)g(of)h (to)n(w)n(ers,)f(let)h(us)f(reform)n(ulate)g(De\014nition)h(5.6.1)e(in) 456 3791 y(a)f(more)f(functorial)h(w)n(a)n(y)-7 b(.)47 b(This)32 b(will)g(b)r(e)f(useful)h(later)f(when)h(w)n(e)f(de\014ne)g (functors)h(b)r(et)n(w)n(een)456 3890 y(to)n(w)n(ers.)605 3990 y(Let)i FL(T)54 b FQ(b)r(e)34 b(a)f(to)n(w)n(er)f(of)h(group)r (oids.)53 b(Then)34 b FL(T)54 b FQ(is)34 b(a)f FO(\014b)l(er)l(e)l(d)i (c)l(ate)l(gory)41 b FQ(o)n(v)n(er)32 b FL(S)6 b FJ(ets)p FQ(.)54 b(F)-7 b(or)456 4090 y(an)n(y)32 b(\014nite)j(set)e FJ(S)5 b FQ(,)35 b(the)f(\014b)r(er)g FL(T)1478 4102 y FI(S)1560 4090 y FQ(o)n(v)n(er)e FJ(S)38 b FQ(is)c(the)g(category)d (with)k(ob)5 b(jects)33 b(all)g(pairs)g(\(\006)p FJ(;)14 b(')p FQ(\))456 4196 y(where)38 b(\006)k FL(2)g FQ(Ob)14 b FL(T)60 b FQ(and)39 b FJ(')9 b FQ(:)32 b FJ(A)p FQ(\(\006\))1684 4149 y FE(\030)1656 4196 y FL(\000)-39 b(!)42 b FJ(S)i FQ(is)38 b(a)h(bijection.)71 b(A)40 b(morphism)e(b)r(et)n(w)n(een)h(t)n (w)n(o)456 4296 y(ob)5 b(jects)40 b(\(\006)845 4308 y FM(1)882 4296 y FJ(;)14 b(')973 4308 y FM(1)1011 4296 y FQ(\))p FJ(;)g FQ(\(\006)1172 4308 y FM(2)1209 4296 y FJ(;)g(')1300 4308 y FM(2)1338 4296 y FQ(\))45 b FL(2)g FQ(Ob)14 b FL(T)1685 4308 y FI(S)1774 4296 y FQ(is)40 b(a)g(morphism)h FJ(f)53 b FL(2)45 b FQ(Mor)2698 4308 y FE(T)2755 4296 y FQ(\(\006)2847 4308 y FM(1)2885 4296 y FJ(;)14 b FQ(\006)2982 4308 y FM(2)3019 4296 y FQ(\))41 b(suc)n(h)f(that)456 4396 y FJ(')510 4408 y FM(1)570 4396 y FQ(=)23 b FJ(')712 4408 y FM(2)762 4396 y FL(\016)12 b FJ(A)p FQ(\()p FJ(f)d FQ(\).)35 b(Since)25 b(b)r(oth)g FL(T)46 b FQ(and)24 b FL(S)6 b FJ(ets)25 b FQ(are)e(group)r(oids,)h(ev) n(ery)f(\014b)r(er)h FL(T)2881 4408 y FI(S)2954 4396 y FQ(is)h(a)f(group)r(oid.)605 4502 y(A)i(bijection)h(of)f(sets)g FJ( )12 b FQ(:)28 b FJ(S)1509 4455 y FE(\030)1480 4502 y FL(\000)-39 b(!)23 b FJ(S)1668 4472 y FE(0)1717 4502 y FQ(giv)n(es)i(rise)g(to)h(a)g(functor)g FJ( )2579 4514 y FE(\003)2626 4502 y FQ(:)i FL(T)2722 4514 y FI(S)2793 4502 y FL(!)23 b(T)2944 4514 y FI(S)2988 4498 y Fx(0)3015 4502 y FQ(:)36 b(on)26 b(ob)5 b(jects)456 4602 y FJ( )510 4614 y FE(\003)548 4602 y FQ(\(\006)p FJ(;)14 b(')p FQ(\))24 b(=)e(\(\006)p FJ(;)14 b( )22 b FL(\016)c FJ(')p FQ(\),)28 b(and)g(on)f(morphisms)g FJ( )2028 4614 y FE(\003)2066 4602 y FQ(\()p FJ(f)9 b FQ(\))23 b(=)g FJ(f)9 b FQ(.)36 b(It)28 b(is)g(ob)n(vious)e(that)1400 4759 y(\()p FJ(\036)19 b FL(\016)f FJ( )s FQ(\))1649 4771 y FE(\003)1710 4759 y FQ(=)23 b FJ(\036)1847 4771 y FE(\003)1904 4759 y FL(\016)18 b FJ( )2018 4771 y FE(\003)2056 4759 y FJ(;)97 b FQ(id)2245 4771 y FE(\003)2307 4759 y FQ(=)22 b(id;)456 4917 y(in)27 b(particular,)g(all)g(functors)g FJ( )1449 4929 y FE(\003)1515 4917 y FQ(are)g(isomorphisms)f(of)i(categories.)605 5016 y(Con)n(v)n(ersely)-7 b(,)26 b(giv)n(en)i(a)f(collection)h(of)g(group)r (oids)f FL(fT)2263 5028 y FI(S)2311 5016 y FL(g)2353 5028 y FI(S)s FE(2)p FM(Ob)10 b FE(S)t FI(ets)2705 5016 y FQ(together)27 b(with)i(equiv-)456 5116 y(ariance)e(functors)h FJ( )1119 5128 y FE(\003)1186 5116 y FQ(as)f(ab)r(o)n(v)n(e,)h(one)g (can)g(reconstruct)f(the)i(group)r(oid)f FL(T)49 b FQ(and)29 b(the)g(functor)456 5216 y FJ(A)9 b FQ(:)28 b FL(T)44 b(!)23 b(S)6 b FJ(ets)p FQ(.)p eop %%Page: 122 30 122 125 bop 456 226 a FM(122)1010 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FQ(In)f(terms)f(of)h(these)f(data,)g FL(t)i FQ(b)r(ecomes)e(a)g (collection)g(of)g(functors)1487 575 y FL(t)1542 541 y FI(S;S)1647 515 y Fx(0)1682 575 y FQ(:)g FL(T)1777 587 y FI(S)1844 575 y FL(\002)18 b(T)1972 587 y FI(S)2016 571 y Fx(0)2066 575 y FL(!)23 b(T)2217 587 y FI(S)s FE(t)p FI(S)2350 571 y Fx(0)2377 575 y FJ(;)456 722 y FQ(while)32 b FL(;)e(2)h FQ(Ob)14 b FL(T)1005 737 y FE(;)1043 722 y FQ(.)51 b(They)32 b(satisfy)f(ob)n(vious)g(comm)n(utativit)n(y)-7 b(,)33 b(asso)r(ciativit)n(y)e(and)h(equiv)-5 b(ari-)456 822 y(ance)27 b(conditions.)605 921 y(Similarly)-7 b(,)27 b(the)h(gluing)f(giv)n(es)g(a)g(collection)g(of)g(functors)1069 1064 y FJ(G)1134 1029 y FI(S)1134 1084 y(\013;\014)1251 1064 y FQ(:)h FL(T)1347 1076 y FI(S)1418 1064 y FL(!)c(T)1570 1079 y FI(S)s FE(nf)p FI(\013;\014)s FE(g)1823 1064 y FJ(;)180 b(S)28 b FL(2)23 b FQ(Ob)14 b FL(S)6 b FJ(ets;)37 b(\013;)14 b(\014)28 b FL(2)23 b FJ(S)456 1211 y FQ(\(the)28 b(pair)f FJ(\013;)14 b(\014)32 b FQ(is)c(unordered\).)36 b(Indeed,)28 b(for)f(\(\006)p FJ(;)14 b(')p FQ(\))23 b FL(2)h FQ(Ob)13 b FL(T)2418 1223 y FI(S)2467 1211 y FQ(,)27 b(w)n(e)h(de\014ne)939 1357 y FJ(G)1004 1323 y FI(S)1004 1377 y(\013;\014)1112 1357 y FQ(\(\006)p FJ(;)14 b(')p FQ(\))24 b(=)f(\(\006)1531 1323 y FE(0)1554 1357 y FJ(;)14 b(')p FL(j)1668 1372 y FI(A)p FM(\(\006)1791 1355 y Fx(0)1814 1372 y FM(\))1844 1357 y FQ(\))111 b(where)27 b(\006)2287 1323 y FE(0)2334 1357 y FQ(=)22 b FJ(G)2486 1373 y FI(')2530 1356 y Fx(\000)p FF(1)2608 1373 y FI(\013;')2715 1356 y Fx(\000)p FF(1)2791 1373 y FI(\014)2836 1357 y FQ(\(\006\))456 1510 y(\(recall)e(that)h FJ(A)p FQ(\(\006)1030 1479 y FE(0)1054 1510 y FQ(\))j(=)e FJ(A)p FQ(\(\006\))6 b FL(n)g(f)p FJ(')1533 1479 y FE(\000)p FM(1)1622 1510 y FJ(\013;)14 b(')1766 1479 y FE(\000)p FM(1)1855 1510 y FJ(\014)t FL(g)p FQ(\).)35 b(F)-7 b(or)21 b(a)g(morphism)f FJ(f)e FQ(:)28 b(\(\006)2827 1522 y FM(1)2864 1510 y FJ(;)14 b(')2955 1522 y FM(1)2993 1510 y FQ(\))23 b FL(!)g FQ(\(\006)3246 1522 y FM(2)3284 1510 y FJ(;)14 b(')3375 1522 y FM(2)3412 1510 y FQ(\))456 1609 y(in)25 b FL(T)595 1621 y FI(S)644 1609 y FQ(,)h(w)n(e)f(de\014ne)g FJ(G)1115 1579 y FI(S)1115 1633 y(\013;\014)1223 1609 y FQ(\()p FJ(f)9 b FQ(\))24 b(=)e FJ(G)1513 1621 y FI(f)1582 1609 y FQ(\(recall)j(the)h(functorialit)n(y)f(of)g(gluing\).)36 b(No)n(w)25 b(the)h(prop)r(er-)456 1710 y(ties)h(of)h(gluing)f(can)g(b) r(e)h(restated)f(as)g(follo)n(ws.)612 1831 y FK(Compatibilit)m(y)i (with)j FJ(A)p FK(:)41 b FQ(already)26 b(incorp)r(orated)g(in)i(the)g (de\014nition.)612 1931 y FK(Compatibilit)m(y)h(with)j FL(t)p FK(:)41 b FQ(for)34 b(an)n(y)g(t)n(w)n(o)h(sets)f FJ(S;)14 b(S)2337 1900 y FE(0)2395 1931 y FQ(and)35 b FJ(\013;)14 b(\014)40 b FL(2)35 b FJ(S)5 b FQ(,)37 b(there)d(exists)h (a)711 2033 y(canonical)24 b(isomorphism)f(of)i(functors)g FJ(G)2031 2003 y FI(S)s FE(t)p FI(S)2164 1978 y Fx(0)2031 2057 y FI(\013;\014)2203 2033 y FL(\016)13 b(t)2313 2003 y FI(S;S)2418 1978 y Fx(0)2467 2033 y FQ(=)23 b FL(t)2610 2003 y FI(S)s FE(nf)p FI(\013;\014)s FE(g)p FI(;S)2924 1978 y Fx(0)2963 2033 y FL(\016)13 b FQ(\()p FJ(G)3115 2003 y FI(S)3115 2057 y(\013;\014)3235 2033 y FL(\002)g FQ(Id\).)612 2134 y FK(Asso)s(ciativit)m(y:)40 b FQ(if)31 b FJ(\013;)14 b(\014)t(;)g(\015)5 b(;)14 b(\016)31 b FL(2)d FJ(S)35 b FQ(are)29 b(distinct)i(then)g(there)f(exists)g(a)g (canonical)f(iso-)711 2245 y(morphism)e(of)h(functors)f FJ(G)1580 2202 y FI(S)s FE(nf)p FI(\015)t(;\016)r FE(g)1580 2270 y FI(\013;\014)1839 2245 y FL(\016)18 b FJ(G)1964 2215 y FI(S)1964 2269 y(\015)t(;\016)2082 2245 y FQ(=)23 b FJ(G)2235 2202 y FI(S)s FE(nf)p FI(\013;\014)s FE(g)2235 2270 y FI(\015)t(;\016)2507 2245 y FL(\016)18 b FJ(G)2632 2215 y FI(S)2632 2269 y(\013;\014)2740 2245 y FQ(.)612 2360 y FK(F)-8 b(unctorialit)m(y:)41 b FQ(already)32 b(incorp)r(orated)g(in)i(the)f(requiremen)n(t)g(that)g FJ(G)2976 2330 y FI(S)2976 2383 y(\013;\014)3118 2360 y FQ(are)f(func-)711 2459 y(tors.)456 2580 y(Finally)-7 b(,)27 b(there)h(is)f(one)g(more)g(prop)r(ert)n(y)g(whic)n(h)g(follo)n (ws)g(just)h(from)f(the)h(de\014nition)g(of)g FJ(G)3292 2550 y FI(S)3292 2604 y(\013;\014)3400 2580 y FQ(.)612 2723 y FK(Equiv)-5 b(ariance:)41 b FQ(for)31 b(an)n(y)g(bijection)g(of) g(sets)h FJ( )12 b FQ(:)29 b FJ(S)2345 2676 y FE(\030)2317 2723 y FL(\000)-40 b(!)30 b FJ(S)2511 2693 y FE(0)2534 2723 y FQ(,)i(w)n(e)f(ha)n(v)n(e)f FJ(G)2975 2693 y FI(S)3019 2668 y Fx(0)2975 2747 y FI( )r(\013; )r(\014)3196 2723 y FL(\016)20 b FJ( )3312 2735 y FE(\003)3380 2723 y FQ(=)711 2836 y(\()p FJ( )s FL(j)823 2851 y FI(S)s FE(nf)p FI(\013;\014)s FE(g)1077 2836 y FQ(\))1109 2848 y FE(\003)1166 2836 y FL(\016)e FJ(G)1291 2806 y FI(S)1291 2860 y(\013;\014)1399 2836 y FQ(.)605 2996 y FP(Definition)32 b FQ(5.6.5)p FP(.)40 b FQ(A)18 b FO(tower)k(of)g(gr)l(oup)l(oids)e FQ(is)e(a)g(collection)g(of)g(group)r(oids)f FL(fT)3098 3008 y FI(S)3146 2996 y FL(g)3188 3008 y FI(S)s FE(2)p FM(Ob)10 b FE(S)t FI(ets)456 3095 y FQ(equipp)r(ed)28 b(with)g(the)g(follo)n(wing)e(structure:)605 3195 y(\(i\))31 b(Equiv)-5 b(ariance)28 b(functors)i FJ( )1598 3207 y FE(\003)1645 3195 y FQ(:)f FL(T)1742 3207 y FI(S)1818 3195 y FL(!)e(T)1973 3207 y FI(S)2017 3191 y Fx(0)2074 3195 y FQ(for)i(an)n(y)h FJ( )g FL(2)e FQ(Mor)2680 3207 y FE(S)t FI(ets)2817 3195 y FQ(\()p FJ(S;)14 b(S)2993 3165 y FE(0)3016 3195 y FQ(\),)31 b(satisfying)456 3295 y(\()p FJ(\036)19 b FL(\016)f FJ( )s FQ(\))705 3307 y FE(\003)766 3295 y FQ(=)23 b FJ(\036)903 3307 y FE(\003)960 3295 y FL(\016)18 b FJ( )1074 3307 y FE(\003)1140 3295 y FQ(and)27 b(id)1371 3307 y FE(\003)1432 3295 y FQ(=)22 b(id)q(.)605 3402 y(\(ii\))29 b(An)f(ob)5 b(ject)28 b FL(;)23 b(2)h FQ(Ob)14 b FL(T)1446 3417 y FE(;)1512 3402 y FQ(and)28 b(a)f(collection)h(of)g(functors)f FL(t)2584 3372 y FI(S;S)2689 3347 y Fx(0)2725 3402 y FQ(:)g FL(T)2820 3414 y FI(S)2887 3402 y FL(\002)19 b(T)3016 3414 y FI(S)3060 3398 y Fx(0)3110 3402 y FL(!)24 b(T)3262 3414 y FI(S)s FE(t)p FI(S)3395 3398 y Fx(0)3421 3402 y FQ(,)456 3502 y(satisfying)j(ob)n(vious)f(comm)n(utativit)n(y)-7 b(,)27 b(asso)r(ciativit)n(y)f(and)h(equiv)-5 b(ariance)27 b(conditions.)605 3601 y(\(iii\))e(A)g(collection)e(of)h(functors)g FJ(G)1689 3571 y FI(S)1689 3625 y(\013;\014)1806 3601 y FQ(:)k FL(T)1902 3613 y FI(S)1974 3601 y FL(!)23 b(T)2125 3616 y FI(S)s FE(nf)p FI(\013;\014)s FE(g)2378 3601 y FQ(,)i(satisfying)f (the)h(ab)r(o)n(v)n(e)d(asso)r(cia-)456 3702 y(tivit)n(y)-7 b(,)27 b(equiv)-5 b(ariance)27 b(and)g(compatibilit)n(y)h(with)g FL(t)p FQ(.)605 3856 y FP(Pr)n(oposition)j FQ(5.6.6)p FP(.)40 b FO(De\014nitions)29 b FQ(5.6.1)f FO(and)j FQ(5.6.5)d FO(ar)l(e)i(e)l(quivalent.)605 4010 y FP(Pr)n(oof.)41 b FQ(It)25 b(w)n(as)e(already)g(sk)n(etc)n(hed)g(ab)r(o)n(v)n(e.)35 b(The)24 b(details)h(are)e(left)i(to)f(the)h(reader)e(as)h(an)456 4109 y(exercise.)p 3384 4109 4 57 v 3388 4057 50 4 v 3388 4109 V 3437 4109 4 57 v 605 4270 a FP(Definition)32 b FQ(5.6.7)p FP(.)40 b FQ(A)18 b FO(tower)k(functor)27 b FL(F)g FQ(b)r(et)n(w)n(een)18 b(t)n(w)n(o)g(to)n(w)n(ers)e(of)j (group)r(oids)e(\()p FL(T)k FJ(;)14 b FL(t)p FJ(;)g(A;)g(G)p FQ(\))456 4370 y(and)24 b(\()p FL(T)713 4340 y FE(0)736 4370 y FJ(;)14 b FL(t)828 4340 y FE(0)852 4370 y FJ(;)g(A)951 4340 y FE(0)974 4370 y FJ(;)g(G)1076 4340 y FE(0)1100 4370 y FQ(\))25 b(is)g(a)f(functor)h FL(F)17 b FQ(:)28 b FL(T)44 b(!)24 b(T)1980 4340 y FE(0)2028 4370 y FQ(whic)n(h)h (preserv)n(es)e(all)i(the)g(structure.)35 b(More)456 4469 y(precisely:)605 4569 y(\(i\))d(There)e(is)h(an)g(isomorphism)f (of)h(functors)g FJ(A)e FL(')f FJ(A)2331 4539 y FE(0)2375 4569 y FL(\016)21 b(F)8 b FQ(.)47 b(Th)n(us)31 b FL(F)39 b FQ(giv)n(es)29 b(rise)i(to)g(an)456 4669 y(equiv)-5 b(arian)n(t)26 b(collection)h(of)h(functors)f FL(F)1740 4638 y FI(S)1797 4669 y FQ(:)h FL(T)1893 4681 y FI(S)1964 4669 y FL(!)23 b(T)2137 4638 y FE(0)2115 4691 y FI(S)2164 4669 y FQ(,)k FJ(S)h FL(2)c FQ(Ob)13 b FL(S)6 b FJ(ets)p FQ(.)605 4768 y(\(ii\))25 b FL(F)32 b FQ(is)24 b(a)g(tensor)f(functor,) i(i.e.,)g(the)f(functors)g FL(F)c(\016)12 b(t)23 b FQ(and)h FL(t)2569 4738 y FE(0)2604 4768 y FL(\016)12 b FQ(\()p FL(F)19 b(\002)12 b(F)c FQ(\))h(:)27 b FL(T)33 b(\002)12 b(T)44 b(!)23 b(T)3421 4738 y FE(0)456 4868 y FQ(are)j(isomorphic.)605 4967 y(\(iii\))f(F)-7 b(or)24 b(an)n(y)g(\014nite)h(set)g FJ(S)5 b FQ(,)24 b(there)h(is)f(an)g(isomorphism)g(of)g(functors)g FL(F)2864 4937 y FI(S)s FE(nf)p FI(\013;\014)s FE(g)3130 4967 y FL(\016)12 b FJ(G)3249 4937 y FI(S)3249 4991 y(\013;\014)3380 4967 y FL(')456 5092 y FJ(G)521 5062 y FE(0)544 5050 y FI(S)544 5113 y(\013;\014)674 5092 y FL(\016)22 b(F)806 5062 y FI(S)863 5092 y FQ(:)30 b FL(T)961 5104 y FI(S)1042 5092 y FL(!)j(T)1224 5062 y FE(0)1203 5119 y FI(S)s FE(nf)p FI(\013;\014)s FE(g)1456 5092 y FQ(.)55 b(These)33 b(isomorphisms)f (are)g(equiv)-5 b(arian)n(t)33 b(with)g(resp)r(ect)h(to)456 5199 y(bijections)27 b(of)h FJ(S)5 b FQ(.)p eop %%Page: 123 31 123 126 bop 1470 226 a FM(5.6.)29 b(TO)n(WERS)g(OF)g(GR)n(OUPOIDS)893 b(123)605 425 y FP(Exer)n(cise)32 b FQ(5.6.8)p FP(.)40 b FQ(Sp)r(ell)h(out)g(prop)r(ert)n(y)f(\(iii\))h(of)g(De\014nition)h (5.6.7)d(in)j(terms)e(of)h(the)456 525 y(gluing)27 b(op)r(erations)f FJ(G)1174 537 y FI(\013;\014)1310 525 y FQ(from)h(De\014nition)h (5.6.1.)605 681 y FP(Example)j FQ(5.6.9)p FP(.)40 b FJ(A)9 b FQ(:)28 b FL(T)44 b(!)23 b(S)6 b FJ(ets)28 b FQ(is)g(a)f(to)n(w)n(er) f(functor)i(for)f(an)n(y)f(to)n(w)n(er)h FL(T)21 b FQ(.)605 838 y(There)k(is)g(an)g(ev)n(en)f(more)h(economical)f(w)n(a)n(y)g(to)h (reform)n(ulate)f(the)h(de\014nition)h(of)f(a)g(to)n(w)n(er.)456 937 y(Lo)r(oking)37 b(at)h(the)h(equiv)-5 b(ariance)38 b(prop)r(erties)f(of)i(the)g(collections)e FL(fT)2699 949 y FI(S)2747 937 y FL(g)h FQ(and)g FL(f)p FJ(G)3106 907 y FI(S)3106 961 y(\013;\014)3214 937 y FL(g)p FQ(,)j(one)456 1038 y(can)34 b(notice)h(that)h(they)f(can)g(b)r(e)g(com)n(bined)g(if)h (w)n(e)f(allo)n(w)f(more)g(maps)h(b)r(et)n(w)n(een)g(sets.)59 b(W)-7 b(e)456 1138 y(in)n(tro)r(duce)29 b(a)h(category)e FL(S)6 b FJ(ets)1400 1150 y FI(])1461 1138 y FQ(with)30 b(the)h(same)e(ob)5 b(jects)30 b(as)f(in)h FL(S)6 b FJ(ets)30 b FQ(\(i.e.,)i(\014nite)e(sets\),)h(but)456 1237 y(with)f(more)e (morphisms:)40 b(all)29 b(maps)g(b)r(et)n(w)n(een)h(sets)f(that)g(are)g (comp)r(osed)g(of)g(bijections)h(and)456 1337 y(the)j(elemen)n(tary)g (injections)h FJ(i)1442 1307 y FI(S)1442 1361 y(\013;\014)1558 1337 y FQ(:)c FJ(S)d FL(n)22 b(f)p FJ(\013;)14 b(\014)t FL(g)32 b FJ(,)-14 b FL(!)33 b FJ(S)5 b FQ(.)55 b(\(This)33 b(de\014nition)h(w)n(as)f(inspired)g(b)n(y)456 1457 y([)p FK(BFM)o FQ(].\))38 b(Let)27 b FL(S)6 b FJ(ets)1125 1420 y FI(])1184 1457 y FQ(b)r(e)28 b(the)f(dual)h(category)d(of)j FL(S)6 b FJ(ets)2217 1469 y FI(])2248 1457 y FQ(,)27 b(i.e.,)h(the)g(category)d(with)j(the)g(same)456 1565 y(ob)5 b(jects)39 b(but)h(with)g(all)f(arro)n(ws)e(in)n(v)n(erted.)71 b(All)40 b(morphisms)f(in)h FL(S)6 b FJ(ets)2764 1529 y FI(])2834 1565 y FQ(are)39 b(comp)r(osed)g(of)456 1665 y(bijections)27 b(and)h(the)g(elemen)n(tary)e(morphisms)923 1813 y FJ(\016)963 1779 y FI(S)960 1834 y(\013;\014)1076 1813 y FQ(:)i FJ(S)g FL(!)23 b FJ(S)g FL(n)18 b(f)p FJ(\013;)c(\014)t FL(g)p FJ(;)180 b(S)28 b FL(2)23 b FQ(Ob)13 b FL(S)6 b FJ(ets)2320 1777 y FI(])2351 1813 y FJ(;)60 b(\013;)14 b(\014)27 b FL(2)d FJ(S)32 b FQ(\(unordered\))o FJ(:)456 1960 y FQ(No)n(w)27 b(if)h(w)n(e)f(de\014ne)1375 2107 y(\()p FJ(\016)1447 2073 y FI(S)1444 2128 y(\013;\014)1552 2107 y FQ(\))1584 2119 y FE(\003)1646 2107 y FQ(=)22 b FJ(G)1798 2073 y FI(S)1798 2128 y(\013;\014)1916 2107 y FQ(:)27 b FL(T)2011 2119 y FI(S)2083 2107 y FL(!)c(T)2234 2122 y FI(S)s FE(nf)p FI(\013;\014)s FE(g)2488 2107 y FJ(;)456 2273 y FQ(w)n(e)33 b(will)h(ha)n(v)n(e)e(\()p FJ(\036)24 b FL(\016)e FJ( )s FQ(\))1202 2285 y FE(\003)1273 2273 y FQ(=)33 b FJ(\036)1420 2285 y FE(\003)1481 2273 y FL(\016)22 b FJ( )1599 2285 y FE(\003)1671 2273 y FQ(for)34 b FJ(\036;)14 b( )36 b FL(2)e FQ(Mor)2220 2292 y FE(S)t FI(ets)2353 2273 y FG(])8 b FQ(.)55 b(Note)34 b(that)g FL(S)6 b FJ(ets)3021 2237 y FI(])3086 2273 y FQ(is)33 b(again)g(a)456 2373 y(symmetric)27 b(tensor)g(category)e(with)j(resp)r (ect)g(to)f FL(t)p FQ(.)605 2529 y FP(Pr)n(oposition)k FQ(5.6.10)p FP(.)39 b FO(A)29 b(tower)h(of)g(gr)l(oup)l(oids)g(is)g (the)f(same)h(as)f(a)h(symmetric)g(tensor)456 2630 y(c)l(ate)l(gory)h FL(T)52 b FO(\014b)l(er)l(e)l(d)30 b(over)h FL(S)6 b FJ(ets)1481 2594 y FI(])1543 2630 y FO(such)30 b(that)h(al)t(l)g(\014b) l(ers)g FL(T)2286 2642 y FI(S)2364 2630 y FQ(\()p FJ(S)f FL(2)24 b FQ(Ob)14 b FL(S)6 b FJ(ets)2845 2594 y FI(])2876 2630 y FQ(\))31 b FO(ar)l(e)g(gr)l(oup)l(oids.)456 2730 y(In)25 b(other)h(wor)l(ds,)h(we)f(have)g(p)l(arts)g FQ(\(i\))g FO(and)g FQ(\(ii\))g FO(of)g(De\014nition)g FQ(5.6.5)e FO(with)i FL(S)6 b FJ(ets)25 b FO(r)l(eplac)l(e)l(d)i(with) 456 2835 y FL(S)6 b FJ(ets)620 2799 y FI(])651 2835 y FO(.)605 2992 y FQ(In)31 b(this)h(language)d(a)i FO(tower)i(functor)40 b FL(F)g FQ(b)r(et)n(w)n(een)31 b(t)n(w)n(o)f(to)n(w)n(ers)f(is)j(just) f(a)g(collection)g(of)456 3091 y(functors)j FL(F)852 3061 y FI(S)910 3091 y FQ(:)c FL(T)1008 3103 y FI(S)1092 3091 y FL(!)36 b(T)1277 3061 y FE(0)1256 3114 y FI(S)1304 3091 y FQ(,)h(equiv)-5 b(arian)n(t)34 b(with)i(resp)r(ect)f(to)g(Mor) 2551 3111 y FE(S)t FI(ets)2684 3091 y FG(])8 b FQ(,)38 b(and)d(suc)n(h)g(that)g(the)456 3191 y(corresp)r(onding)25 b(functor)i FL(F)17 b FQ(:)28 b FL(T)44 b(!)23 b(T)1667 3161 y FE(0)1717 3191 y FQ(is)k(a)g(tensor)g(functor.)36 b(A)28 b FO(natur)l(al)h(tr)l(ansformation)34 b FQ(\010)456 3291 y(b)r(et)n(w)n(een)f(t)n(w)n(o)f(to)n(w)n(er)f(functors)i FL(F)8 b FJ(;)14 b FL(G)g FQ(:)30 b FL(T)53 b(!)32 b(T)2003 3261 y FE(0)2059 3291 y FQ(is)h(a)f(Mor)2373 3310 y FE(S)t FI(ets)2505 3291 y FG(])9 b FQ(-equiv)-5 b(arian)n(t)31 b(collection)i(of)456 3390 y(natural)24 b(transformations)g(\010)1401 3360 y FI(S)1474 3390 y FQ(b)r(et)n(w)n(een)i(the)g(functors)f FL(F)2321 3360 y FI(S)2369 3390 y FJ(;)14 b FL(G)2460 3360 y FI(S)2508 3390 y FQ(.)37 b(Then,)26 b(as)f(usual,)g FL(F)17 b FQ(:)28 b FL(T)44 b(!)456 3490 y(T)522 3460 y FE(0)579 3490 y FQ(is)34 b(called)g(an)f FO(e)l(quivalenc)l(e)k(of)f (towers)41 b FQ(if)35 b(there)e(exists)h(a)g(to)n(w)n(er)e(functor)i FL(F)3053 3460 y FE(0)3085 3490 y FQ(:)c FL(T)3205 3460 y FE(0)3261 3490 y FL(!)k(T)456 3590 y FQ(suc)n(h)27 b(that)h(the)g(to)n(w)n(er)e(functors)h FL(F)8 b(F)1649 3559 y FE(0)1700 3590 y FQ(and)27 b FL(F)1929 3559 y FE(0)1953 3590 y FL(F)35 b FQ(are)27 b(isomorphic)f(to)i(Id.)605 3689 y(After)d(in)n(tro)r(ducing)f(all)g(this)h(abstract)e(nonsense)h (let)g(us)h(no)n(w)f(giv)n(e)f(some)h(examples)g(and)456 3789 y(applications.)605 3945 y FP(Example)31 b FQ(5.6.11)p FP(.)39 b FQ(Let)33 b FL(C)k FQ(b)r(e)c(an)f(ab)r(elian)g(category)e (and)i FJ(R)g FL(2)f FQ(ind)p FL(\000C)2958 3915 y Fv(\002)p FM(2)3079 3945 y FQ(b)r(e)i(a)f(sym-)456 4045 y(metric)27 b(ob)5 b(ject.)961 4015 y FM(3)1035 4045 y FQ(W)-7 b(e)28 b(de\014ne)g(the)g(to)n(w)n(er)e(of)i(group)r(oids)e FL(F)8 b FJ(un)p FQ(\()p FL(C)d FQ(\))27 b(as)g(follo)n(ws.)612 4171 y FK(Ob)5 b(jects:)41 b FQ(all)19 b(pairs)g(\()p FJ(S;)14 b(F)e FQ(\))21 b(where)e FJ(S)24 b FQ(is)c(a)g(\014nite)g(set) g(and)g FJ(F)31 b FQ(is)20 b(a)g(functor)f FL(C)3017 4141 y Fv(\002)p FI(S)3140 4171 y FL(!)k(V)7 b FJ(ec)3379 4183 y FI(f)3421 4171 y FQ(.)612 4281 y FK(Morphisms:)38 b FQ(Mor)o(\(\()p FJ(S)1410 4293 y FM(1)1448 4281 y FJ(;)14 b(F)1538 4293 y FM(1)1575 4281 y FQ(\))p FJ(;)g FQ(\()p FJ(S)1727 4293 y FM(2)1765 4281 y FJ(;)g(F)1855 4293 y FM(2)1892 4281 y FQ(\)\))20 b(consists)e(of)g(all)h(pairs)f(\()p FJ(f)t(;)c(')p FQ(\))19 b(where)f FJ(')9 b FQ(:)29 b FJ(S)3276 4293 y FM(1)3364 4234 y FE(\030)3336 4281 y FL(\000)-40 b(!)711 4387 y FJ(S)762 4399 y FM(2)826 4387 y FQ(is)26 b(a)g(bijection,)h FJ(f)18 b FQ(:)28 b FJ(F)1500 4399 y FM(1)1589 4340 y FE(\030)1560 4387 y FL(\000)-39 b(!)23 b FJ(')1746 4399 y FE(\003)1784 4387 y FJ(F)1837 4399 y FM(2)1902 4387 y FQ(is)j(an)g(isomorphism)f(of)h(functors,)h (and)f FJ(')3233 4399 y FE(\003)3271 4387 y FJ(F)3324 4399 y FM(2)3389 4387 y FQ(is)711 4508 y(the)i(comp)r(osition)f FL(C)1367 4478 y Fv(\002)p FI(S)1460 4486 y FF(1)1547 4457 y FI(')1591 4465 y Fx(\003)1519 4508 y FL(\000)-13 b(!)23 b(C)1726 4478 y Fv(\002)p FI(S)1819 4486 y FF(2)1906 4460 y FI(F)1948 4468 y FF(2)1878 4508 y FL(\000)-17 b(!)23 b(V)7 b FJ(ec)2165 4520 y FI(f)2207 4508 y FQ(.)612 4607 y FK(Boundary)32 b(functor:)42 b FJ(A)p FQ(\()p FJ(S;)14 b(F)e FQ(\))24 b(=)f FJ(S)5 b FQ(.)612 4710 y FK(Disjoin)m(t)31 b(union:)40 b FQ(\()p FJ(S)1356 4722 y FM(1)1405 4710 y FL(t)11 b FJ(S)1522 4722 y FM(2)1559 4710 y FJ(;)j(F)1649 4722 y FM(1)1698 4710 y FL(\012)d FJ(F)1827 4722 y FM(2)1873 4710 y FQ(:)28 b FL(C)1973 4680 y Fv(\002)p FM(\()p FI(S)2092 4688 y FF(1)2124 4680 y FE(t)p FI(S)2210 4688 y FF(2)2242 4680 y FM(\))2295 4710 y FL(!)23 b(V)7 b FJ(ec)2534 4722 y FI(f)2576 4710 y FQ(\),)25 b(and)f(similarly)f(for)h(mor-)711 4810 y(phisms.)37 b(The)28 b(ob)5 b(ject)27 b FL(;)g FQ(is)h(the)g(ob)n(vious)e(one.)612 4909 y FK(Gluing:)39 b FQ(giv)n(en)18 b(b)n(y)g FJ(G)1340 4921 y FI(\013;\014)1448 4909 y FQ(\()p FJ(S)5 b FQ(\))23 b(=)g FJ(S)5 b FL(nf)p FJ(\013;)14 b(\014)t FL(g)j FQ(and)i FJ(G)2237 4921 y FI(\013;\014)2344 4909 y FQ(\()p FJ(F)12 b FQ(\))24 b(=)f FJ(F)12 b FQ(\()p FJ(:)i(:)g(:)g(;)g(R)2894 4879 y FM(\(1\))2982 4909 y FJ(;)g(:)g(:)g(:)g(;)g(R)3231 4879 y FM(\(2\))3320 4909 y FJ(;)g(:)g(:)g(:)f FQ(\),)711 5015 y(where)27 b FJ(R)1015 4985 y FM(\(1\))1104 5015 y FJ(;)14 b(R)1205 4985 y FM(\(2\))1321 5015 y FQ(are)27 b(put)h(in)g(the)g(places)f(corresp)r(onding)f(to)h(the)h(indices)g FJ(\013;)14 b(\014)t FQ(.)p 456 5122 499 4 v 605 5192 a Fp(3)640 5216 y Fo(Here)23 b(and)h(b)r(elo)n(w)g(w)n(e)g(use)g(the)h (same)e(notation)i(as)f(in)f(Section)i(2.4.)p eop %%Page: 124 32 124 127 bop 456 226 a FM(124)1010 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FP(Definition)j FQ(5.6.12)p FP(.)39 b FQ(Let)26 b FL(C)31 b FQ(b)r(e)c(an)f(ab)r(elian)g(category)e(and)i FJ(R)d FL(2)h FQ(ind)p FL(\000C)2977 395 y Fv(\002)p FM(2)3092 425 y FQ(b)r(e)i(a)g(sym-)456 525 y(metric)19 b(ob)5 b(ject.)34 b(A)20 b FO(r)l(epr)l(esentation)g FQ(of)g(a)f(to)n(w)n(er)f FL(T)41 b FQ(in)20 b FL(C)k FQ(is)c(a)f(to)n(w)n(er)f(functor)i FJ(\032)9 b FQ(:)27 b FL(T)45 b(!)23 b(F)8 b FJ(un)p FQ(\()p FL(C)d FQ(\).)605 662 y(The)31 b(follo)n(wing)f(theorem,)h(whic)n(h)g(follo)n(ws)f (immediately)h(from)f(the)i(de\014nitions,)g(eluci-)456 762 y(dates)27 b(the)h(notion)f(of)h(a)f(mo)r(dular)g(functor.)605 899 y FP(Theorem)32 b FQ(5.6.13)p FP(.)39 b FO(A)h FL(C)5 b FO(-extende)l(d)38 b(mo)l(dular)j(functor)e(is)h(the)g(same)g(as)g(a) h(r)l(epr)l(esen-)456 999 y(tation)f FJ(\034)50 b FO(of)42 b(the)e(T)-6 b(eichm)q(\177)-43 b(ul)t(ler)43 b(tower)d FL(T)7 b FJ(eich)40 b FO(in)h FL(C)k FO(with)c(the)g(additional)i (normalization)456 1098 y(c)l(ondition)30 b FJ(\034)9 b FQ(\()p FJ(S)951 1068 y FM(2)989 1098 y FQ(\))24 b(=)e(id)10 b(:)27 b FL(C)1310 1068 y FM(0)1370 1098 y FQ(=)c FL(V)7 b FJ(ec)1591 1110 y FI(f)1656 1098 y FL(!)23 b(V)7 b FJ(ec)1895 1110 y FI(f)1938 1098 y FO(.)605 1236 y FQ(In)32 b(a)g(similar)f(w)n(a)n(y)f(one)i(can)f(rewrite)g(the)i(notion)e(of)h (MS)g(data)g(\(see)f(Section)h(5.3\).)49 b(In)456 1335 y(order)22 b(to)i(in)n(tro)r(duce)g(the)h(corresp)r(onding)d(to)n(w)n (er)h(of)h(group)r(oids)f FL(MS)6 b FQ(,)25 b(w)n(e)f(will)g(\014rst)g (need)g(the)456 1435 y(follo)n(wing)i(de\014nition.)605 1572 y FP(Definition)32 b FQ(5.6.14)p FP(.)39 b FQ(A)28 b FO(marking)i(gr)l(aph)f FQ(is)e(a)g(graph)g FJ(m)g FQ(without)h(cycles)e(\(a)i(\\forest"\))456 1672 y(with)g(the)g(follo)n (wing)e(additional)h(data:)605 1772 y(\(i\))h(The)g(v)n(ertices)f(of)g FJ(m)h FQ(are)e(split)i(in)n(to)g(t)n(w)n(o)e(subsets,)i(\\in)n (ternal")e(and)h(\\external")1361 1906 y(V)-7 b(ertices\()p FJ(m)p FQ(\))23 b(=)g(In)n(t\()p FJ(m)p FQ(\))c FL(t)g FQ(Ext)o(\()p FJ(m)p FQ(\))p FJ(;)456 2041 y FQ(so)34 b(that)i(ev)n(ery)e(external)g(v)n(ertex)g(is)h(1-v)-5 b(alen)n(t,)37 b(and)e(there)g(are)f(no)h(edges)f(connecting)h(t)n(w)n (o)456 2141 y(external)26 b(v)n(ertices.)605 2240 y(\(ii\))e(F)-7 b(or)23 b(ev)n(ery)f(in)n(ternal)h(v)n(ertex)g FJ(v)j FL(2)d FQ(In)n(t\()p FJ(m)p FQ(\),)i(an)f(order)e(on)h(the)h(set)f(of)h (all)f(edges)g(ending)456 2340 y(at)k FJ(v)k FQ(is)c(giv)n(en.)605 2477 y FP(Remark)32 b FQ(5.6.15)p FP(.)39 b FQ(The)24 b(marking)f(graphs)g(with)i(3-v)-5 b(alen)n(t)23 b(in)n(ternal)h(v)n (ertices)f(are)g(essen-)456 2577 y(tially)k(the)h(same)f(as)g (\\Bratelli)f(diagrams")g(used)h(in)h(ph)n(ysics)f(literature.)605 2714 y(Graphs)20 b(of)h(this)g(t)n(yp)r(e)g(app)r(eared)e(in)i(our)f (discussion)g(of)h(parameterizations)e(of)h(extended)456 2814 y(surfaces)31 b(\(see)i(Section)f(5.2\).)52 b(In)33 b(the)g(\014gures,)g(w)n(e)f(use)h FL(\003)f FQ(for)h(in)n(ternal)f(v)n (ertices)f(and)i FL(\017)f FQ(for)456 2913 y(external)e(v)n(ertices.)45 b(T)-7 b(o)30 b(sho)n(w)g(the)h(order,)g(w)n(e)f(dra)n(w)g(the)h(edges) f(in)h(a)f(clo)r(c)n(kwise)g(order)g(and)456 3013 y(mark)c(the)i (\014rst)g(edge)f(b)n(y)g(an)g(arro)n(w.)605 3113 y(W)-7 b(e)30 b(de\014ne)h(a)e(CW)h(complex)g FL(M)1667 3125 y FM(0)1734 3113 y FQ(in)g(a)g(w)n(a)n(y)e(parallel)h(to)h(the)g (de\014nition)h(of)f FL(M)p FQ(\(\006\))g(for)456 3212 y(gen)n(us)g(0)h(\(see)h(Section)f(5.2\).)48 b(The)32 b(v)n(ertices)e(of)i FL(M)2114 3224 y FM(0)2182 3212 y FQ(are)f(all)g(marking)f(graphs.)47 b(W)-7 b(e)32 b(de\014ne)456 3312 y(the)25 b(simple)h(mo)n(v)n(es)e FJ(Z)q(;)14 b(B)t(;)g(F)37 b FQ(b)n(y)26 b(Figures)e(5.5,)h(5.6)g(and)g(5.7,)g(resp)r(ectiv)n(ely) -7 b(.)35 b(The)26 b(relations)e(in)456 3412 y FL(M)556 3424 y FM(0)620 3412 y FQ(are)j(obtained)g(from)g(MF1{MF7)g(b)n(y)h (forgetting)e(the)i(surfaces.)605 3549 y FP(Example)j FQ(5.6.16)p FP(.)39 b FQ(The)27 b FO(Mo)l(or)l(e{Seib)l(er)l(g)k(tower) k FL(MS)e FQ(is)27 b(the)g(to)n(w)n(er)e(of)i(group)r(oids)e(de-)456 3649 y(\014ned)j(as)e(follo)n(ws.)612 3766 y FK(Ob)5 b(jects:)41 b FQ(all)27 b(marking)f(graphs.)612 3865 y FK(Morphisms:)38 b FQ(Mor)o(\()p FJ(m)1400 3877 y FM(1)1437 3865 y FJ(;)14 b(m)1547 3877 y FM(2)1584 3865 y FQ(\))29 b(consists)e(of)h(all)f(paths)h(in)g(the)g(CW)h(complex)e FL(M)3227 3877 y FM(0)3292 3865 y FQ(con-)711 3965 y(necting)d FJ(m)1071 3977 y FM(1)1131 3965 y FQ(with)g FJ(m)1389 3977 y FM(2)1426 3965 y FQ(,)h(mo)r(dulo)e(homotop)n(y)-7 b(.)34 b(\(In)24 b(other)f(w)n(ords,)g(as)g(a)g(group)r(oid)f FL(MS)711 4065 y FQ(is)28 b(the)g(fundamen)n(tal)f(group)r(oid)g(of)g FL(M)1960 4077 y FM(0)1997 4065 y FQ(.\))612 4164 y FK(Boundary)32 b(functor:)42 b FJ(A)p FQ(\()p FJ(m)p FQ(\))24 b(=)f(Ext)o(\()p FJ(m)p FQ(\).)612 4264 y FK(Disjoin)m(t)31 b(union)g(and)h FL(;)p FK(:)41 b FQ(ob)n(vious.)612 4363 y FK(Gluing:)e FQ(if)j FJ(\013;)14 b(\014)49 b FL(2)c FQ(Ext\()p FJ(m)p FQ(\))c(are)f(in)h(di\013eren)n(t)g(connected)f(comp)r(onen)n(ts,)k (then)d(w)n(e)711 4463 y(de\014ne)31 b FJ(G)1019 4475 y FI(\013;\014)1127 4463 y FQ(\()p FJ(m)p FQ(\))g(to)f(b)r(e)h(the)g (graph)e(obtained)i(b)n(y)f(iden)n(tifying)g(the)h(v)n(ertices)f FJ(\013)h FQ(and)711 4563 y FJ(\014)t FQ(.)37 b(The)25 b(order)f(at)h(the)g(new)h(in)n(ternal)e(v)n(ertex)g FJ(\013)g FQ(=)e FJ(\014)30 b FQ(is)25 b(giv)n(en)f(b)n(y)h FJ(e)2854 4575 y FI(\013)2924 4563 y FJ(<)e(e)3051 4575 y FI(\014)3121 4563 y FQ(where)h FJ(e)3397 4575 y FI(\013)711 4662 y FQ(is)k(the)g(edge)f(of)g FJ(m)h FQ(ending)f(at)h FJ(\013)p FQ(.)456 4779 y(Note)f(that)h FL(MS)34 b FQ(is)27 b(a)h(\\partial")d(to)n(w)n(er)i(in)h(the)g(sense)f(of)g(Remark)g (5.6.3.)605 4917 y FP(Theorem)32 b FQ(5.6.17)p FP(.)39 b FO(L)l(et)26 b FL(C)31 b FO(b)l(e)26 b(a)h(semisimple)h(ab)l(elian)f (c)l(ate)l(gory.)38 b(Then)27 b(MS)g(data)g(for)g FL(C)456 5016 y FO(is)k(the)h(same)f(as)h(a)g(non-de)l(gener)l(ate)f(r)l(epr)l (esentation)h FJ(\032)f FO(of)h(the)f(Mo)l(or)l(e{Seib)l(er)l(g)j (tower)d FL(MS)456 5116 y FO(in)f FL(C)35 b FO(with)c(the)f(additional) j(normalization)f(c)l(ondition)g FJ(\032)p FQ(\()p FL(\003)p FQ(\))24 b(=)g(id)9 b(:)28 b FL(V)7 b FJ(ec)2763 5128 y FI(f)2829 5116 y FL(!)25 b(V)7 b FJ(ec)3070 5128 y FI(f)3112 5116 y FO(,)31 b(wher)l(e)g FL(\003)456 5216 y FO(is)f(the)g(marking)g(gr)l(aph)h(with)f(one)g(vertex)g(and)g(no)g (e)l(dges.)p eop %%Page: 125 33 125 128 bop 1470 226 a FM(5.6.)29 b(TO)n(WERS)g(OF)g(GR)n(OUPOIDS)893 b(125)605 425 y FP(Pr)n(oof.)41 b FQ(Giv)n(en)30 b(a)g(collection)g(of) g(MS)h(data,)g(let)g(us)f(construct)g(a)g(represen)n(tation)f FJ(\032)i FQ(of)456 525 y(the)24 b(to)n(w)n(er)f FL(MS)6 b FQ(.)36 b(F)-7 b(or)23 b(a)h(marking)e(graph)h FJ(m)p FQ(,)i(de\014ne)f(the)h(functor)f FJ(\032)p FQ(\()p FJ(m)p FQ(\))9 b(:)28 b FL(C)2868 495 y Fv(\002)p FM(Ext)o(\()p FI(m)p FM(\))3163 525 y FL(!)23 b(V)7 b FJ(ec)3402 537 y FI(f)456 624 y FQ(similarly)27 b(to)i(\(5.4.3\))o(.)40 b(In)29 b(other)f(w)n(ords,)g(if)h FJ(W)1938 636 y FI(v)2006 624 y FQ(are)f(the)h(ob)5 b(jects)28 b(assigned)g(to)g(the)h(external) 456 724 y(v)n(ertices)d FJ(v)g FL(2)e FQ(Ext)o(\()p FJ(m)p FQ(\),)29 b(then)f(w)n(e)f(let)1227 903 y FJ(\032)p FQ(\()p FJ(m)p FQ(\)\()p FL(f)p FJ(W)1559 915 y FI(v)1599 903 y FL(g)p FQ(\))c(=)1861 824 y Fy(O)1784 1006 y FI(u)p FE(2)p FM(In)n(t\()p FI(m)p FM(\))2064 903 y FL(h)p FJ(X)2165 918 y FI(e)2196 901 y FF(1)2196 935 y FG(u)2240 903 y FJ(;)14 b(:)g(:)g(:)f(;)h(X)2493 932 y FI(e)2524 904 y FG(k)2555 912 y(u)2524 941 y(u)2603 903 y FL(i)p FJ(;)456 1171 y FQ(where)26 b FJ(e)734 1141 y FM(1)734 1191 y FI(u)777 1171 y FJ(;)14 b(:)g(:)g(:)g(;)g(e)1001 1141 y FI(k)1036 1149 y FG(u)1001 1191 y FI(u)1106 1171 y FQ(are)26 b(the)i(edges)e(adjacen)n(t)g(to)h FJ(u)p FQ(,)g(in)g(the)h (order)e(de\014ned)h(b)n(y)g FJ(u)p FQ(,)f(and)h FJ(X)3321 1183 y FI(e)3380 1171 y FQ(=)456 1271 y FJ(W)534 1283 y FI(v)601 1271 y FQ(if)g FJ(e)g FQ(connects)g FJ(u)g FQ(with)h(an)f(external)f(v)n(ertex)g FJ(v)s FQ(,)i(or)e FJ(X)2293 1283 y FI(e)2352 1271 y FQ(=)c FJ(R)28 b FQ(if)g FJ(e)f FQ(connects)g(t)n(w)n(o)f(in)n(ternal)456 1370 y(v)n(ertices.)605 1470 y(The)21 b(de\014nition)g(of)g(the)g (functorial)f(isomorphisms)g(whic)n(h)g(w)n(e)h(assign)e(to)i(the)g (morphisms)456 1569 y(of)31 b(graphs)f(is)h(ob)n(vious.)46 b(W)-7 b(e)32 b(also)e(ha)n(v)n(e)g(ob)n(vious)g(isomorphisms)g FJ(\032)p FQ(\()p FJ(m)2742 1581 y FM(1)2800 1569 y FL(t)21 b FJ(m)2949 1581 y FM(2)2986 1569 y FQ(\))30 b FL(')e FJ(\032)p FQ(\()p FJ(m)3289 1581 y FM(1)3327 1569 y FQ(\))21 b FL(\012)456 1669 y FJ(\032)p FQ(\()p FJ(m)604 1681 y FM(2)641 1669 y FQ(\))h(and)f FJ(\032)p FQ(\()p FJ(G)990 1681 y FI(\013;\014)1098 1669 y FQ(\()p FJ(m)p FQ(\)\))j FL(')f FJ(G)1444 1681 y FI(\013;\014)1552 1669 y FQ(\()p FJ(\032)p FQ(\()p FJ(m)p FQ(\)\);)h(in)e(the)g(latter)f(isomorphism)g (b)r(oth)h(sides)f(coincide)456 1775 y(with)28 b FJ(\032)p FQ(\()p FJ(m)p FQ(\)\()p FJ(:)14 b(:)g(:)g(;)g(R)1069 1745 y FM(\(1\))1158 1775 y FJ(;)g(:)g(:)g(:)f(;)h(R)1406 1745 y FM(\(2\))1495 1775 y FJ(;)g(:)g(:)g(:)g FQ(\).)605 1875 y(No)n(w,)39 b(a)e(comparison)e(of)i(the)h(relations)e(MS1{MS7)g (and)h(the)g(relations)f(MF1{MF7,)456 1974 y(used)24 b(in)h(the)g(de\014nition)h(of)e FL(M)1434 1986 y FM(0)1471 1974 y FQ(,)i(sho)n(ws)d(that)i(the)g(so)f(de\014ned)h FJ(\032)g FQ(is)g(indeed)g(a)f(represen)n(tation)456 2074 y(of)j FL(MS)6 b FQ(.)605 2173 y(Con)n(v)n(ersely)-7 b(,)29 b(giv)n(en)g(a)h(represen)n(tation)f FJ(\032)h FQ(of)h(the)f(to)n(w)n(er)f FL(MS)6 b FQ(,)31 b(de\014ne)g(the)g(MS)f (data)g(as)456 2273 y(follo)n(ws:)1294 2436 y FL(h)p FJ(W)1404 2448 y FM(1)1441 2436 y FJ(;)14 b(:)g(:)g(:)g(;)g(W)1704 2448 y FI(n)1750 2436 y FL(i)23 b FQ(=)g FJ(\032)p FQ(\()p FJ(m)2041 2448 y FI(n)2086 2436 y FQ(\)\()p FJ(W)2228 2448 y FM(1)2266 2436 y FJ(;)14 b(:)g(:)g(:)g(;)g(W)2529 2448 y FI(n)2574 2436 y FQ(\))456 2599 y(where)21 b FJ(m)763 2611 y FI(n)831 2599 y FQ(is)h(the)g(\\standard")f(marking)g(graph,)h (with)h(one)e(in)n(ternal)h(v)n(ertex)f(and)h FJ(n)g FQ(external)456 2698 y(v)n(ertices.)44 b(Again,)30 b(it)h(is)f(clear)g (ho)n(w)g(to)g(de\014ne)g(the)h(isomorphisms)e FJ(Z)q(;)14 b(\033)n(;)g(G)31 b FQ(and)g(c)n(hec)n(k)e(that)456 2798 y(all)e(the)h(relations)e(are)h(satis\014ed.)p 3384 2798 4 57 v 3388 2745 50 4 v 3388 2798 V 3437 2798 4 57 v 605 2987 a(It)d(is)f(clear)f(b)n(y)h(its)g(de\014nition)h(that)f(the)h (to)n(w)n(er)d FL(MS)30 b FQ(is)23 b(just)h(the)f(pro)5 b(jection)23 b(on)f(the)i(lev)n(el)456 3087 y(of)29 b(marking)f(graphs) h(of)g(another)g(to)n(w)n(er)f FL(P)7 b(T)g FJ(eich)2050 3099 y FM(0)2086 3087 y FQ(:)41 b(the)30 b FO(p)l(ar)l(ametrize)l(d)j (T)-6 b(eichm)q(\177)-43 b(ul)t(ler)33 b(tower)456 3187 y(in)25 b(genus)g(zer)l(o)p FQ(.)35 b(On)23 b(its)g(hand,)g FL(P)7 b(T)g FJ(eich)1723 3199 y FM(0)1782 3187 y FQ(is)23 b(the)g(gen)n(us)f(zero)f(part)i(of)f(a)g(to)n(w)n(er)g FL(P)7 b(T)g FJ(eich)22 b FQ(whic)n(h)456 3286 y(app)r(eared)k (implicitly)j(in)e(Section)h(5.2)f(and)g(whic)n(h)h(w)n(e)f(no)n(w)g (pro)r(ceed)g(to)g(de\014ne.)605 3452 y FP(Example)k FQ(5.6.18)p FP(.)39 b FQ(The)23 b FO(p)l(ar)l(ameterize)l(d)j(T)-6 b(eichm)q(\177)-43 b(ul)t(ler)27 b(tower)32 b FL(P)7 b(T)g FJ(eich)22 b FQ(is)g(the)h(to)n(w)n(er)f(of)456 3551 y(group)r(oids)k(de\014ned)i(as)f(follo)n(ws.)612 3683 y FK(Ob)5 b(jects:)41 b FQ(all)23 b(pairs)g(\(\006)p FJ(;)14 b(M)9 b FQ(\),)25 b(where)e(\006)h(is)g(an)g(extended)g (surface)f(and)h FJ(M)31 b FQ(=)23 b(\()p FJ(C)q(;)14 b FL(f)p FJ( )3330 3695 y FI(a)3371 3683 y FL(g)p FQ(\))711 3782 y(is)28 b(a)f(parameterization)e(of)j(\006)g(\(see)f(De\014nition) h(5.2.1\).)612 3889 y FK(Morphisms:)38 b FQ(Mor)o(\(\(\006)1419 3901 y FM(1)1457 3889 y FJ(;)14 b(M)1575 3901 y FM(1)1611 3889 y FQ(\))p FJ(;)g FQ(\(\006)1772 3901 y FM(2)1810 3889 y FJ(;)g(M)1928 3901 y FM(2)1965 3889 y FQ(\)\))19 b(consists)e(of)i(all)f(pairs)f(\()p FJ(f)t(;)d(')p FQ(\))19 b(where)f FJ(f)g FQ(:)28 b(\006)3350 3901 y FM(1)3438 3842 y FE(\030)3410 3889 y FL(\000)-39 b(!)711 3989 y FQ(\006)771 4001 y FM(2)846 3989 y FQ(is)37 b(a)f(homeomorphism)g(of)h (extended)h(surfaces)e(and)h FJ(')g FQ(is)g(a)g(path)g(in)h FL(M)p FQ(\(\006)3375 4001 y FM(2)3412 3989 y FQ(\))711 4088 y(connecting)i FJ(f)9 b FQ(\()p FJ(M)1302 4100 y FM(1)1339 4088 y FQ(\))40 b(with)h FJ(M)1694 4100 y FM(2)1731 4088 y FQ(.)76 b(The)40 b(comp)r(osition)g(of)g(morphisms)g(is)g(giv)n (en)g(b)n(y)711 4188 y(\()p FJ(f)t(;)14 b(')p FQ(\))19 b FL(\016)f FQ(\()p FJ(g)s(;)c( )s FQ(\))23 b(=)g(\()p FJ(f)k FL(\016)18 b FJ(g)s(;)c(')19 b FL(\016)f FJ(f)9 b FQ(\()p FJ( )s FQ(\)\).)612 4287 y FK(Boundary)32 b(functor:)42 b FJ(A)p FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\))23 b(=)g FJ(A)p FQ(\(\006\))h(=)f FJ(\031)2193 4299 y FM(0)2230 4287 y FQ(\()p FJ(@)5 b FQ(\006\))26 b(|)f(the)h(set)f(of)h(b)r(oundary)e (com-)711 4387 y(p)r(onen)n(ts)k(of)f(\006.)612 4487 y FK(Disjoin)m(t)k(union)g(and)h FL(;)p FK(:)41 b FQ(the)28 b(usual)f(ones.)612 4586 y FK(Gluing:)39 b FJ(G)1026 4598 y FI(\013;\014)1134 4586 y FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\))27 b(=)f(\()p FL(t)1590 4598 y FI(\013;\014)1698 4586 y FQ(\(\006\))p FJ(;)14 b FL(t)1914 4598 y FI(\013;\014)2023 4586 y FJ(M)9 b FQ(\),)30 b(where)f FL(t)2495 4598 y FI(\013;\014)2603 4586 y FQ(\(\006\))h(is)g(obtained)f(from)g(\006)711 4686 y(b)n(y)f(gluing)f(the)i(b)r(oundary)e(comp)r(onen)n(ts)h FJ(\013;)14 b(\014)t FQ(,)28 b(and)g(the)h(parameterization)d FL(t)3247 4698 y FI(\013;\014)3355 4686 y FJ(M)711 4786 y FQ(is)i(obtained)g(from)g FJ(M)37 b FQ(b)n(y)28 b(adding)g FJ(\013)d FQ(=)f FJ(\014)32 b FQ(as)c(a)g(new)g(cut)h(and)f(k)n(eeping) g(the)g(homeo-)711 4885 y(morphisms)f FJ( )1186 4897 y FI(a)1254 4885 y FQ(unc)n(hanged.)605 5016 y(Note)j(that)g(b)n(y)g (Theorem)f(5.2.9)g(the)h(path)g FJ(')h FQ(is)e(uniquely)i(de\014ned)f (b)n(y)g FJ(f)9 b FQ(,)30 b(so)f(w)n(e)h(could)456 5116 y(as)e(w)n(ell)i(omit)f FJ(')h FQ(from)f(the)h(ab)r(o)n(v)n(e)e (de\014nition)i(of)g(morphisms.)41 b(Ho)n(w)n(ev)n(er,)29 b(it)g(will)h(b)r(e)g(useful)456 5216 y(for)d(us)g(to)h(ha)n(v)n(e)e (the)i(de\014nition)g(in)g(this)g(form.)p eop %%Page: 126 34 126 129 bop 456 226 a FM(126)1010 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FQ(No)n(w)k(w)n(e)h(can)f(reform)n(ulate)g(the)h(main)f(results)h (of)f(the)i(previous)d(sections)h(in)h(a)g(m)n(uc)n(h)456 525 y(more)26 b(transparen)n(t)g(w)n(a)n(y)-7 b(.)605 685 y FP(Theorem)32 b FQ(5.6.19)p FP(.)39 b FQ(\(i\))22 b FO(The)g(towers)g(of)g(gr)l(oup)l(oids)h FL(T)7 b FJ(eich)21 b FO(and)g FL(P)7 b(T)g FJ(eich)21 b FO(ar)l(e)g(e)l(quivalent.)456 785 y(Similarly,)31 b(their)g(genus)e(zer)l(o)h(p)l(arts)g FL(T)7 b FJ(eich)1852 797 y FM(0)1918 785 y FO(and)31 b FL(P)7 b(T)g FJ(eich)2349 797 y FM(0)2415 785 y FO(ar)l(e)30 b(e)l(quivalent.)605 884 y FQ(\(ii\))g FO(The)h(towers)f FL(P)7 b(T)g FJ(eich)1446 896 y FM(0)1512 884 y FO(and)30 b FL(MS)36 b FO(ar)l(e)30 b(e)l(quivalent.)605 1045 y FP(Pr)n(oof.)41 b FQ(\(i\))20 b(T)-7 b(o)19 b(pro)n(v)n(e)e(the)j (\014rst)f(statemen)n(t,)i(consider)d(the)i(ob)n(vious)e(forgetting)h (functor)456 1144 y FL(P)7 b(T)g FJ(eich)27 b FL(!)i(T)7 b FJ(eich)p FQ(.)47 b(It)31 b(su\016ces)g(to)g(c)n(hec)n(k)f(that)h (this)g(functor)g(is)g(bijectiv)n(e)g(on)g(morphisms.)456 1244 y(By)f(Theorem)f(5.2.9,)h(for)g(ev)n(ery)f(t)n(w)n(o)h (parameterizations)e FJ(M)t(;)14 b(M)2568 1214 y FE(0)2621 1244 y FQ(of)31 b(an)f(extended)g(surface)456 1344 y(\006)h(there)g (exists)g(a)g(unique)h(path)g(in)f FL(M)p FQ(\(\006\))h(connecting)f (them.)49 b(Th)n(us,)32 b(in)g(a)f(pair)g(\()p FJ(f)t(;)14 b(')p FQ(\))30 b FL(2)456 1443 y FQ(Mor)606 1455 y FE(P)5 b(T)t FI(eich)827 1443 y FQ(,)31 b(the)f(path)h FJ(')f FQ(is)g(uniquely)h(determined)f(b)n(y)g FJ(f)9 b FQ(,)31 b(whic)n(h)f(is)g(equiv)-5 b(alen)n(t)30 b(to)g(sa)n(ying)456 1545 y(that)d(the)g(forgetting)f(functor)h(giv)n(es)e(a)i(bijection)g (Mor)2204 1557 y FE(P)5 b(T)t FI(eich)2477 1498 y FE(\030)2448 1545 y FL(\000)-39 b(!)23 b FQ(Mor)2730 1557 y FE(T)t FI(eich)2899 1545 y FQ(.)37 b(The)27 b(pro)r(of)f(for)456 1645 y(gen)n(us)g(zero)h(is)g(completely)h(parallel.)605 1745 y(\(ii\))c(T)-7 b(o)22 b(pro)n(v)n(e)f(the)i(second)f(statemen)n (t,)i(consider)d(the)i(functor)g FL(P)7 b(T)g FJ(eich)2890 1757 y FM(0)2949 1745 y FL(!)24 b(MS)29 b FQ(whic)n(h)456 1844 y(assigns)18 b(to)i(the)h(pair)e(\(\006)p FJ(;)14 b(M)9 b FQ(\))21 b(the)f(marking)f(graph)g(of)h FJ(M)9 b FQ(.)34 b(Ob)n(viously)-7 b(,)21 b(ev)n(ery)e(marking)g(graph)456 1944 y(can)34 b(b)r(e)i(obtained)f(in)g(this)h(w)n(a)n(y)-7 b(.)58 b(Th)n(us,)37 b(it)f(su\016ces)e(to)h(pro)n(v)n(e)f(that)h(this) h(functor)f(giv)n(es)f(a)456 2044 y(bijection)25 b(of)f(the)h(spaces)f (of)g(morphisms.)36 b(This)24 b(is)h(immediate)f(from)h(comparing)e (the)i(mo)n(v)n(es)456 2143 y(and)i(relations)f(and)i(the)g(follo)n (wing)e(rigidit)n(y)h(lemma.)605 2304 y FP(Lemma)k FQ(5.6.20)p FP(.)40 b FO(L)l(et)33 b FQ(\006)g FO(b)l(e)h(an)f(extende)l(d)h (surfac)l(e,)h FJ(M)k FL(2)30 b FJ(M)9 b FQ(\(\006\))34 b FO(b)l(e)f(a)h(p)l(ar)l(ameteriza-)456 2410 y(tion,)27 b(and)g FJ(m)f FO(the)g(c)l(orr)l(esp)l(onding)i(marking)f(gr)l(aph.)39 b(L)l(et)25 b FJ(f)18 b FQ(:)28 b(\006)2501 2363 y FE(\030)2473 2410 y FL(\000)-39 b(!)23 b FQ(\006)j FO(b)l(e)g(a)h(home)l(omorphism) 456 2510 y(which)k(pr)l(eserves)g(the)e(gr)l(aph)i FJ(m)f FO(p)l(ointwise.)1871 2480 y FM(4)1948 2510 y FO(Then)g FJ(f)39 b FO(is)30 b(homotopic)i(to)e(identity.)605 2670 y FQ(This)e(completes)f(the)h(pro)r(of)f(of)g(Theorem)g(5.6.19.)p 3384 2670 4 57 v 3388 2618 50 4 v 3388 2670 V 3437 2670 4 57 v 605 2847 a(A)36 b(comparison)e(of)h(the)h(theorems)f(ab)r(o)n(v) n(e)f(mak)n(es)h(the)h(relation)e(b)r(et)n(w)n(een)i(gen)n(us)f(zero) 456 2947 y(mo)r(dular)27 b(functors)g(and)g(w)n(eakly)g(ribb)r(on)g (structures)g(on)g(a)g(semisimple)h(category)e(ob)n(vious.)1072 3170 y FK(5.7.)46 b(Cen)m(tral)32 b(extension)f(of)h(mo)s(dular)e (functor)605 3320 y FQ(In)21 b(Section)g(5.5)g(w)n(e)f(ha)n(v)n(e)g (constructed)h(a)f FL(C)5 b FQ(-extended)21 b(mo)r(dular)f(functor)h (\(MF\))h(starting)456 3420 y(from)33 b(an)n(y)f(mo)r(dular)h(tensor)g (category)f FL(C)38 b FQ(satisfying)33 b FJ(p)2253 3389 y FM(+)2307 3420 y FJ(=p)2391 3389 y FE(\000)2480 3420 y FQ(=)f(1.)54 b(As)34 b(with)g(TQFT)f(con-)456 3519 y(structed)23 b(from)h FL(C)5 b FQ(,)24 b(the)g(gluing)f(axiom)g(fails) h(when)g FJ(p)2116 3489 y FM(+)2171 3519 y FJ(=p)2255 3489 y FE(\000)2333 3519 y FL(6)p FQ(=)f(1.)35 b(There)23 b(are)g(t)n(w)n(o)g(approac)n(hes)456 3619 y(to)k(deal)g(with)h(the)g (general)f(case.)605 3718 y(First,)g(w)n(e)f(can)h(con)n(ten)n(t)f (ourselv)n(es)f(with)i(a)g(mo)r(di\014cation)f(of)h(the)g(gluing)f (axiom,)h(whic)n(h)456 3818 y(sa)n(ys)h(that)j(it)g(holds)f(only)f(up)i (to)f(a)g(m)n(ultiplicativ)n(e)g(factor.)44 b(This)30 b(is)h(similar)e(to)h(the)h(notion)456 3918 y(of)c(a)g(pro)5 b(jectiv)n(e)27 b(represen)n(tation)f(of)h(a)g(group.)605 4017 y(The)21 b(second)f(approac)n(h)g(is)g(to)h(try)g(to)g(construct)f (a)h(kind)g(of)g(a)g(\\cen)n(tral)e(extension")h(of)h(the)456 4117 y(mo)r(dular)29 b(functor.)42 b(This)30 b(w)n(as)e(done)h(indep)r (enden)n(tly)i(b)n(y)e(sev)n(eral)f(authors;)h(our)g(exp)r(osition)456 4217 y(follo)n(ws)d(an)i(unpublished)g(man)n(uscript)f([)p FK(BFM)o FQ(])h(b)n(y)f(Beilinson,)h(F)-7 b(eigin,)27 b(and)h(Masur.)605 4316 y(W)-7 b(e)36 b(b)r(egin)f(with)h(some)f (preliminaries.)59 b(Let)36 b FJ(V)54 b FQ(b)r(e)36 b(a)f(symplectic)h (real)e(v)n(ector)g(space)456 4416 y(of)k(dimension)h(2)p FJ(g)s FQ(,)h FJ(g)45 b FL(2)c FH(N)t FQ(.)77 b(Let)38 b(\003)1665 4428 y FI(V)1761 4416 y FQ(b)r(e)h(the)g(set)g(of)g(all)f (Lagrangian)e(subspaces)i(of)g FJ(V)19 b FQ(,)456 4515 y(i.e.,)37 b(maximal)e(isotropic)g(subspaces)f(of)h FJ(V)19 b FQ(.)61 b(This)36 b(is)f(a)g(compact)g(manifold.)61 b(Let)35 b FJ(T)3266 4527 y FI(V)3359 4515 y FQ(b)r(e)456 4615 y(the)c FO(Poinc)l(ar)n(\023)-40 b(e)35 b(gr)l(oup)l(oid)e FQ(of)e(\003)1448 4627 y FI(V)1506 4615 y FQ(;)i(b)n(y)e(de\014nition,) i(ob)5 b(jects)31 b(of)g(this)h(group)r(oid)e(are)g(p)r(oin)n(ts)i(of) 456 4715 y(\003)514 4727 y FI(V)609 4715 y FQ(and)39 b(morphisms)f(are)f(homotop)n(y)g(classes)h(of)g(paths)g(connecting)g (t)n(w)n(o)g(p)r(oin)n(ts.)70 b(It)39 b(is)456 4814 y(con)n(v)n(enien)n (t)d(to)h(de\014ne)h FJ(T)1286 4826 y FI(V)1381 4814 y FQ(for)f FJ(V)58 b FQ(=)40 b(0)d(as)g(the)g(category)f(with)i(only)f (one)g(ob)5 b(ject)38 b(0)f(and)456 4914 y(Hom)629 4926 y FI(T)668 4934 y FF(0)704 4914 y FQ(\(0)p FJ(;)14 b FQ(0\))23 b(=)g FH(Z)o FQ(.)605 5014 y(The)28 b(pro)r(of)f(of)g(the)h (follo)n(wing)f(lemma)g(is)h(straigh)n(tforw)n(ard)c(and)k(will)g(b)r (e)g(omitted.)p 456 5122 499 4 v 605 5192 a Fp(4)640 5216 y Fo(It)c(is)f(not)h(su\016cien)n(t)h(to)f(require)f(that)i Fm(f)7 b Fo(\()p Fm(m)p Fo(\))21 b(=)f Fm(m)p Fo(,)j(as)h Fm(f)31 b Fo(could)24 b(in)n(terc)n(hange)h(comp)r(onen)n(ts)g(of)e Fm(m)p Fo(.)p eop %%Page: 127 35 127 130 bop 1087 226 a FM(5.7.)29 b(CENTRAL)h(EXTENSION)f(OF)f(MODULAR) h(FUNCTOR)511 b(127)605 425 y FP(Lemma)31 b FQ(5.7.1)p FP(.)40 b FQ(\(i\))35 b FO(F)-6 b(or)34 b(any)h(two)g(symple)l(ctic)g (ve)l(ctor)g(sp)l(ac)l(es)g FJ(V)2714 437 y FM(1)2751 425 y FO(,)h FJ(V)2860 437 y FM(2)2898 425 y FO(,)g(ther)l(e)e(exists)g (a)456 525 y(c)l(anonic)l(al)d(map)f FQ(\003)1061 537 y FI(V)1100 545 y FF(1)1155 525 y FL(\002)18 b FQ(\003)1296 537 y FI(V)1335 545 y FF(2)1394 525 y FL(!)23 b FQ(\003)1558 537 y FI(V)1597 545 y FF(1)1630 537 y FE(\010)p FI(V)1721 545 y FF(2)1757 525 y FO(.)605 624 y FQ(\(ii\))35 b FO(L)l(et)f FJ(N)41 b FL(\032)31 b FJ(V)53 b FO(b)l(e)35 b(an)g(isotr)l(opic)h (subsp)l(ac)l(e,)g(i.e.,)i(such)d(that)f(the)h(r)l(estriction)g(of)g (the)456 724 y(symple)l(ctic)29 b(form)f(on)g FJ(N)37 b FO(is)28 b FQ(0)p FO(.)38 b(Then)29 b(the)f(sp)l(ac)l(e)g FJ(N)2105 694 y FE(?)2161 724 y FJ(=)-5 b(N)37 b FO(is)28 b(symple)l(ctic,)i(and)e(ther)l(e)g(exists)g(a)456 824 y(c)l(anonic)l(al)33 b(map)g FQ(\003)1066 841 y FI(N)1125 824 y Fx(?)1174 841 y FI(=)l(N)1295 824 y FL(!)28 b FQ(\003)1464 836 y FI(V)1554 824 y FO(which)34 b(assigns)f(to)f(a)h(L)l(agr)l (angian)g(subsp)l(ac)l(e)g FJ(L)27 b FL(\032)h FJ(N)3276 794 y FE(?)3332 824 y FJ(=)-5 b(N)456 934 y FO(the)30 b(subsp)l(ac)l(e)h FJ(\031)978 904 y FE(\000)p FM(1)1067 934 y FQ(\()p FJ(L)p FQ(\))24 b FL(\032)f FJ(N)1376 904 y FE(?)1456 934 y FL(\032)h FJ(V)18 b FO(,)31 b(wher)l(e)g FJ(\031)12 b FQ(:)29 b FJ(N)2089 904 y FE(?)2168 934 y FL(!)24 b FJ(N)2351 904 y FE(?)2407 934 y FJ(=)-5 b(N)39 b FO(is)30 b(the)h(natur)l(al)f(pr)l(oje)l(ction.)456 1033 y(The)g(induc)l(e)l(d)g(map)h(of)g(fundamental)f(gr)l(oup)l(oids)h FJ(T)2097 1050 y FI(N)2156 1034 y Fx(?)2204 1050 y FI(=)l(N)2321 1033 y FL(!)23 b FJ(T)2476 1045 y FI(V)2563 1033 y FO(is)30 b(an)g(e)l(quivalenc)l(e.)605 1195 y FP(Cor)n(ollar)-6 b(y)33 b FQ(5.7.2)p FP(.)39 b FO(F)-6 b(or)30 b(any)h(p)l(oint)f FJ(a)23 b FL(2)h FQ(\003)2056 1207 y FI(V)2113 1195 y FO(,)30 b(the)g(fundamental)h(gr)l(oup)f FJ(\031)3057 1207 y FM(1)3094 1195 y FQ(\(\003)3184 1207 y FI(V)3242 1195 y FJ(;)14 b(a)p FQ(\))30 b FO(is)456 1295 y(isomorphic)i(to)e FH(Z)o FO(.)605 1455 y FQ(Corollary)d(5.7.2)h(implies)i(that)f(the)h (group)e FH(Z)23 b FQ(acts)29 b(freely)g(on)g(Mor)2775 1467 y FI(T)2814 1475 y FG(V)2868 1455 y FQ(\()p FJ(L)2957 1467 y FM(1)2994 1455 y FJ(;)14 b(L)3088 1467 y FM(2)3125 1455 y FQ(\))29 b(for)g(an)n(y)456 1554 y FJ(L)513 1566 y FM(1)549 1554 y FJ(;)14 b(L)643 1566 y FM(2)717 1554 y FL(2)37 b FQ(\003)867 1566 y FI(V)925 1554 y FQ(.)62 b(\(In)36 b(other)g(w)n(ords,)g(Mor)1802 1566 y FI(T)1841 1574 y FG(V)1895 1554 y FQ(\()p FJ(L)1984 1566 y FM(1)2021 1554 y FJ(;)14 b(L)2115 1566 y FM(2)2152 1554 y FQ(\))36 b(is)g(a)g FH(Z)o FO(-t)o(orsor)9 b FQ(.\))57 b(Hence)36 b(w)n(e)g(ha)n(v)n(e)f(a)456 1654 y(non-canonical)25 b(iden)n(ti\014cation)1574 1806 y(Mor)1724 1818 y FI(T)1763 1826 y FG(V)1818 1806 y FQ(\()p FJ(L)1907 1818 y FM(1)1944 1806 y FJ(;)14 b(L)2038 1818 y FM(2)2074 1806 y FQ(\))2158 1759 y FE(\030)2130 1806 y FL(\000)-40 b(!)23 b FH(Z)p FJ(:)-1890 b FQ(\(5.7.1\))456 1959 y(Let)26 b(us)g(c)n(ho)r(ose)f(suc)n (h)h(iden)n(ti\014cations)g(for)g(all)g FJ(L)1985 1971 y FM(1)2022 1959 y FJ(;)14 b(L)2116 1971 y FM(2)2175 1959 y FL(2)24 b FQ(\003)2312 1971 y FI(V)2369 1959 y FQ(.)36 b(If)27 b FJ(')9 b FQ(:)28 b FJ(L)2681 1971 y FM(1)2741 1959 y FL(!)23 b FJ(L)2904 1971 y FM(2)2967 1959 y FQ(and)k FJ( )12 b FQ(:)28 b FJ(L)3302 1971 y FM(2)3361 1959 y FL(!)456 2059 y FJ(L)513 2071 y FM(3)578 2059 y FQ(are)g(t)n(w)n(o)f(morphisms)h(in)h FJ(T)1444 2071 y FI(V)1501 2059 y FQ(,)g(corresp)r(onding)e(to)h(n)n(um)n(b)r (ers)g FJ(m;)14 b(n)25 b FL(2)g FH(Z)o FQ(,)e(then)29 b(in)g(general)456 2158 y FJ( )s(')9 b FQ(:)28 b FJ(L)684 2170 y FM(1)744 2158 y FL(!)23 b FJ(L)907 2170 y FM(3)971 2158 y FQ(corresp)r(onds)j(to)h(some)g FJ(p)c FL(6)p FQ(=)g FJ(m)18 b FQ(+)g FJ(n)p FQ(.)37 b(The)28 b(di\013erence)1465 2311 y FJ(\026)p FQ(\()p FJ(L)1604 2323 y FM(1)1641 2311 y FJ(;)14 b(L)1735 2323 y FM(2)1771 2311 y FJ(;)g(L)1865 2323 y FM(3)1902 2311 y FQ(\))23 b(:=)g FJ(p)18 b FL(\000)g FJ(m)h FL(\000)f FJ(n)-1980 b FQ(\(5.7.2\))456 2463 y(is)27 b(called)g(the)h FO(Maslov)k(index)38 b FQ(of)27 b(the)h(subspaces)f FJ(L)2103 2475 y FM(1)2139 2463 y FJ(;)14 b(L)2233 2475 y FM(2)2270 2463 y FJ(;)g(L)2364 2475 y FM(3)2401 2463 y FQ(.)605 2563 y(Let)23 b(\006)f(b)r(e)h(an)f(extended)h(surface,)g (as)f(in)h(Section)f(5.1.)34 b(W)-7 b(e)23 b(denote)g(b)n(y)f FJ(cl)r FQ(\(\006\))g(the)h(surface)456 2663 y(without)k(b)r(oundary)f (obtained)h(from)g(\006)g(b)n(y)g(gluing)f(disks)h(to)g(all)g(b)r (oundary)f(circles,)g(and)h(let)1548 2815 y FJ(H)7 b FQ(\(\006\))23 b(:=)g(H)1944 2827 y FM(1)1981 2815 y FQ(\()p FJ(cl)r FQ(\(\006\))p FJ(;)14 b FH(R)p FQ(\))p FJ(:)-1890 b FQ(\(5.7.3\))456 2972 y(The)30 b(in)n(tersection)f(form)h (mak)n(es)f FJ(H)7 b FQ(\(\006\))31 b(a)f(symplectic)g(space)f(of)i (dimension)f(2)p FJ(g)i FQ(where)e FJ(g)j FQ(is)456 3072 y(the)28 b(gen)n(us)e(of)i(\006)g(\(i.e.,)g(of)f FJ(cl)r FQ(\(\006\)\).)37 b(In)n(tro)r(duce)27 b(the)h(notations)1459 3224 y(\003)1517 3236 y FM(\006)1591 3224 y FQ(:=)23 b(\003)1760 3239 y FI(H)t FM(\(\006\))1922 3224 y FJ(;)97 b(T)2091 3236 y FM(\006)2165 3224 y FQ(:=)23 b FJ(T)2325 3236 y FM(\003)2370 3244 y FF(\006)2418 3224 y FJ(:)-1985 b FQ(\(5.7.4\))456 3382 y(When)30 b(\006)g(is)g(of)g(gen)n(us)f(zero,)h (w)n(e)f(ha)n(v)n(e)g FJ(H)7 b FQ(\(\006\))27 b(=)g(0)i(and)h(\003)2336 3394 y FM(\006)2417 3382 y FQ(is)g(a)g(p)r(oin)n(t.)44 b(In)30 b(this)g(case,)g(it)h(is)456 3481 y(con)n(v)n(enien)n(t)18 b(to)h(de\014ne)g FJ(T)1231 3493 y FM(\006)1301 3481 y FQ(as)g(the)g(category)f(with)h(only)g(one)g(ob)5 b(ject)19 b(0)g(and)g(Hom)2983 3493 y FI(T)3022 3501 y FF(\006)3071 3481 y FQ(\(0)p FJ(;)14 b FQ(0\))22 b(=)h FH(Z)o FQ(.)605 3581 y(The)28 b(next)f(lemma)h(is)f(left)i(as)e(an)g(exercise.)605 3741 y FP(Lemma)k FQ(5.7.3)p FP(.)40 b FQ(\(i\))23 b FO(Ther)l(e)g(exists)f(a)g(c)l(anonic)l(al)i(map)f FJ(a)9 b FQ(:)28 b(\003)2473 3753 y FM(\006)2520 3761 y FF(1)2558 3741 y FL(\002)r FQ(\003)2683 3753 y FM(\006)2730 3761 y FF(2)2790 3741 y FL(!)23 b FQ(\003)2954 3753 y FM(\006)3001 3761 y FF(1)3033 3753 y FE(t)p FM(\006)3125 3761 y FF(2)3162 3741 y FO(.)36 b FQ(\()p FO(How-)456 3840 y(ever,)30 b(it)g(is)g(not)g(a)g(home)l(omorphism.)p FQ(\))605 3940 y(\(ii\))35 b FO(L)l(et)f(the)h(surfac)l(e)g FQ(\006)f FO(b)l(e)h(obtaine)l(d)g(by)g(sewing)g(two)g(surfac)l(es)g(along)g(one) g(b)l(oundary)456 4040 y(c)l(omp)l(onent)8 b FQ(:)39 b(\006)24 b(=)f(\006)1142 4052 y FM(1)1198 4040 y FL(t)1253 4052 y FI(\013;\014)1380 4040 y FQ(\006)1440 4052 y FM(2)1477 4040 y FO(.)40 b(Then)31 b FJ(H)7 b FQ(\(\006)1927 4052 y FM(1)1983 4040 y FL(t)20 b FQ(\006)2118 4052 y FM(2)2155 4040 y FQ(\))k FL(')g FJ(H)7 b FQ(\(\006\))p FO(.)40 b(Ther)l(efor)l(e,)33 b(ther)l(e)d(exists)g(a)456 4149 y(c)l(anonic)l(al)h(home)l(omorphism)h FJ(g)1477 4161 y FI(\013;\014)1593 4149 y FQ(:)c(\003)1702 4161 y FM(\006)1749 4169 y FF(1)1782 4161 y FE(t)p FM(\006)1874 4169 y FF(2)1962 4102 y FE(\030)1933 4149 y FL(\000)-39 b(!)23 b FQ(\003)2123 4161 y FM(\006)2174 4149 y FO(.)605 4249 y FQ(\(iii\))39 b FO(L)l(et)g FQ(\006)f FO(b)l(e)h(obtaine)l(d)h(fr)l(om)f FQ(\006)1742 4219 y FE(0)1804 4249 y FO(by)g(gluing)g(two)g(b)l (oundary)h(cir)l(cles)f FJ(\013)3022 4261 y FM(1)3059 4249 y FJ(;)14 b(\013)3149 4261 y FM(2)3225 4249 y FO(in)39 b(the)456 4348 y(same)g(c)l(onne)l(cte)l(d)g(c)l(omp)l(onent)8 b FQ(:)56 b(\006)39 b(=)h FL(t)1792 4360 y FI(\013)1835 4368 y FF(1)1868 4360 y FI(;\013)1931 4368 y FF(2)1967 4348 y FQ(\006)2027 4318 y FE(0)2050 4348 y FO(.)66 b(These)40 b(two)f(cir)l(cles)h(give)g(a)f(cycle)h FJ(\013)g FL(2)456 4451 y FJ(H)7 b FQ(\(\006\))p FO(.)42 b(Then)32 b(we)f(claim)h(that)f FJ(H)7 b FQ(\(\006)1630 4421 y FE(0)1654 4451 y FQ(\))25 b FL(')g FJ(\013)1854 4421 y FE(?)1911 4451 y FJ(=)p FH(R)p FJ(\013)p FO(.)48 b(Ther)l(efor)l(e,)34 b(we)d(have)h(a)f(c)l (anonic)l(al)i(map)456 4558 y FJ(g)496 4570 y FI(\013)539 4578 y FF(1)571 4570 y FI(;\013)634 4578 y FF(2)679 4558 y FQ(:)28 b(\003)788 4570 y FM(\006)835 4554 y Fx(0)885 4558 y FL(!)23 b FQ(\003)1049 4570 y FM(\006)1130 4558 y FO(which)31 b(induc)l(es)f(an)g(e)l(quivalenc)l(e)h FJ(T)2257 4570 y FM(\006)2304 4554 y Fx(0)2382 4511 y FE(\030)2353 4558 y FL(\000)-39 b(!)23 b FJ(T)2534 4570 y FM(\006)2585 4558 y FO(.)605 4717 y FP(Exer)n(cise)32 b FQ(5.7.4)p FP(.)40 b FQ(Let)21 b(\006)g(b)r(e)g(an)g(extended)h (surface,)f(and)g(let)h FJ(C)27 b FQ(b)r(e)22 b(a)e(cut)i(system)f(on)f (\006,)456 4817 y(i.e.,)h(a)e(\014nite)h(set)g(of)f(closed)g(simple)h (non-in)n(tersecting)e(curv)n(es)g(on)h(\006)h(suc)n(h)f(that)h(the)g (connected)456 4917 y(comp)r(onen)n(ts)31 b(\006)977 4929 y FI(a)1049 4917 y FQ(of)h(\006)22 b FL(n)e FJ(C)39 b FQ(ha)n(v)n(e)31 b(gen)n(us)g(zero)g(\(cf.)h(De\014nition)h(5.2.1\).) 49 b(By)32 b(Lemma)g(5.7.3,)456 5016 y(this)23 b(de\014nes)h(a)f(map) 1127 4954 y Fy(Q)1219 5016 y FQ(\003)1277 5028 y FM(\006)1324 5036 y FG(a)1388 5016 y FL(!)g FQ(\003)1552 5028 y FM(\006)1603 5016 y FQ(.)35 b(Since,)25 b(b)n(y)e(de\014nition,)i(eac)n(h)d(\003) 2638 5028 y FM(\006)2685 5036 y FG(a)2749 5016 y FQ(is)h(a)g(p)r(oin)n (t,)i(this)f(map)456 5116 y(giv)n(es)k(an)h(elemen)n(t)h FJ(y)1128 5128 y FI(C)1209 5116 y FL(2)d FQ(\003)1349 5128 y FM(\006)1400 5116 y FQ(.)42 b(Sho)n(w)29 b(that)h FJ(y)1909 5128 y FI(C)1994 5116 y FQ(is)f(the)h(subspace)f(in)g(H)2733 5128 y FM(1)2771 5116 y FQ(\()p FJ(cl)r FQ(\(\006\))p FJ(;)14 b FH(R)p FQ(\))36 b(spanned)456 5216 y(b)n(y)27 b(the)h(classes)e([)p FJ(c)p FQ(])p FJ(;)14 b(c)23 b FL(2)h FJ(C)6 b FQ(.)p eop %%Page: 128 36 128 131 bop 456 226 a FM(128)1010 b(5.)29 b(MODULAR)g(FUNCTOR)605 425 y FQ(No)n(w)d(w)n(e)f(can)h(de\014ne)h(the)f(\\cen)n(tral)f (extension")g(of)h(the)h(T)-7 b(eic)n(hm)r(\177)-44 b(uller)26 b(to)n(w)n(er)e(whic)n(h)i(w)n(as)456 525 y(de\014ned)i(in)f(Section)h (5.6.)605 681 y FP(Definition)k FQ(5.7.5)p FP(.)40 b FQ(The)23 b(cen)n(tral)g(extension)2119 662 y FH(^)2114 681 y FL(T)7 b FJ(eich)23 b FQ(of)h(the)g(T)-7 b(eic)n(hm)r(\177)-44 b(uller)23 b(to)n(w)n(er)f FL(T)7 b FJ(eich)456 781 y FQ(is)27 b(the)h(to)n(w)n(er)e(of)i(group)r(oids)e(de\014ned)i(as)f (follo)n(ws.)612 902 y FK(Ob)5 b(jects:)41 b FQ(all)27 b(pairs)g(\(\006)p FJ(;)14 b(y)s FQ(\),)28 b(where)f(\006)g(is)h(an)f (extended)h(surface)f(and)g(and)g FJ(y)f FL(2)e FQ(\003)3260 914 y FM(\006)3311 902 y FQ(.)612 1009 y FK(Morphisms:)38 b FQ(Mor)o(\(\(\006)1419 1021 y FM(1)1457 1009 y FJ(;)14 b(y)1535 1021 y FM(1)1571 1009 y FQ(\))p FJ(;)g FQ(\(\006)1732 1021 y FM(2)1770 1009 y FJ(;)g(y)1848 1021 y FM(2)1885 1009 y FQ(\)\))19 b(consists)f(of)g(all)g(pairs)f(\()p FJ(f)t(;)d(\036)p FQ(\),)22 b(where)c FJ(f)f FQ(:)28 b(\006)3290 1021 y FM(1)3379 962 y FE(\030)3350 1009 y FL(\000)-39 b(!)711 1109 y FQ(\006)771 1121 y FM(2)838 1109 y FQ(is)30 b(an)f(orien)n(tation)g(preserving)f(homeomorphism)g (and)i FJ(\036)d FL(2)g FQ(Mor)2965 1121 y FI(T)3004 1129 y FF(\006)3044 1141 y(2)3085 1109 y FQ(\()p FJ(f)3158 1121 y FE(\003)3196 1109 y FJ(y)3237 1121 y FM(1)3274 1109 y FJ(;)14 b(y)3352 1121 y FM(2)3389 1109 y FQ(\).)711 1208 y(Here)27 b FJ(f)948 1220 y FE(\003)995 1208 y FQ(:)h(\003)1104 1220 y FM(\006)1151 1228 y FF(1)1211 1208 y FL(!)23 b FQ(\003)1375 1220 y FM(\006)1422 1228 y FF(2)1486 1208 y FQ(is)28 b(the)g(map)f(induced)h(from)f FJ(f)9 b FQ(.)612 1308 y FK(Boundary)32 b(functor:)42 b FJ(A)p FQ(\(\006)p FJ(;)14 b(y)s FQ(\))25 b(=)f FJ(\031)1852 1320 y FM(0)1889 1308 y FQ(\()p FJ(@)5 b FQ(\006\))29 b(is)f(the)h(set)g(of)f(b)r (oundary)g(comp)r(onen)n(ts)g(of)711 1407 y(\006.)612 1507 y FK(Disjoin)m(t)j(union:)40 b FQ(\(\006)1365 1519 y FM(1)1403 1507 y FJ(;)14 b(y)1481 1519 y FM(1)1517 1507 y FQ(\))22 b FL(t)f FQ(\(\006)1739 1519 y FM(2)1777 1507 y FJ(;)14 b(y)1855 1519 y FM(2)1892 1507 y FQ(\))30 b(=)f(\(\006)2140 1519 y FM(1)2198 1507 y FL(t)22 b FQ(\006)2335 1519 y FM(2)2372 1507 y FJ(;)14 b(a)p FQ(\()p FJ(y)2526 1519 y FM(1)2584 1507 y FL(\010)21 b FJ(y)2711 1519 y FM(2)2748 1507 y FQ(\)\),)33 b(where)e FJ(a)9 b FQ(:)29 b(\003)3275 1519 y FM(\006)3322 1527 y FF(1)3380 1507 y FL(\002)711 1607 y FQ(\003)769 1619 y FM(\006)816 1627 y FF(2)876 1607 y FL(!)23 b FQ(\003)1040 1619 y FM(\006)1087 1627 y FF(1)1119 1619 y FE(t)p FM(\006)1211 1627 y FF(2)1276 1607 y FQ(is)k(as)g(in)h(Lemma)f(5.7.3\(i\).)37 b(The)27 b(ob)5 b(ject)28 b FL(;)f FQ(is)g(the)h(ob)n(vious)e(one.)612 1706 y FK(Gluing:)39 b FJ(G)1026 1718 y FI(\013;\014)1134 1706 y FQ(\(\006)p FJ(;)14 b(y)s FQ(\))28 b(=)e(\()p FL(t)1545 1718 y FI(\013;\014)1653 1706 y FQ(\(\006\))p FJ(;)14 b(g)1854 1718 y FI(\013;\014)1962 1706 y FQ(\()p FJ(y)s FQ(\)\),)31 b(where)f FJ(g)2439 1718 y FI(\013;\014)2555 1706 y FQ(:)f(\003)2665 1718 y FM(\006)2743 1706 y FL(!)e FQ(\003)2911 1721 y FE(t)2956 1730 y FG(\013;\014)3052 1721 y FM(\(\006\))3185 1706 y FQ(is)j(as)f(in)711 1809 y(Lemma)e(5.7.3\(ii\),)h(\(iii\).)605 1963 y(This)j(group)r(oid)f(is)g (a)h(cen)n(tral)f(extension)g(of)h(the)g(usual)g(T)-7 b(eic)n(hm)r(\177)-44 b(uller)30 b(group)r(oid)g(in)h(the)456 2081 y(follo)n(wing)23 b(sense:)35 b(w)n(e)24 b(ha)n(v)n(e)f(an)h(ob)n (vious)g(functor)2054 2062 y FH(^)2049 2081 y FL(T)7 b FJ(eich)23 b FL(!)g(T)7 b FJ(eich)24 b FQ(compatible)g(with)h(all)f (the)456 2200 y(op)r(erations,)f(and)i(for)f(eac)n(h)f(\(\006)p FJ(;)14 b(y)s FQ(\))24 b FL(2)f FQ(Ob)1782 2180 y FH(^)1777 2200 y FL(T)7 b FJ(eich)p FQ(,)25 b(the)g(k)n(ernel)f(of)g(the)h(map)f (Aut)2970 2223 y Fz(^)2964 2236 y FE(T)t FI(eich)3133 2200 y FQ(\(\006)p FJ(;)14 b(y)s FQ(\))23 b FL(!)456 2307 y FQ(Aut)596 2319 y FE(T)t FI(eich)766 2307 y FQ(\(\006\))e(is)f (Aut)1128 2319 y FI(T)1167 2327 y FF(\006)1215 2307 y FQ(\()p FJ(y)s FQ(\))j(=)g FH(Z)14 b FQ(\(see)20 b(\(5.7.1\)\).)35 b(In)20 b(other)g(w)n(ords,)h(denoting)f(for)g(an)g(extended)456 2407 y(surface)26 b(\006)i(and)f FJ(y)f FL(2)e FQ(\003)1188 2419 y FM(\006)1266 2407 y FQ(the)k(extended)g(mapping)g(class)e(group) h(b)n(y)1484 2532 y(^)1479 2553 y(\000\(\006)p FJ(;)14 b(y)s FQ(\))23 b(:=)f(Aut)2017 2577 y Fz(^)2010 2590 y FE(T)t FI(eich)2179 2553 y FQ(\(\006)p FJ(;)14 b(y)s FQ(\))p FJ(;)-1951 b FQ(\(5.7.5\))456 2704 y(\(up)28 b(to)f(an)g(isomorphism,)g(this)g(do)r(es)g(not)h(dep)r(end)g(on)f(the) h(c)n(hoice)f(of)g FJ(y)s FQ(\),)h(w)n(e)f(can)g(write)g(the)456 2803 y(follo)n(wing)f(exact)h(sequence:)1394 2949 y(0)c FL(!)g FH(Z)16 b FL(!)1755 2928 y FQ(^)1749 2949 y(\000\(\006)p FJ(;)e(y)s FQ(\))23 b FL(!)h FQ(\000\(\006\))f FL(!)g FQ(0)p FJ(:)-2050 b FQ(\(5.7.6\))456 3092 y(Note)26 b(that)g(for)g (\006)g(of)g(gen)n(us)f(zero,)g(\003)1620 3104 y FM(\006)1698 3092 y FQ(is)g(a)h(p)r(oin)n(t,)h(and)f(w)n(e)f(ha)n(v)n(e)g(a)h (canonical)f(isomorphism)461 3174 y(^)456 3195 y(\000)o(\(\006\))j(=)f FH(Z)13 b FL(\002)20 b FQ(\000\(\006\),)31 b(i.e.,)g(the)f(ab)r(o)n(v)n (e)f(exact)g(sequence)g(splits.)45 b(F)-7 b(or)29 b(p)r(ositiv)n(e)h (gen)n(us,)f(this)i(is)456 3295 y(not)c(so.)605 3449 y FP(Example)k FQ(5.7.6)p FP(.)40 b FQ(Let)c(\006)h(=)f FJ(S)1642 3461 y FM(1)p FI(;)p FM(1)1768 3449 y FQ(b)r(e)h(the)f(torus) f(with)i(one)e(puncture,)k(and)c(let)i FJ(\013;)14 b(\014)456 3549 y FQ(b)r(e)36 b(the)g(meridian)f(and)g(the)h(parallel)f(of)g(the)h (torus,)h(so)e(that)h FJ(H)7 b FQ(\(\006\))37 b(=)f FH(R)p FQ([)p FJ(\013)p FQ(])30 b FL(\010)23 b FH(R)p FQ([)p FJ(\014)5 b FQ(])42 b(\(see)456 3648 y(Figure)23 b(5.19\).)35 b(Then)24 b(\003)1224 3660 y FM(\006)1298 3648 y FQ(=)f FH(RP)1492 3618 y FM(1)1557 3648 y FQ(=)g FJ(S)1701 3618 y FM(1)1738 3648 y FQ(.)35 b(Let)25 b FJ(s;)14 b(t)23 b FL(2)g FQ(\000)2201 3660 y FM(1)p FI(;)p FM(1)2315 3648 y FQ(b)r(e)i(the)f(elemen)n(ts)g(of)g(the)h(mapping)456 3748 y(class)h(group)h(de\014ned)h(in)g(Example)e(5.1.11.)1638 4718 y @beginspecial 0 @llx 0 @lly 75 @urx 96 @ury 750 @rwi @setspecial %%BeginDocument: figures/s11ab.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: s11ab.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Tue Jun 8 12:58:35 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 75 96 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.3300 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -55.0 155.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8822 m -1000 -1000 l 7561 -1000 l 7561 8822 l cp clip 0.01980 0.01980 sc 15.000 slw % Ellipse n 4500 4950 1050 1425 0 360 DrawEllipse gs col0 s gr % Polyline gs clippath 5209 4014 m 5061 3760 l 5298 3934 l 5050 3658 l 4960 3738 l cp clip n 5160 3870 m 5025 3720 l gs col0 s gr gr % arrowhead n 5209 4014 m 5061 3760 l 5298 3934 l 5222 3939 l 5209 4014 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 5682 5064 m 5966 4989 l 5736 5172 l 6069 5005 l 6015 4898 l cp clip n 5865 5040 m 6015 4965 l gs col0 s gr gr % arrowhead n 5682 5064 m 5966 4989 l 5736 5172 l 5752 5096 l 5682 5064 l cp gs 0.00 setgray ef gr col0 s 30.000 slw % Ellipse n 4462 4948 562 750 0 360 DrawEllipse gs col-1 s gr % Ellipse n 4500 7500 600 300 0 360 DrawEllipse gs col-1 s gr % Arc 15.000 slw gs n 5587.5 4507.5 603.1 158.9 21.1 arcn gs col-1 s gr gr % Arc gs [90] 0 sd n 5587.5 5100.0 676.0 -146.3 -33.7 arc gs col-1 s gr gr [] 0 sd /Symbol ff 390.00 scf sf 3225 4425 m gs 1 -1 sc (b) col-1 sh gr % Polyline 30.000 slw n 3900 7500 m 3900 7497 l 3900 7490 l 3899 7478 l 3898 7461 l 3897 7439 l 3896 7415 l 3894 7388 l 3891 7361 l 3889 7334 l 3886 7308 l 3882 7284 l 3879 7260 l 3874 7238 l 3869 7216 l 3864 7194 l 3857 7173 l 3850 7150 l 3845 7134 l 3839 7117 l 3832 7100 l 3825 7082 l 3818 7064 l 3809 7044 l 3801 7024 l 3791 7003 l 3781 6981 l 3770 6958 l 3759 6935 l 3747 6911 l 3734 6886 l 3721 6861 l 3708 6836 l 3694 6810 l 3679 6784 l 3665 6758 l 3650 6732 l 3634 6706 l 3619 6680 l 3603 6654 l 3587 6628 l 3571 6602 l 3554 6576 l 3538 6550 l 3523 6528 l 3509 6506 l 3494 6484 l 3479 6461 l 3463 6437 l 3447 6413 l 3430 6388 l 3413 6362 l 3395 6335 l 3377 6308 l 3359 6280 l 3340 6251 l 3321 6222 l 3302 6191 l 3283 6161 l 3264 6129 l 3245 6097 l 3226 6065 l 3207 6033 l 3189 6000 l 3171 5967 l 3153 5934 l 3135 5901 l 3118 5868 l 3102 5834 l 3086 5801 l 3070 5768 l 3055 5735 l 3041 5701 l 3027 5668 l 3013 5634 l 3000 5600 l 2989 5569 l 2978 5538 l 2967 5506 l 2956 5473 l 2946 5440 l 2936 5406 l 2927 5371 l 2918 5336 l 2909 5299 l 2900 5262 l 2892 5224 l 2884 5186 l 2877 5146 l 2870 5107 l 2864 5066 l 2858 5025 l 2853 4984 l 2849 4943 l 2845 4902 l 2842 4860 l 2839 4819 l 2838 4778 l 2837 4737 l 2836 4696 l 2837 4656 l 2838 4616 l 2839 4577 l 2842 4539 l 2845 4501 l 2849 4463 l 2854 4426 l 2859 4390 l 2865 4355 l 2872 4319 l 2879 4284 l 2888 4250 l 2896 4216 l 2906 4182 l 2917 4147 l 2929 4113 l 2941 4079 l 2954 4045 l 2969 4010 l 2984 3976 l 3001 3941 l 3019 3906 l 3037 3872 l 3057 3837 l 3078 3803 l 3100 3768 l 3123 3734 l 3146 3701 l 3171 3667 l 3197 3635 l 3223 3603 l 3250 3571 l 3278 3541 l 3307 3511 l 3336 3482 l 3366 3454 l 3396 3427 l 3426 3401 l 3457 3376 l 3488 3353 l 3520 3330 l 3552 3308 l 3584 3288 l 3616 3268 l 3649 3250 l 3682 3232 l 3716 3216 l 3750 3200 l 3783 3186 l 3816 3172 l 3851 3160 l 3886 3148 l 3921 3136 l 3958 3126 l 3995 3116 l 4034 3106 l 4073 3098 l 4113 3090 l 4154 3083 l 4195 3077 l 4237 3071 l 4280 3066 l 4324 3062 l 4367 3059 l 4411 3057 l 4456 3056 l 4500 3055 l 4544 3056 l 4589 3057 l 4633 3059 l 4676 3062 l 4720 3066 l 4763 3071 l 4805 3077 l 4846 3083 l 4887 3090 l 4927 3098 l 4966 3106 l 5005 3116 l 5042 3126 l 5079 3136 l 5114 3148 l 5149 3160 l 5184 3172 l 5217 3186 l 5250 3200 l 5284 3216 l 5318 3232 l 5351 3250 l 5384 3268 l 5416 3288 l 5448 3308 l 5480 3330 l 5512 3353 l 5543 3376 l 5574 3401 l 5604 3427 l 5634 3454 l 5664 3482 l 5693 3511 l 5722 3541 l 5750 3571 l 5777 3603 l 5803 3635 l 5829 3667 l 5854 3701 l 5877 3734 l 5900 3768 l 5922 3803 l 5943 3837 l 5963 3872 l 5981 3906 l 5999 3941 l 6016 3976 l 6031 4010 l 6046 4045 l 6059 4079 l 6071 4113 l 6083 4147 l 6094 4182 l 6104 4216 l 6113 4250 l 6121 4284 l 6128 4319 l 6135 4355 l 6141 4390 l 6146 4426 l 6151 4463 l 6155 4501 l 6158 4539 l 6161 4577 l 6162 4616 l 6163 4656 l 6164 4696 l 6163 4737 l 6162 4778 l 6161 4819 l 6158 4860 l 6155 4902 l 6151 4943 l 6147 4984 l 6142 5025 l 6136 5066 l 6130 5107 l 6123 5146 l 6116 5186 l 6108 5224 l 6100 5262 l 6091 5299 l 6082 5336 l 6073 5371 l 6064 5406 l 6054 5440 l 6044 5473 l 6033 5506 l 6022 5538 l 6011 5569 l 6000 5600 l 5987 5634 l 5973 5668 l 5959 5701 l 5945 5735 l 5930 5768 l 5914 5801 l 5898 5834 l 5882 5868 l 5865 5901 l 5847 5934 l 5829 5967 l 5811 6000 l 5793 6033 l 5774 6065 l 5755 6097 l 5736 6129 l 5717 6161 l 5698 6191 l 5679 6222 l 5660 6251 l 5641 6280 l 5623 6308 l 5605 6335 l 5587 6362 l 5570 6388 l 5553 6413 l 5537 6437 l 5521 6461 l 5506 6484 l 5491 6506 l 5477 6528 l 5463 6550 l 5446 6576 l 5429 6602 l 5413 6628 l 5397 6654 l 5381 6680 l 5366 6706 l 5350 6732 l 5335 6758 l 5321 6784 l 5306 6810 l 5292 6836 l 5279 6861 l 5266 6886 l 5253 6911 l 5241 6935 l 5230 6958 l 5219 6981 l 5209 7003 l 5199 7024 l 5191 7044 l 5182 7064 l 5175 7082 l 5168 7100 l 5161 7117 l 5155 7134 l 5150 7150 l 5143 7173 l 5136 7194 l 5131 7216 l 5126 7238 l 5121 7260 l 5118 7284 l 5114 7308 l 5111 7334 l 5109 7361 l 5106 7388 l 5104 7415 l 5103 7439 l 5102 7461 l 5101 7478 l 5100 7490 l 5100 7497 l 5100 7500 l gs col-1 s gr /Symbol ff 390.00 scf sf 6300 4800 m gs 1 -1 sc (a) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1710 4918 a FP(Figure)32 b(5.19)605 5116 y FQ(F)-7 b(or)27 b FJ(y)g FQ(=)c([)p FJ(\013)p FQ(])28 b(w)n(e)g(will)g(describ)r(e)g(the)g(cen)n(tral)f(extension)2430 5095 y(^)2425 5116 y(\000\(\006)p FJ(;)14 b(y)s FQ(\).)38 b(Note)28 b(that)g FJ(t)3154 5128 y FE(\003)3192 5116 y FQ(\([)p FJ(\013)p FQ(]\))d(=)456 5216 y([)p FJ(\013)p FQ(],)33 b FJ(s)650 5228 y FE(\003)688 5216 y FQ([)p FJ(\013)p FQ(])e(=)e([)p FJ(\014)t FQ(].)50 b(Let)32 b(us)f(c)n(ho)r(ose)g(a)g(path)h FJ(\036)g FQ(in)g(\003)2124 5228 y FM(\006)2207 5216 y FQ(connecting)f(the)h(p)r(oin)n(ts)g([)p FJ(\014)t FQ(])g(and)g([)p FJ(\013)p FQ(].)p eop %%Page: 129 37 129 132 bop 1087 226 a FM(5.7.)29 b(CENTRAL)h(EXTENSION)f(OF)f(MODULAR) h(FUNCTOR)511 b(129)456 425 y FQ(No)n(w,)33 b(de\014ne)h(elemen)n(ts) 1266 410 y(^)1264 425 y FJ(t;)18 b FQ(^)-46 b FJ(s;)16 b FQ(^)-44 b FJ(c)32 b FL(2)1567 404 y FQ(^)1562 425 y(\000\(\006)p FJ(;)14 b(y)s FQ(\))33 b(b)n(y)1974 410 y(^)1973 425 y FJ(t)f FQ(=)f(\()p FJ(t;)14 b FQ(id\),)38 b(^)-45 b FJ(s)32 b FQ(=)f(\()p FJ(s;)14 b(\036)p FQ(\),)38 b(^)-44 b FJ(c)32 b FQ(=)f(\()p FJ(c;)14 b FQ(id\),)35 b(where)456 525 y FJ(c)30 b FQ(=)h FJ(s)657 495 y FM(2)726 525 y FQ(acts)h(on)g FJ(H)7 b FQ(\(\006\))33 b(b)n(y)f FJ(v)i FL(7!)d(\000)p FJ(v)s FQ(,)i(and)f(th)n(us,)i(acts)e(trivially)f (on)h(\003)2777 537 y FM(\006)2828 525 y FQ(.)51 b(Then)33 b(w)n(e)f(claim)456 633 y(that)27 b(the)h(group)1019 612 y(^)1014 633 y(\000\(\006)p FJ(;)14 b(y)s FQ(\))28 b(is)f(generated)g(b)n(y)g(the)h(elemen)n(ts)2359 617 y(^)2358 633 y FJ(t;)17 b FQ(^)-45 b FJ(s;)16 b FQ(^)-44 b FJ(c;)14 b(\015)32 b FQ(with)c(the)g(relations)1241 775 y(^)-45 b FJ(s)1277 741 y FM(2)1337 775 y FQ(=)23 b FJ(\015)6 b FQ(^)-43 b FJ(c)o(;)97 b FQ(\()s(^)-45 b FJ(s)1700 760 y FQ(^)1699 775 y FJ(t)p FQ(\))1761 741 y FM(3)1822 775 y FQ(=)26 b(^)-46 b FJ(s)1948 741 y FM(2)1986 775 y FJ(;)97 b(\015)5 b(;)15 b FQ(^)-43 b FJ(c)27 b FQ(are)f(cen)n(tral,)-2207 b(\(5.7.7\))456 920 y(where)27 b FJ(\015)g FQ(=)c(\(id)p FJ(;)14 b(\015)5 b FQ(\))28 b(is)f(the)h(generator)e(of)h(the)h(fundamen)n(tal)g(group)e FJ(\031)2695 932 y FM(1)2733 920 y FQ(\(\003)2823 932 y FM(\006)2875 920 y FJ(;)14 b(y)s FQ(\))22 b(=)h FH(Z)o FQ(.)605 1020 y(Similarly)-7 b(,)39 b(if)f(w)n(e)f(consider)f(a)h (torus)f(without)i(punctures,)h(then)f(the)g(mapping)e(class)456 1119 y(group)h(\000\()p FJ(S)837 1131 y FM(1)p FI(;)p FM(0)927 1119 y FJ(;)14 b(y)s FQ(\))38 b(is)h(generated)e(b)n(y)h(the)h (same)f(elemen)n(ts)g(with)h(the)g(additional)e(relation)457 1219 y(^)-43 b FJ(c)492 1189 y FM(2)552 1219 y FQ(=)22 b(1.)37 b(The)28 b(pro)r(of)f(of)g(b)r(oth)h(of)g(these)f(statemen)n (ts)h(is)f(left)h(to)g(the)g(reader)e(as)h(an)g(exercise.)605 1372 y FP(Remark)32 b FQ(5.7.7)p FP(.)39 b FQ(One)25 b(sees)f(that)h(for)f(\006)f(=)g FJ(S)2063 1384 y FM(1)p FI(;)p FM(1)2153 1372 y FQ(,)i(the)g(exact)f(sequence)g(\(5.7.6\))g (trivially)456 1471 y(splits.)51 b(F)-7 b(or)32 b(\006)f(=)f FJ(S)1111 1483 y FM(1)p FI(;)p FM(0)1201 1471 y FQ(,)k(w)n(e)e(ha)n(v)n (e)f(\000\(\006\))g(=)g(SL)1982 1483 y FM(2)2019 1471 y FQ(\()p FH(Z)p FQ(\),)d(and)k(one)g(can)g(c)n(hec)n(k)f(that)i(the)g (ab)r(o)n(v)n(e)456 1582 y(exact)e(sequence)g(do)r(es)g(not)h(split,)h (but)f(it)h(\\splits)e(o)n(v)n(er)f FH(Q)5 b FQ(":)51 b(if)32 b(w)n(e)g(denote)f(b)n(y)3049 1561 y(^)3044 1582 y(\000)o(\(\006)p FJ(;)14 b(y)s FQ(\))3300 1594 y Fz(Q)3380 1582 y FQ(=)461 1670 y(^)456 1691 y(\000)o(\(\006)p FJ(;)g(y)s FQ(\))d FL(\002)788 1703 y Fz(Z)842 1691 y FH(Q)36 b FQ(the)24 b(group)f(obtained)h(b)n(y)f(adding)h(to)2123 1670 y(^)2118 1691 y(\000)o(\(\006\))h(fractional)e(p)r(o)n(w)n(ers)f (of)i FJ(\015)5 b FQ(,)25 b(then)f(the)456 1791 y(exact)j(sequence)1377 1934 y(0)22 b FL(!)h FH(Q)35 b FL(!)1746 1913 y FQ(^)1741 1934 y(\000\(\006)p FJ(;)14 b(y)s FQ(\))1998 1946 y Fz(Q)2070 1934 y FL(!)23 b FQ(\000\(\006\))h FL(!)f FQ(0)456 2079 y(do)r(es)28 b(split.)42 b(Ho)n(w)n(ev)n(er,)27 b(it)j(can)f(b)r(e)g (sho)n(wn)f(that)i(for)e FJ(g)g(>)d FQ(1)k(the)h(exact)e(sequence)h (\(5.7.6\))f(for)456 2179 y(\000)508 2191 y FI(g)r(;)p FM(0)627 2179 y FQ(do)r(es)f(not)g(split)h(ev)n(en)g(o)n(v)n(er)d FH(Q)6 b FQ(.)605 2332 y(No)n(w)29 b(w)n(e)h(can)f(form)n(ulate)g(the)i (notion)e(of)h(a)f(mo)r(dular)h(functor)f(with)i(a)e(cen)n(tral)g(c)n (harge.)456 2431 y(Recall)f(that)h(w)n(e)f(ha)n(v)n(e)f(de\014ned)i (the)g(notion)f(of)h(a)f(represen)n(tation)f(of)h(a)g(to)n(w)n(er)f(of) i(group)r(oids)456 2531 y(in)k(an)f(ab)r(elian)h(category)e FL(C)37 b FQ(\(see)c(De\014nition)g(5.6.12\),)g(and)g(the)g(mo)r(dular) f(functor)h(can)f(b)r(e)456 2630 y(de\014ned)c(as)f(a)g(represen)n (tation)f(of)h(the)h(T)-7 b(eic)n(hm)r(\177)-44 b(uller)27 b(to)n(w)n(er)g(\(see)g(Theorem)g(5.6.13\).)605 2783 y FP(Definition)32 b FQ(5.7.8)p FP(.)40 b FQ(Let)20 b FL(C)25 b FQ(b)r(e)c(an)g(ab)r(elian)f(category)-7 b(.)32 b(A)21 b FL(C)5 b FO(-extende)l(d)23 b(mo)l(dular)g(functor)456 2901 y(with)36 b FQ(\()p FO(multiplic)l(ative)6 b FQ(\))31 b FO(c)l(entr)l(al)e(char)l(ge)34 b FJ(K)29 b FL(2)23 b FJ(k)1980 2871 y FE(\002)2063 2901 y FQ(is)k(a)f(represen)n(tation)f (of)i(the)g(to)n(w)n(er)3223 2882 y FH(^)3218 2901 y FL(T)7 b FJ(eich)o FQ(,)456 3001 y(with)36 b(the)h(additional)e (normalization)g(condition)h FJ(\034)9 b FQ(\()p FJ(S)2246 2971 y FM(2)2284 3001 y FQ(\))38 b(=)f FJ(k)s FQ(,)h(and)e(suc)n(h)g (that)g(for)g(ev)n(ery)456 3101 y(extended)28 b(surface)g(\006)g(and)g FJ(y)f FL(2)e FQ(\003)1546 3113 y FM(\006)1626 3101 y FQ(the)k(generator)d FJ(\015)33 b FQ(of)28 b(Aut)2452 3113 y FI(T)2491 3121 y FF(\006)2539 3101 y FQ(\()p FJ(y)s FQ(\))d(=)f FH(Z)17 b FL(\032)24 b FQ(Aut)3077 3124 y Fz(^)3070 3137 y FE(T)t FI(eich)3239 3101 y FQ(\(\006)p FJ(;)14 b(y)s FQ(\))456 3204 y(acts)27 b(as)g(m)n(ultiplication)g(b)n (y)h FJ(K)6 b FQ(.)605 3356 y(F)-7 b(or)36 b(those)g(readers)f(who)i (do)f(not)h(lik)n(e)f(the)h(language)e(of)i(to)n(w)n(ers)e(of)i(group)r (oids,)g(this)456 3456 y(de\014nition)28 b(can)f(b)r(e)h(sp)r(elled)g (out)f(explicitly)h(as)f(follo)n(ws.)605 3609 y FP(Definition)32 b FQ(5.7.9)p FP(.)40 b FQ(A)23 b FO(mo)l(dular)k(functor)e(with)33 b FQ(\()p FO(multiplic)l(ative)6 b FQ(\))28 b FO(c)l(entr)l(al)e(char)l (ge)31 b FJ(K)d FL(2)456 3708 y FJ(k)502 3678 y FE(\002)585 3708 y FQ(is)g(the)g(follo)n(wing)e(collection)h(of)h(data:)605 3808 y(\(i\))33 b(Let)g(\006)f(b)r(e)h(a)f(compact)g(orien)n(ted)g (surface)g(with)h(b)r(oundary)-7 b(,)33 b(with)g(a)f(p)r(oin)n(t)g(and) h(an)456 3908 y(ob)5 b(ject)31 b(of)i FL(C)j FQ(attac)n(hed)c(to)g(an)n (y)f(b)r(oundary)g(circle,)i(and)f(let)h FJ(y)g FL(2)e FQ(\003)2635 3920 y FM(\006)2686 3908 y FQ(.)50 b(T)-7 b(o)32 b(an)n(y)g(suc)n(h)f(\(\006)p FJ(;)14 b(y)s FQ(\))456 4007 y(the)28 b(mo)r(dular)f(functor)g(assigns)f(a)h(\014nite)i (dimensional)e(v)n(ector)f(space)h FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(y)s FQ(\).)605 4114 y(\(ii\))31 b(T)-7 b(o)29 b(an)n(y)g(morphism)1437 4092 y(~)1420 4114 y FJ(f)17 b FQ(:)29 b(\(\006)p FJ(;)14 b(y)s FQ(\))27 b FL(!)g FQ(\(\006)1964 4084 y FE(0)1987 4114 y FJ(;)14 b(y)2068 4084 y FE(0)2091 4114 y FQ(\))30 b(the)g(mo)r(dular)g(functor)f (assigns)g(an)g(iso-)456 4220 y(morphism)e(of)g(the)h(corresp)r(onding) e(v)n(ector)g(spaces)2137 4198 y(~)2119 4220 y FJ(f)2160 4232 y FE(\003)2207 4220 y FQ(:)i FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(y)s FQ(\))2560 4173 y FE(\030)2531 4220 y FL(\000)-39 b(!)23 b FJ(\034)9 b FQ(\(\006)2800 4190 y FE(0)2824 4220 y FJ(;)14 b(y)2905 4190 y FE(0)2928 4220 y FQ(\).)605 4327 y(\(iii\))36 b(F)-7 b(unctorial)35 b(isomorphisms)e FJ(\034)9 b FQ(\()p FL(;)p FQ(\))1921 4280 y FE(\030)1893 4327 y FL(\000)-40 b(!)36 b FJ(k)s FQ(,)h FJ(\034)9 b FQ(\(\006)2280 4339 y FM(1)2342 4327 y FL(t)23 b FQ(\006)2480 4339 y FM(2)2518 4327 y FJ(;)14 b(y)2596 4339 y FM(1)2656 4327 y FL(\010)23 b FJ(y)2785 4339 y FM(2)2822 4327 y FQ(\))2918 4280 y FE(\030)2890 4327 y FL(\000)-40 b(!)36 b FJ(\034)9 b FQ(\(\006)3171 4339 y FM(1)3209 4327 y FJ(;)14 b(y)3287 4339 y FM(1)3324 4327 y FQ(\))24 b FL(\012)456 4427 y FJ(\034)9 b FQ(\(\006)593 4439 y FM(2)631 4427 y FJ(;)14 b(y)709 4439 y FM(2)746 4427 y FQ(\).)605 4529 y(\(iv\))28 b(A)g(symmetric)f(ob)5 b(ject)28 b FJ(R)23 b FL(2)h FQ(ind)p FL(\000C)1904 4499 y Fv(\002)p FM(2)2020 4529 y FQ(\(see)k(Section)f(2.4\).)605 4629 y(\(v\))h FK(Gluing)j(isomorphism:)i FQ(Let)28 b(\006)1857 4599 y FE(0)1908 4629 y FQ(b)r(e)g(the)h(surface)e(obtained)g(from)h(\006)g (b)n(y)f(cutting)456 4728 y(\006)g(along)g(a)g(circle.)36 b(Then)28 b(w)n(e)f(require)g(that)h(there)f(is)g(an)h(isomorphism)1380 4871 y FJ(\034)9 b FQ(\(\006)1517 4837 y FE(0)1541 4871 y FJ(;)14 b(y)s FQ(;)g FJ(R)1723 4837 y FM(\(1\))1811 4871 y FJ(;)g(R)1912 4837 y FM(\(2\))2001 4871 y FQ(\))23 b FL(!)g FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(g)s FQ(\()p FJ(y)s FQ(\)\))-2063 b(\(5.7.8\))456 5016 y(where)27 b FJ(g)j FQ(is)d(as)g(in)h(Lemma)g(5.7.3\(ii\),)f(\(iii\).)605 5116 y(These)37 b(data)g(ha)n(v)n(e)f(to)h(satisfy)g(the)h(same)e (axioms)g(as)h(in)h(De\014nition)f(5.1.12)f(and)h(the)456 5216 y(follo)n(wing)h(additional)g(relation.)70 b(Note)39 b(that)h(for)e(ev)n(ery)g(\(\006)p FJ(;)14 b(y)s FQ(\))39 b(the)h(group)e FJ(\031)3058 5228 y FM(1)3095 5216 y FQ(\(\003)3185 5228 y FM(\006)3237 5216 y FJ(;)14 b(y)s FQ(\))39 b(is)p eop %%Page: 130 38 130 133 bop 456 226 a FM(130)1010 b(5.)29 b(MODULAR)g(FUNCTOR)456 425 y FQ(canonically)i(isomorphic)h(to)h FH(Z)o FQ(.)47 b(\(The)33 b(orien)n(tation)f(of)h(\006)g(giv)n(es)f(a)g(c)n(hoice)g (for)h(the)g(sign)g(of)456 525 y(the)e(generator)e FJ(\015)5 b FQ(.\))46 b(Then)31 b(w)n(e)g(require)f(that)h FJ(\015)1979 537 y FE(\003)2026 525 y FQ(:)e FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(y)s FQ(\))29 b FL(!)g FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(y)s FQ(\))32 b(b)r(e)f(a)f(m)n(ultiplication)456 624 y(b)n(y)d FJ(K)6 b FQ(.)605 789 y FP(Theorem)32 b FQ(5.7.10)p FP(.)39 b FO(A)n(ny)25 b(mo)l(dular)h(tensor)f(c)l(ate)l (gory)h(gives)h(rise)e(to)h(a)f(mo)l(dular)h(functor)456 889 y(with)32 b(c)l(entr)l(al)f(char)l(ge)h FJ(K)g FQ(=)25 b FJ(p)1406 859 y FM(+)1461 889 y FJ(=p)1545 859 y FE(\000)1601 889 y FO(.)43 b(Conversely,)34 b(if)e FJ(\034)41 b FO(is)32 b(a)g FL(C)5 b FO(-extende)l(d)30 b(mo)l(dular)i(functor)456 989 y(with)d(c)l(entr)l(al)f(char)l(ge)i FJ(K)6 b FO(,)28 b(then)h(it)f(de\014nes)h(on)g FL(C)k FO(a)c(structur)l(e)e(of)i(a)g (we)l(akly)h(ribb)l(on)f(c)l(ate)l(gory.)456 1088 y(If)h(this)g(c)l (ate)l(gory)g(is)h(rigid,)g(then)f FL(C)k FO(is)c(a)g(mo)l(dular)h(c)l (ate)l(gory)f(with)h FJ(p)2628 1058 y FM(+)2683 1088 y FJ(=p)2767 1058 y FE(\000)2845 1088 y FQ(=)23 b FJ(K)6 b FO(.)605 1253 y FP(Pr)n(oof.)41 b FQ(The)36 b(pro)r(of)g(is)g (similar)f(to)i(the)f(pro)r(of)g(in)g(the)h(case)f(of)g(zero)f(cen)n (tral)g(c)n(harge)456 1353 y(\()p FJ(p)530 1323 y FM(+)614 1353 y FQ(=)30 b FJ(p)751 1323 y FE(\000)807 1353 y FQ(\).)49 b(It)32 b(is)f(based)g(on)g(an)h(analogue)d(of)j(Theorem)f(5.2.9,)g (giving)g(the)h(set)f(of)h(mo)n(v)n(es)456 1452 y(and)e(relations)g (among)f(the)j(parameterizations.)44 b(Ho)n(w)n(ev)n(er,)29 b(no)n(w)h(w)n(e)h(ha)n(v)n(e)e(to)i(extend)g(the)456 1552 y(notion)c(of)g(parameterization)f(as)h(follo)n(ws.)605 1655 y(Let)32 b(\006)g(b)r(e)g(an)g(extended)g(surface)f(and)h FJ(y)h FL(2)e FQ(\003)2112 1667 y FM(\006)2163 1655 y FQ(.)50 b(An)32 b FO(extende)l(d)i(p)l(ar)l(ameterization)3386 1634 y FQ(^)3355 1655 y FJ(M)456 1755 y FQ(is)g(a)g(pair)g(\()p FJ(M)t(;)14 b(')p FQ(\),)37 b(where)d FJ(M)43 b FQ(is)34 b(a)g(parameterization)f(of)h(\006)h(\(see)f(De\014nition)h(5.2.1\),)h (and)456 1854 y FJ(')25 b FL(2)h FQ(Mor)766 1866 y FI(T)805 1874 y FF(\006)854 1854 y FQ(\()p FJ(y)s(;)14 b(y)1008 1866 y FI(M)1081 1854 y FQ(\),)30 b(where)e FJ(y)1448 1866 y FI(M)1547 1854 y FL(2)e FQ(\003)1686 1866 y FM(\006)1766 1854 y FQ(is)j(the)h(Lagrangian)c(subspace)i(de\014ned)i(b)n(y)f(the)g (cut)456 1954 y(system)e FJ(C)34 b FQ(of)27 b FJ(M)37 b FQ(\(see)27 b(Example)g(5.7.4\).)605 2054 y(Since)g(the)g(mo)n(v)n (es)e FJ(B)t(;)14 b(F)r(;)g(Z)33 b FQ(do)27 b(not)g(c)n(hange)e FJ(y)2071 2066 y FI(M)2145 2054 y FQ(,)i(w)n(e)f(can)g(lift)i(eac)n(h)e (of)g(them)i(to)e(a)h(mo)n(v)n(e)456 2157 y(b)r(et)n(w)n(een)33 b(extended)g(parameterizations)e(b)n(y)i(letting)2230 2136 y(^)2210 2157 y FJ(B)j FQ(=)c(\()p FJ(B)t(;)14 b FQ(id)q(\),)35 b(etc.)54 b(W)-7 b(e)34 b(also)e(ha)n(v)n(e)g(a)456 2256 y(new)f(mo)n(v)n(e)f FJ(\015)14 b FQ(:)29 b(\()p FJ(M)t(;)14 b(')p FQ(\))29 b Fw( )g FQ(\()p FJ(M)t(;)14 b(\015)26 b FL(\016)20 b FJ(')p FQ(\),)33 b(where)e FJ(\015)36 b FQ(is)31 b(the)g(generator)e(of)j(Aut)2933 2268 y FI(T)2972 2276 y FF(\006)3021 2256 y FQ(\()p FJ(y)3094 2268 y FI(M)3167 2256 y FJ(;)14 b(y)3245 2268 y FI(M)3319 2256 y FQ(\))29 b(=)456 2364 y FH(Z)o FQ(.)64 b(Finally)-7 b(,)41 b(the)e(mo)n(v)n(e)f FJ(S)43 b FQ(can)38 b(b)r(e)h(lifted)h(to)e(a)g(mo)n(v)n(e)2335 2343 y(^)2321 2364 y FJ(S)43 b FQ(as)38 b(in)h(Example)f(5.7.6.)68 b(Then)456 2467 y(eac)n(h)29 b(of)g(relations)g(MF1{MF7)g(mak)n(es)g (sense)g(as)g(a)g(relation)g(among)g(the)h(mo)n(v)n(es)3127 2446 y(^)3109 2467 y FJ(Z)6 b(;)14 b(:)g(:)g(:)g(;)3375 2446 y FQ(^)3357 2467 y FJ(F)d FQ(.)456 2567 y(As)37 b(for)g(relations)f(MF8,)k(MF9,)f(they)f(can)f(b)r(e)h(uniquely)f (lifted)h(to)g(relations)e(among)g(the)456 2670 y(mo)n(v)n(es)e(b)r(et) n(w)n(een)i(the)g(extended)g(parameterizations)d(b)n(y)j(replacing)e FJ(Z)q(;)14 b(:)g(:)g(:)g(S)40 b FQ(b)n(y)3159 2649 y(^)3142 2670 y FJ(Z)5 b(;)14 b(:)g(:)g(:)g(;)3403 2649 y FQ(^)3389 2670 y FJ(S)456 2773 y FQ(and)34 b(inserting)h(an)f(appropriate)g(p)r (o)n(w)n(er)f(of)i FJ(\015)40 b FQ(to)35 b(mak)n(e)f(it)h(in)n(to)g(a)f (closed)g(lo)r(op)h(in)3238 2752 y(^)3207 2773 y FJ(M)9 b FQ(\(\006\).)456 2877 y(W)-7 b(e)26 b(will)g(denote)g(the)g(corresp)r (onding)e(axioms)h(b)n(y)h(MF)2213 2860 y(^)2213 2877 y(8)o(,)h(MF)2434 2860 y(^)2434 2877 y(9.)36 b(Let)26 b(us)g(also)f(add)h(an)f(axiom)456 2977 y(MF)607 2960 y(^)586 2977 y(10)30 b(requiring)g(that)i FJ(\015)j FQ(b)r(e)d(cen)n (tral.)47 b(Then)31 b(it)h(is)f(easy)f(to)h(deduce)h(from)e(Theorem)h (5.2.9)456 3080 y(that)c(the)h(corresp)r(onding)e(2-complex)1747 3059 y(^)1706 3080 y FL(M)p FQ(\(\006\))i(is)g(connected)f(and)h (simply-connected.)605 3180 y(No)n(w)35 b(to)h(sho)n(w)f(that)h(ev)n (ery)e(MTC)i(de\014nes)f(a)h(mo)r(dular)f(functor,)j(w)n(e)d(can)g (follo)n(w)g(the)456 3283 y(same)23 b(approac)n(h)e(as)i(b)r(efore,)h (i.e.,)h(\014rst)e(de\014ne)h FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(y)s(;)2223 3262 y FQ(^)2192 3283 y FJ(M)9 b FQ(\),)24 b(and)g(then)g(assign)e(to)h(ev)n(ery)g(mo)n(v)n(e)475 3370 y(^)456 3391 y FJ(E)14 b FQ(:)615 3370 y(^)584 3391 y FJ(M)45 b Fw( )860 3370 y FQ(^)829 3391 y FJ(M)919 3361 y FE(0)978 3391 y FQ(an)35 b(isomorphism)f FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(y)s(;)1881 3370 y FQ(^)1849 3391 y FJ(M)9 b FQ(\))37 b FL(!)f FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(y)s(;)2413 3370 y FQ(^)2382 3391 y FJ(M)2472 3361 y FE(0)2495 3391 y FQ(\))36 b(so)f(that)h(all)f(the)h(relations) 456 3495 y(MF1{MF)820 3478 y(^)800 3495 y(10)26 b(are)h(satis\014ed.) 605 3595 y(Let)i(us)f(de\014ne)h FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(y)s(;)1390 3574 y FQ(^)1358 3595 y FJ(M)9 b FQ(\))25 b(=)g FJ(\034)9 b FQ(\(\006)p FJ(;)14 b(M)9 b FQ(\))29 b(\(th)n(us,)g(it)g(do)r(es)g(not)f(dep)r(end)h(on)g(the)g (c)n(hoice)f(of)456 3703 y FJ(y)35 b FQ(and)d FJ(')p FQ(\))h(and)f(assign)f(to)h(the)h(mo)n(v)n(es)1756 3682 y(^)1738 3703 y FJ(Z)6 b(;)1858 3682 y FQ(^)1838 3703 y FJ(B)t(;)1961 3682 y FQ(^)1942 3703 y FJ(F)44 b FQ(the)33 b(same)f(isomorphisms)e(as)i(b)r(efore)g(\(i.e.,)456 3802 y FJ(Z)q(;)14 b(\033)n(;)g(G)p FQ(\).)45 b(Assign)29 b(to)h FJ(\015)35 b FQ(the)30 b(isomorphism)f(giv)n(en)g(b)n(y)h(m)n (ultiplication)g(b)n(y)f FJ(p)2912 3772 y FM(+)2967 3802 y FJ(=p)3051 3772 y FE(\000)3106 3802 y FQ(.)44 b(Finally)-7 b(,)456 3910 y(assign)19 b(to)803 3889 y(^)789 3910 y FJ(S)26 b FQ(the)c(op)r(erator)d FJ(S=)1424 3839 y Fy(p)p 1507 3839 237 4 v 71 x FJ(p)1549 3886 y FM(+)1603 3910 y FJ(=p)1687 3886 y FE(\000)1743 3910 y FQ(,)j(where)f FJ(S)26 b FQ(is)21 b(de\014ned)g(in)g(Theorem)g(3.1.17.)33 b(Explicit)456 4022 y(calculation)21 b(sho)n(ws)g(that)i(for)e(so)h (de\014ned)1790 4001 y(^)1776 4022 y FJ(S)5 b FQ(,)24 b(relations)d(MF)2341 4004 y(^)2341 4022 y(8)o(,)j(MF)2559 4004 y(^)2559 4022 y(9)e(are)f(satis\014ed.)35 b(F)-7 b(or)22 b(MF)3380 4004 y(^)3380 4022 y(8)o(,)456 4122 y(this)27 b(calculation)g(essen)n(tially)g(coincides)g(with)h(the)g (one)f(done)g(in)h(Example)f(5.7.6.)605 4221 y(The)37 b(pro)r(of)g(in)g(the)g(opp)r(osite)g(direction)g(is)f(absolutely)h (parallel)f(to)h(the)g(one)g(for)f(the)456 4321 y(gen)n(us)26 b(zero)h(case;)g(th)n(us,)g(w)n(e)h(omit)f(it.)p 3384 4321 4 57 v 3388 4268 50 4 v 3388 4321 V 3437 4321 4 57 v 1292 4568 a FK(5.8.)46 b(F)-8 b(rom)31 b(2D)g(MF)h(to)g(3D)f(TQFT) 605 4717 y FQ(Starting)39 b(from)f(a)h(mo)r(dular)f(tensor)g(category)f FL(C)44 b FQ(with)39 b FJ(p)2506 4687 y FM(+)2561 4717 y FJ(=p)2645 4687 y FE(\000)2743 4717 y FQ(=)i(1,)h(w)n(e)c(ha)n(v)n(e) g(con-)456 4817 y(structed)18 b(a)g FL(C)5 b FQ(-extended)18 b(3-dimensional)f(T)-7 b(op)r(ological)16 b(Quan)n(tum)i(Field)h (Theory)e(\(Section)i(4.4\))456 4917 y(and)43 b(a)g FL(C)5 b FQ(-extended)43 b(2-dimensional)f(mo)r(dular)h(functor)g(\(Section)h (5.1\).)84 b(W)-7 b(e)43 b(ha)n(v)n(e)g(also)456 5016 y(sho)n(w)n(ed)27 b(that)i(con)n(v)n(ersely)-7 b(,)27 b(if)i FL(C)k FQ(is)c(a)f(semisimple)h(ab)r(elian)f(category)f(then)i (an)n(y)f FL(C)5 b FQ(-extended)456 5116 y(2-dimensional)23 b(mo)r(dular)i(functor)g(giv)n(es)f(rise)h(to)g(a)g(structure)f(of)h(a) g(mo)r(dular)g(category)e(on)i FL(C)456 5216 y FQ(\(pro)n(vided)h(that) i(the)g(rigidit)n(y)f(condition)g(is)h(satis\014ed\).)p eop %%Page: 131 39 131 134 bop 1444 226 a FM(5.8.)29 b(FR)n(OM)g(2D)h(MF)e(TO)i(3D)f(TQFT) 867 b(131)605 425 y FQ(Sc)n(hematically)-7 b(,)27 b(w)n(e)g(ha)n(v)n (e:)1757 567 y FL(C)5 b FQ(-extended)28 b(3D)f(TQFT)1236 839 y(MTC)h FL(C)1974 608 y FD(4)p FC(4)1935 621 y FB(j)1898 634 y(j)1861 646 y(j)1825 658 y(j)1788 671 y(j)1751 683 y(j)1714 696 y(j)1677 708 y(j)1641 720 y(j)1604 733 y(j)1567 745 y(j)1530 758 y(j)1533 863 y FD(f)p FC(n)1993 1014 y FD(&)p FC(.)1937 987 y FB(U)1899 974 y(U)1860 962 y(U)1822 949 y(U)1784 936 y(U)1746 924 y(U)1707 911 y(U)1669 899 y(U)1631 886 y(U)1592 874 y(U)1554 861 y(U)1932 1002 y(U)1894 990 y(U)1855 977 y(U)1817 965 y(U)1779 952 y(U)1741 940 y(U)1702 927 y(U)1664 915 y(U)1626 902 y(U)1587 890 y(U)1549 877 y(U)1812 1096 y FL(C)5 b FQ(-extended)27 b(2D)g(MF)2915 824 y FJ(:)605 1226 y FQ(This)18 b(indicates)h(that)f (there)g(m)n(ust)h(b)r(e)g(also)e(a)h(direct)g(construction)g(relating) f(\()p FL(C)5 b FQ(-extended\))456 1326 y(3D)27 b(TQFT)h(with)g(\()p FL(C)5 b FQ(-extended\))27 b(2D)h(MF.)605 1426 y FK(3D)k(TQFT)g FL(!)f FK(2D)h(MF)o(.)51 b FQ(This)33 b(implication)f(has)g(already)f (b)r(een)i(discussed)f(b)r(efore:)456 1525 y(in)k(fact,)i(the)e(axioms) f(of)h(2D)f(MF)i(\(except)f(the)g(gluing)f(axiom\))g(are)g(part)h(of)f (the)i(axioms)456 1625 y(of)30 b(3D)g(TQFT,)g(cf.)h(Remark)e(5.1.2.)44 b(T)-7 b(o)30 b(pro)n(v)n(e)f(that)h(the)h(gluing)f(axiom)f(also)h (follo)n(ws)f(from)456 1725 y(the)d(axioms)e(of)h(3D)h(TQFT,)f(w)n(e)g (again)g(use)g(the)h(v)n(ersion)e(of)h(extended)h(surface)f(from)g (De\014ni-)456 1824 y(tion)i(5.1.10.)605 1924 y(Let)34 b(\006)820 1894 y FE(0)820 1947 y FI(V)912 1924 y FQ(b)r(e)g(the)h (surface)e(obtained)h(from)f(a)h(surface)f(\006)h(b)n(y)g(cutting)g(a)g (circle)f(from)h(it)456 2023 y(and)39 b(lab)r(eling)g(the)h(t)n(w)n(o)f (new)h(b)r(oundary)e(comp)r(onen)n(ts)i(with)g(ob)5 b(jects)39 b FJ(V)58 b FQ(and)40 b FJ(V)3157 1993 y FE(\003)3196 2023 y FQ(,)i(as)d(in)456 2123 y(De\014nition)28 b(5.1.12)e(\(see)h (Figure)g(5.20\).)784 2821 y @beginspecial 0 @llx 0 @lly 308 @urx 66 @ury 3080 @rwi @setspecial %%BeginDocument: figures/sivp.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: sivp.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Mon Jun 7 09:34:41 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 308 66 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -14.0 89.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8383 m -1000 -1000 l 27808 -1000 l 27808 8383 l cp clip 0.01200 0.01200 sc 30.000 slw % Ellipse n 21590 4762 375 1612 0 360 DrawEllipse gs col-1 s gr % Ellipse n 5475 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 19155 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 21975 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 60.000 slw n 16515 4545 m 16635 4335 l gs col-1 s gr % Polyline 30.000 slw gs clippath 13467 4785 m 13899 4875 l 13467 4965 l 14025 4965 l 14025 4785 l cp clip n 11490 4875 m 13980 4875 l gs col-1 s gr gr % arrowhead n 13467 4785 m 13899 4875 l 13467 4965 l 13539 4875 l 13467 4785 l cp gs 0.00 setgray ef gr col-1 s % Polyline n 1200 2700 m 1202 2700 l 1206 2701 l 1213 2703 l 1225 2705 l 1242 2709 l 1265 2713 l 1294 2719 l 1328 2726 l 1369 2734 l 1415 2744 l 1465 2754 l 1521 2765 l 1580 2777 l 1642 2790 l 1706 2803 l 1771 2816 l 1837 2829 l 1902 2842 l 1967 2855 l 2031 2867 l 2093 2880 l 2154 2892 l 2212 2903 l 2268 2914 l 2322 2924 l 2374 2934 l 2424 2943 l 2472 2952 l 2517 2961 l 2561 2969 l 2603 2976 l 2644 2983 l 2683 2990 l 2722 2997 l 2759 3003 l 2795 3009 l 2830 3014 l 2865 3020 l 2900 3025 l 2934 3030 l 2968 3035 l 3002 3040 l 3036 3044 l 3070 3049 l 3105 3053 l 3139 3058 l 3174 3062 l 3209 3066 l 3245 3070 l 3281 3074 l 3318 3077 l 3355 3081 l 3393 3084 l 3431 3088 l 3470 3091 l 3509 3094 l 3549 3097 l 3589 3099 l 3629 3102 l 3671 3105 l 3712 3107 l 3754 3109 l 3796 3111 l 3838 3113 l 3881 3115 l 3924 3116 l 3967 3118 l 4011 3119 l 4055 3120 l 4099 3121 l 4143 3122 l 4187 3123 l 4232 3123 l 4278 3124 l 4323 3124 l 4370 3125 l 4416 3125 l 4464 3125 l 4513 3125 l 4550 3125 l 4589 3125 l 4629 3125 l 4669 3125 l 4710 3124 l 4752 3124 l 4794 3123 l 4838 3123 l 4883 3122 l 4929 3121 l 4975 3120 l 5023 3119 l 5071 3118 l 5121 3117 l 5171 3115 l 5222 3114 l 5275 3112 l 5328 3110 l 5382 3108 l 5436 3105 l 5492 3103 l 5548 3100 l 5604 3097 l 5662 3094 l 5719 3090 l 5777 3087 l 5836 3083 l 5894 3079 l 5953 3074 l 6012 3070 l 6071 3065 l 6130 3060 l 6189 3055 l 6248 3049 l 6307 3044 l 6365 3038 l 6423 3032 l 6481 3025 l 6539 3019 l 6596 3012 l 6652 3005 l 6709 2998 l 6764 2991 l 6820 2983 l 6875 2975 l 6929 2967 l 6983 2958 l 7037 2950 l 7091 2941 l 7144 2932 l 7197 2922 l 7250 2913 l 7301 2903 l 7352 2893 l 7403 2882 l 7454 2872 l 7506 2860 l 7557 2849 l 7610 2837 l 7663 2824 l 7716 2811 l 7771 2797 l 7827 2783 l 7883 2768 l 7941 2752 l 8001 2736 l 8061 2719 l 8124 2701 l 8188 2683 l 8253 2663 l 8321 2643 l 8390 2622 l 8461 2600 l 8534 2578 l 8608 2555 l 8684 2531 l 8762 2506 l 8841 2480 l 8921 2455 l 9002 2428 l 9084 2402 l 9165 2375 l 9247 2348 l 9328 2321 l 9408 2294 l 9487 2268 l 9563 2242 l 9637 2217 l 9707 2194 l 9774 2171 l 9836 2150 l 9894 2130 l 9947 2112 l 9995 2096 l 10038 2081 l 10075 2068 l 10106 2057 l 10132 2048 l 10154 2041 l 10170 2035 l 10182 2031 l 10191 2028 l 10196 2026 l 10199 2025 l 10200 2025 l gs col-1 s gr % Polyline n 1200 7350 m 1202 7349 l 1205 7348 l 1213 7345 l 1224 7340 l 1240 7333 l 1261 7324 l 1288 7313 l 1321 7300 l 1360 7284 l 1404 7265 l 1453 7245 l 1507 7223 l 1565 7199 l 1626 7173 l 1689 7147 l 1755 7120 l 1821 7093 l 1888 7066 l 1954 7039 l 2020 7012 l 2084 6986 l 2147 6960 l 2208 6936 l 2267 6912 l 2323 6890 l 2378 6868 l 2430 6848 l 2480 6828 l 2528 6809 l 2574 6792 l 2617 6775 l 2659 6760 l 2699 6745 l 2738 6731 l 2775 6717 l 2811 6705 l 2845 6693 l 2879 6681 l 2912 6670 l 2944 6660 l 2975 6650 l 3013 6638 l 3050 6627 l 3087 6616 l 3124 6606 l 3160 6596 l 3197 6586 l 3233 6577 l 3269 6568 l 3305 6560 l 3341 6551 l 3378 6544 l 3414 6536 l 3451 6529 l 3487 6523 l 3524 6516 l 3560 6510 l 3597 6505 l 3633 6500 l 3669 6495 l 3705 6490 l 3741 6486 l 3777 6482 l 3813 6478 l 3848 6475 l 3884 6471 l 3919 6468 l 3954 6466 l 3988 6463 l 4023 6461 l 4058 6458 l 4093 6456 l 4128 6454 l 4164 6452 l 4200 6450 l 4231 6448 l 4263 6447 l 4295 6445 l 4329 6443 l 4363 6441 l 4397 6440 l 4433 6438 l 4470 6436 l 4507 6435 l 4546 6433 l 4585 6431 l 4625 6430 l 4666 6428 l 4708 6427 l 4751 6425 l 4795 6424 l 4839 6423 l 4883 6422 l 4929 6420 l 4974 6419 l 5020 6419 l 5066 6418 l 5113 6417 l 5159 6416 l 5206 6416 l 5252 6416 l 5299 6415 l 5345 6415 l 5391 6415 l 5436 6415 l 5482 6416 l 5526 6416 l 5571 6417 l 5615 6418 l 5659 6418 l 5703 6419 l 5746 6421 l 5789 6422 l 5832 6423 l 5875 6425 l 5916 6427 l 5957 6429 l 5999 6431 l 6040 6433 l 6082 6435 l 6125 6438 l 6168 6440 l 6211 6443 l 6255 6446 l 6300 6450 l 6344 6453 l 6390 6457 l 6435 6461 l 6481 6465 l 6528 6469 l 6574 6473 l 6621 6478 l 6668 6483 l 6714 6488 l 6761 6493 l 6808 6498 l 6854 6503 l 6900 6509 l 6946 6514 l 6991 6520 l 7036 6526 l 7080 6532 l 7123 6538 l 7166 6543 l 7208 6550 l 7249 6556 l 7290 6562 l 7329 6568 l 7368 6574 l 7406 6580 l 7443 6587 l 7479 6593 l 7515 6599 l 7549 6606 l 7584 6612 l 7617 6618 l 7650 6625 l 7690 6633 l 7730 6641 l 7769 6650 l 7808 6659 l 7847 6667 l 7886 6676 l 7924 6686 l 7963 6695 l 8002 6705 l 8041 6715 l 8079 6725 l 8118 6735 l 8157 6745 l 8196 6756 l 8234 6766 l 8273 6777 l 8311 6788 l 8349 6798 l 8387 6809 l 8424 6819 l 8461 6830 l 8497 6840 l 8533 6850 l 8569 6860 l 8603 6870 l 8638 6880 l 8672 6889 l 8705 6899 l 8738 6908 l 8771 6916 l 8803 6925 l 8836 6934 l 8868 6942 l 8900 6950 l 8931 6958 l 8962 6965 l 8993 6973 l 9025 6980 l 9058 6987 l 9092 6995 l 9126 7002 l 9163 7010 l 9200 7018 l 9239 7026 l 9280 7034 l 9323 7042 l 9368 7051 l 9415 7060 l 9464 7069 l 9514 7078 l 9567 7088 l 9620 7098 l 9675 7108 l 9730 7117 l 9786 7127 l 9840 7137 l 9893 7146 l 9943 7155 l 9991 7164 l 10034 7171 l 10073 7178 l 10107 7184 l 10135 7189 l 10157 7193 l 10174 7196 l 10186 7198 l 10194 7199 l 10198 7200 l 10200 7200 l gs col-1 s gr % Polyline n 5100 3150 m 5101 3151 l 5104 3154 l 5112 3162 l 5123 3173 l 5135 3185 l 5147 3197 l 5158 3208 l 5168 3218 l 5177 3227 l 5188 3238 l 5196 3246 l 5206 3256 l 5216 3266 l 5227 3278 l 5238 3290 l 5250 3303 l 5262 3317 l 5273 3331 l 5284 3345 l 5294 3359 l 5304 3373 l 5313 3388 l 5320 3400 l 5327 3413 l 5334 3427 l 5340 3442 l 5347 3458 l 5354 3474 l 5360 3491 l 5366 3509 l 5372 3527 l 5377 3545 l 5382 3562 l 5387 3580 l 5391 3597 l 5395 3615 l 5398 3631 l 5402 3647 l 5405 3664 l 5408 3682 l 5412 3701 l 5415 3721 l 5418 3741 l 5421 3762 l 5425 3784 l 5428 3806 l 5430 3828 l 5433 3849 l 5436 3871 l 5438 3892 l 5440 3914 l 5443 3935 l 5444 3954 l 5446 3974 l 5448 3995 l 5450 4016 l 5452 4038 l 5454 4060 l 5455 4084 l 5457 4107 l 5459 4130 l 5461 4154 l 5462 4177 l 5464 4199 l 5465 4221 l 5466 4241 l 5467 4261 l 5468 4280 l 5469 4298 l 5470 4315 l 5471 4334 l 5472 4352 l 5472 4370 l 5473 4388 l 5473 4405 l 5474 4423 l 5474 4441 l 5474 4458 l 5475 4474 l 5475 4491 l 5475 4506 l 5475 4521 l 5475 4535 l 5475 4549 l 5475 4562 l 5475 4575 l 5475 4590 l 5475 4605 l 5475 4620 l 5475 4637 l 5475 4653 l 5475 4670 l 5475 4688 l 5475 4705 l 5475 4722 l 5475 4738 l 5475 4755 l 5475 4770 l 5475 4785 l 5475 4800 l 5475 4815 l 5475 4830 l 5475 4846 l 5475 4862 l 5475 4880 l 5475 4898 l 5474 4916 l 5474 4935 l 5474 4955 l 5473 4974 l 5472 4994 l 5472 5013 l 5471 5033 l 5470 5053 l 5469 5068 l 5468 5085 l 5467 5102 l 5466 5120 l 5465 5139 l 5464 5159 l 5462 5179 l 5461 5200 l 5460 5221 l 5458 5242 l 5457 5263 l 5455 5284 l 5454 5304 l 5452 5323 l 5451 5342 l 5450 5360 l 5449 5378 l 5448 5395 l 5446 5414 l 5445 5432 l 5444 5451 l 5442 5470 l 5441 5490 l 5440 5509 l 5438 5529 l 5436 5549 l 5435 5569 l 5433 5588 l 5431 5607 l 5429 5626 l 5427 5644 l 5425 5662 l 5422 5680 l 5420 5698 l 5417 5715 l 5414 5734 l 5411 5753 l 5408 5772 l 5404 5792 l 5400 5813 l 5395 5834 l 5390 5856 l 5386 5877 l 5381 5898 l 5375 5918 l 5370 5937 l 5365 5955 l 5360 5973 l 5355 5989 l 5350 6005 l 5344 6022 l 5338 6039 l 5331 6056 l 5324 6073 l 5317 6090 l 5309 6107 l 5301 6123 l 5292 6139 l 5284 6154 l 5276 6168 l 5267 6181 l 5259 6194 l 5251 6206 l 5243 6218 l 5234 6229 l 5225 6240 l 5215 6252 l 5205 6264 l 5193 6278 l 5179 6292 l 5164 6308 l 5148 6325 l 5133 6341 l 5120 6355 l 5109 6365 l 5103 6372 l 5100 6375 l gs col-1 s gr % Polyline [120] 0 sd n 5100 3150 m 5097 3153 l 5091 3160 l 5081 3171 l 5067 3185 l 5052 3202 l 5037 3220 l 5022 3237 l 5009 3253 l 4997 3268 l 4987 3283 l 4978 3297 l 4970 3311 l 4963 3325 l 4956 3338 l 4950 3352 l 4944 3367 l 4938 3383 l 4932 3400 l 4926 3417 l 4920 3436 l 4914 3455 l 4908 3475 l 4903 3495 l 4897 3515 l 4892 3535 l 4887 3555 l 4882 3574 l 4877 3593 l 4873 3613 l 4868 3630 l 4864 3648 l 4860 3666 l 4855 3685 l 4850 3705 l 4845 3726 l 4840 3747 l 4835 3769 l 4830 3791 l 4825 3813 l 4820 3836 l 4816 3859 l 4811 3881 l 4806 3903 l 4802 3924 l 4798 3946 l 4794 3967 l 4790 3988 l 4787 4007 l 4783 4026 l 4780 4046 l 4776 4066 l 4773 4088 l 4770 4110 l 4766 4132 l 4763 4155 l 4760 4179 l 4756 4203 l 4753 4227 l 4750 4251 l 4747 4275 l 4744 4298 l 4742 4322 l 4739 4345 l 4737 4367 l 4734 4389 l 4732 4411 l 4730 4433 l 4728 4454 l 4726 4476 l 4724 4499 l 4722 4522 l 4720 4546 l 4719 4570 l 4717 4595 l 4715 4620 l 4714 4646 l 4712 4671 l 4711 4697 l 4710 4722 l 4708 4747 l 4708 4772 l 4707 4796 l 4706 4819 l 4706 4841 l 4705 4863 l 4705 4884 l 4705 4905 l 4705 4926 l 4705 4946 l 4706 4967 l 4706 4988 l 4707 5009 l 4708 5031 l 4708 5053 l 4710 5076 l 4711 5098 l 4712 5120 l 4714 5143 l 4715 5165 l 4717 5187 l 4719 5208 l 4720 5229 l 4722 5249 l 4724 5268 l 4726 5288 l 4728 5306 l 4730 5325 l 4732 5346 l 4735 5367 l 4737 5388 l 4740 5410 l 4743 5432 l 4746 5455 l 4749 5478 l 4753 5501 l 4756 5524 l 4760 5547 l 4763 5570 l 4767 5592 l 4770 5613 l 4774 5634 l 4777 5653 l 4781 5672 l 4784 5690 l 4788 5708 l 4791 5727 l 4795 5746 l 4800 5765 l 4804 5784 l 4809 5803 l 4813 5822 l 4818 5841 l 4823 5860 l 4828 5879 l 4833 5896 l 4838 5914 l 4843 5930 l 4848 5945 l 4853 5960 l 4858 5974 l 4863 5988 l 4868 6003 l 4874 6018 l 4879 6033 l 4886 6048 l 4892 6064 l 4898 6080 l 4905 6095 l 4912 6111 l 4918 6126 l 4924 6140 l 4931 6154 l 4936 6167 l 4942 6180 l 4948 6193 l 4954 6207 l 4960 6221 l 4967 6236 l 4973 6252 l 4980 6267 l 4987 6282 l 4994 6297 l 5001 6311 l 5007 6324 l 5013 6336 l 5019 6347 l 5025 6358 l 5032 6369 l 5039 6380 l 5047 6390 l 5057 6402 l 5067 6414 l 5079 6427 l 5089 6438 l 5096 6446 l 5099 6449 l 5100 6450 l gs col-1 s gr [] 0 sd % Polyline n 15600 7350 m 15602 7349 l 15605 7348 l 15613 7345 l 15624 7340 l 15640 7333 l 15661 7324 l 15688 7313 l 15721 7300 l 15760 7284 l 15804 7265 l 15853 7245 l 15907 7223 l 15965 7199 l 16026 7173 l 16089 7147 l 16155 7120 l 16221 7093 l 16288 7066 l 16354 7039 l 16420 7012 l 16484 6986 l 16547 6960 l 16608 6936 l 16667 6912 l 16723 6890 l 16778 6868 l 16830 6848 l 16880 6828 l 16928 6809 l 16974 6792 l 17017 6775 l 17059 6760 l 17099 6745 l 17138 6731 l 17175 6717 l 17211 6705 l 17245 6693 l 17279 6681 l 17312 6670 l 17344 6660 l 17375 6650 l 17415 6637 l 17455 6625 l 17494 6614 l 17533 6603 l 17571 6593 l 17609 6583 l 17647 6573 l 17685 6564 l 17723 6555 l 17760 6547 l 17797 6539 l 17834 6531 l 17871 6524 l 17908 6517 l 17944 6511 l 17980 6505 l 18015 6500 l 18050 6495 l 18084 6490 l 18118 6485 l 18151 6481 l 18183 6478 l 18215 6474 l 18246 6471 l 18276 6468 l 18306 6465 l 18336 6463 l 18364 6461 l 18393 6459 l 18421 6456 l 18449 6454 l 18478 6453 l 18506 6451 l 18534 6449 l 18563 6447 l 18593 6445 l 18623 6443 l 18654 6441 l 18687 6439 l 18721 6437 l 18756 6434 l 18793 6432 l 18832 6430 l 18873 6427 l 18916 6425 l 18961 6422 l 19008 6419 l 19056 6417 l 19105 6414 l 19154 6411 l 19203 6408 l 19251 6405 l 19297 6403 l 19340 6400 l 19380 6398 l 19414 6396 l 19444 6394 l 19468 6393 l 19487 6392 l 19500 6391 l 19508 6390 l 19513 6390 l 19515 6390 l gs col-1 s gr % Polyline n 15585 2700 m 15587 2700 l 15591 2701 l 15598 2703 l 15610 2705 l 15627 2709 l 15650 2713 l 15679 2719 l 15713 2726 l 15754 2734 l 15800 2744 l 15850 2754 l 15906 2765 l 15965 2777 l 16027 2790 l 16091 2803 l 16156 2816 l 16222 2829 l 16287 2842 l 16352 2855 l 16416 2867 l 16478 2880 l 16539 2892 l 16597 2903 l 16653 2914 l 16707 2924 l 16759 2934 l 16809 2943 l 16857 2952 l 16902 2961 l 16946 2969 l 16988 2976 l 17029 2983 l 17068 2990 l 17107 2997 l 17144 3003 l 17180 3009 l 17215 3014 l 17250 3020 l 17285 3025 l 17325 3031 l 17365 3037 l 17405 3042 l 17445 3048 l 17484 3053 l 17524 3058 l 17564 3063 l 17604 3068 l 17644 3072 l 17684 3077 l 17725 3081 l 17765 3085 l 17805 3089 l 17846 3093 l 17886 3097 l 17926 3100 l 17965 3104 l 18004 3107 l 18043 3110 l 18081 3113 l 18119 3116 l 18156 3118 l 18192 3121 l 18227 3123 l 18262 3125 l 18296 3127 l 18329 3128 l 18361 3130 l 18393 3131 l 18424 3133 l 18454 3134 l 18484 3135 l 18513 3136 l 18543 3138 l 18575 3139 l 18608 3140 l 18640 3141 l 18673 3141 l 18706 3142 l 18741 3143 l 18776 3144 l 18812 3144 l 18850 3145 l 18889 3146 l 18930 3146 l 18973 3147 l 19017 3147 l 19063 3147 l 19111 3148 l 19159 3148 l 19208 3149 l 19255 3149 l 19302 3149 l 19346 3149 l 19387 3149 l 19423 3150 l 19454 3150 l 19480 3150 l 19499 3150 l 19514 3150 l 19523 3150 l 19528 3150 l 19530 3150 l gs col-1 s gr % Polyline n 21600 3135 m 21602 3135 l 21608 3135 l 21618 3134 l 21633 3134 l 21654 3133 l 21680 3132 l 21711 3130 l 21746 3129 l 21784 3127 l 21824 3125 l 21865 3124 l 21905 3122 l 21945 3120 l 21983 3119 l 22020 3117 l 22055 3116 l 22088 3114 l 22120 3113 l 22150 3112 l 22179 3110 l 22207 3109 l 22234 3108 l 22261 3107 l 22288 3106 l 22315 3105 l 22340 3104 l 22366 3103 l 22392 3102 l 22418 3101 l 22445 3100 l 22473 3099 l 22501 3097 l 22530 3096 l 22559 3095 l 22589 3093 l 22620 3092 l 22651 3090 l 22682 3089 l 22713 3087 l 22745 3085 l 22776 3083 l 22807 3081 l 22839 3079 l 22869 3077 l 22900 3074 l 22930 3072 l 22959 3069 l 22988 3067 l 23017 3064 l 23045 3061 l 23073 3059 l 23100 3056 l 23128 3053 l 23155 3049 l 23182 3046 l 23210 3042 l 23238 3038 l 23266 3034 l 23295 3030 l 23325 3026 l 23355 3021 l 23385 3016 l 23416 3011 l 23447 3006 l 23479 3000 l 23511 2995 l 23543 2989 l 23574 2983 l 23606 2977 l 23638 2971 l 23669 2965 l 23700 2960 l 23730 2954 l 23760 2948 l 23790 2942 l 23819 2936 l 23847 2930 l 23875 2924 l 23903 2919 l 23930 2913 l 23958 2908 l 23981 2903 l 24005 2898 l 24030 2892 l 24054 2887 l 24080 2882 l 24105 2876 l 24132 2871 l 24159 2865 l 24186 2858 l 24215 2852 l 24244 2845 l 24274 2838 l 24304 2831 l 24335 2823 l 24367 2816 l 24400 2808 l 24433 2799 l 24466 2790 l 24500 2782 l 24534 2772 l 24569 2763 l 24604 2753 l 24639 2743 l 24675 2733 l 24710 2723 l 24746 2712 l 24783 2701 l 24819 2690 l 24856 2679 l 24893 2667 l 24931 2655 l 24970 2643 l 25000 2633 l 25031 2623 l 25062 2612 l 25094 2601 l 25128 2590 l 25162 2578 l 25198 2566 l 25235 2553 l 25274 2540 l 25314 2526 l 25356 2511 l 25400 2495 l 25446 2479 l 25495 2461 l 25545 2443 l 25598 2424 l 25652 2404 l 25709 2384 l 25768 2362 l 25829 2340 l 25891 2317 l 25955 2294 l 26019 2270 l 26084 2247 l 26148 2223 l 26211 2200 l 26273 2177 l 26332 2155 l 26388 2135 l 26440 2116 l 26488 2098 l 26530 2082 l 26568 2068 l 26600 2057 l 26626 2047 l 26646 2039 l 26662 2034 l 26673 2029 l 26680 2027 l 26683 2026 l 26685 2025 l gs col-1 s gr % Ellipse n 19548 4762 375 1612 0 360 DrawEllipse gs col-1 s gr % Polyline n 21600 6360 m 21602 6360 l 21608 6360 l 21617 6361 l 21632 6361 l 21652 6362 l 21678 6363 l 21709 6364 l 21745 6366 l 21784 6367 l 21826 6369 l 21869 6371 l 21913 6373 l 21957 6374 l 22000 6376 l 22041 6378 l 22080 6380 l 22117 6381 l 22153 6383 l 22187 6385 l 22218 6386 l 22249 6388 l 22278 6389 l 22305 6391 l 22332 6393 l 22359 6394 l 22384 6396 l 22410 6398 l 22437 6399 l 22465 6401 l 22493 6403 l 22521 6405 l 22549 6408 l 22578 6410 l 22608 6412 l 22637 6415 l 22667 6417 l 22698 6420 l 22729 6423 l 22760 6426 l 22790 6429 l 22821 6431 l 22852 6434 l 22882 6437 l 22912 6440 l 22942 6443 l 22971 6446 l 22999 6449 l 23027 6452 l 23055 6454 l 23081 6457 l 23108 6460 l 23134 6462 l 23160 6465 l 23186 6468 l 23212 6470 l 23238 6473 l 23265 6476 l 23292 6479 l 23320 6481 l 23348 6484 l 23377 6487 l 23405 6490 l 23435 6493 l 23464 6497 l 23493 6500 l 23523 6503 l 23552 6506 l 23581 6509 l 23609 6512 l 23637 6516 l 23665 6519 l 23691 6522 l 23718 6525 l 23743 6528 l 23768 6531 l 23791 6534 l 23815 6537 l 23838 6540 l 23860 6543 l 23886 6546 l 23912 6549 l 23938 6553 l 23964 6557 l 23990 6561 l 24017 6565 l 24043 6569 l 24070 6573 l 24097 6577 l 24124 6582 l 24150 6586 l 24176 6591 l 24202 6595 l 24227 6600 l 24252 6604 l 24275 6609 l 24298 6613 l 24320 6618 l 24342 6622 l 24362 6626 l 24383 6631 l 24403 6635 l 24424 6640 l 24446 6645 l 24467 6650 l 24490 6655 l 24512 6661 l 24535 6667 l 24558 6673 l 24582 6679 l 24605 6685 l 24629 6692 l 24653 6698 l 24676 6705 l 24699 6712 l 24722 6718 l 24744 6725 l 24766 6732 l 24788 6738 l 24809 6745 l 24829 6751 l 24850 6758 l 24869 6763 l 24888 6770 l 24908 6776 l 24928 6782 l 24948 6789 l 24970 6796 l 24992 6803 l 25015 6810 l 25038 6818 l 25061 6825 l 25086 6833 l 25110 6840 l 25134 6848 l 25159 6856 l 25183 6863 l 25208 6870 l 25232 6877 l 25256 6884 l 25279 6891 l 25303 6897 l 25326 6904 l 25350 6910 l 25372 6916 l 25394 6921 l 25417 6927 l 25441 6933 l 25465 6939 l 25491 6945 l 25517 6951 l 25544 6957 l 25571 6963 l 25599 6969 l 25628 6976 l 25657 6982 l 25687 6988 l 25716 6994 l 25746 7000 l 25776 7006 l 25805 7012 l 25834 7018 l 25863 7023 l 25891 7029 l 25919 7034 l 25947 7040 l 25975 7045 l 26003 7050 l 26028 7055 l 26054 7060 l 26081 7064 l 26109 7069 l 26137 7075 l 26167 7080 l 26199 7086 l 26233 7091 l 26268 7098 l 26306 7104 l 26346 7111 l 26389 7119 l 26432 7126 l 26477 7134 l 26523 7142 l 26567 7149 l 26610 7157 l 26649 7164 l 26684 7170 l 26714 7175 l 26738 7179 l 26755 7182 l 26766 7183 l 26772 7185 l 26775 7185 l gs col-1 s gr /Times-Roman ff 450.00 scf sf 21735 7050 m gs 1 -1 sc (2) col-1 sh gr /Symbol ff 900.00 scf sf 15900 5100 m gs 1 -1 sc (S) col-1 sh gr /Times-Roman ff 600.00 scf sf 12180 4635 m gs 1 -1 sc (cut) col-1 sh gr /Symbol ff 900.00 scf sf 1500 5100 m gs 1 -1 sc (S) col-1 sh gr /Times-Italic ff 750.00 scf sf 5760 4920 m gs 1 -1 sc (p) col-1 sh gr /Times-Italic ff 750.00 scf sf 4815 7095 m gs 1 -1 sc (c) col-1 sh gr /Times-Italic ff 750.00 scf sf 22275 4920 m gs 1 -1 sc (p) col-1 sh gr /Times-Italic ff 750.00 scf sf 19275 6975 m gs 1 -1 sc (c) col-1 sh gr /Times-Italic ff 750.00 scf sf 21375 6975 m gs 1 -1 sc (c) col-1 sh gr /Times-Italic ff 750.00 scf sf 18360 4920 m gs 1 -1 sc (p) col-1 sh gr /Times-Roman ff 450.00 scf sf 18690 5145 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 450.00 scf sf 22650 5115 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 450.00 scf sf 19605 7050 m gs 1 -1 sc (1) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1710 3021 a FP(Figure)32 b(5.20)605 3184 y FQ(In)21 b(accordance)e(with)i(the)g(pro)r(of)f(of)h(Prop)r(osition)e (5.1.8,)i(instead)f(of)h(\006)2819 3153 y FE(0)2819 3206 y FI(V)2897 3184 y FQ(w)n(e)f(consider)g(the)456 3283 y(surface)k(\006)793 3253 y FE(00)858 3283 y FQ(=)f(\006)1006 3253 y FE(00)1006 3306 y FI(V)1089 3283 y FQ(obtained)i(from)g(\006) 1682 3253 y FE(0)1682 3306 y FI(V)1765 3283 y FQ(b)n(y)g(replacing)f (the)h(b)r(oundary)g(circles)f(with)i(mark)n(ed)456 3383 y(p)r(oin)n(ts)f(with)h(tangen)n(t)f(v)n(ectors)f(at)h(them.)37 b(W)-7 b(e)26 b(can)f(shrink)g(\006)2414 3353 y FE(00)2456 3383 y FQ(,)h(so)f(that)g(it)h(is)g(\\inside")e(\006,)i(as)456 3482 y(in)h(Figure)g(5.21)g(b)r(elo)n(w.)818 4176 y @beginspecial 0 @llx 0 @lly 300 @urx 66 @ury 3000 @rwi @setspecial %%BeginDocument: figures/sivp2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: sivp2.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Fri Jun 11 10:01:43 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 300 66 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -5.0 89.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8383 m -1000 -1000 l 26383 -1000 l 26383 8383 l cp clip 0.01200 0.01200 sc 30.000 slw % Ellipse n 19155 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Ellipse n 21975 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline gs clippath 13467 4785 m 13899 4875 l 13467 4965 l 14025 4965 l 14025 4785 l cp clip n 11490 4875 m 13980 4875 l gs col-1 s gr gr % arrowhead n 13467 4785 m 13899 4875 l 13467 4965 l 13539 4875 l 13467 4785 l cp gs 0.00 setgray ef gr col-1 s % Polyline 15.000 slw gs clippath 19260 5733 m 19200 6021 l 19140 5733 l 19140 6105 l 19260 6105 l cp clip n 19200 4800 m 19200 6075 l gs col-1 s gr gr % arrowhead n 19260 5733 m 19200 6021 l 19140 5733 l 19200 5781 l 19260 5733 l cp gs 0.00 setgray ef gr col-1 s % Polyline gs clippath 22035 5733 m 21975 6021 l 21915 5733 l 21915 6105 l 22035 6105 l cp clip n 21975 4800 m 21975 6075 l gs col-1 s gr gr % arrowhead n 22035 5733 m 21975 6021 l 21915 5733 l 21975 5781 l 22035 5733 l cp gs 0.00 setgray ef gr col-1 s % Polyline 60.000 slw n 15718 3432 m 15838 3222 l gs col-1 s gr % Polyline n 15562 3441 m 15682 3231 l gs col-1 s gr % Polyline 30.000 slw n 1200 2700 m 1202 2700 l 1206 2701 l 1213 2703 l 1225 2705 l 1242 2709 l 1265 2713 l 1294 2719 l 1328 2726 l 1369 2734 l 1415 2744 l 1465 2754 l 1521 2765 l 1580 2777 l 1642 2790 l 1706 2803 l 1771 2816 l 1837 2829 l 1902 2842 l 1967 2855 l 2031 2867 l 2093 2880 l 2154 2892 l 2212 2903 l 2268 2914 l 2322 2924 l 2374 2934 l 2424 2943 l 2472 2952 l 2517 2961 l 2561 2969 l 2603 2976 l 2644 2983 l 2683 2990 l 2722 2997 l 2759 3003 l 2795 3009 l 2830 3014 l 2865 3020 l 2900 3025 l 2934 3030 l 2968 3035 l 3002 3040 l 3036 3044 l 3070 3049 l 3105 3053 l 3139 3058 l 3174 3062 l 3209 3066 l 3245 3070 l 3281 3074 l 3318 3077 l 3355 3081 l 3393 3084 l 3431 3088 l 3470 3091 l 3509 3094 l 3549 3097 l 3589 3099 l 3629 3102 l 3671 3105 l 3712 3107 l 3754 3109 l 3796 3111 l 3838 3113 l 3881 3115 l 3924 3116 l 3967 3118 l 4011 3119 l 4055 3120 l 4099 3121 l 4143 3122 l 4187 3123 l 4232 3123 l 4278 3124 l 4323 3124 l 4370 3125 l 4416 3125 l 4464 3125 l 4513 3125 l 4550 3125 l 4589 3125 l 4629 3125 l 4669 3125 l 4710 3124 l 4752 3124 l 4794 3123 l 4838 3123 l 4883 3122 l 4929 3121 l 4975 3120 l 5023 3119 l 5071 3118 l 5121 3117 l 5171 3115 l 5222 3114 l 5275 3112 l 5328 3110 l 5382 3108 l 5436 3105 l 5492 3103 l 5548 3100 l 5604 3097 l 5662 3094 l 5719 3090 l 5777 3087 l 5836 3083 l 5894 3079 l 5953 3074 l 6012 3070 l 6071 3065 l 6130 3060 l 6189 3055 l 6248 3049 l 6307 3044 l 6365 3038 l 6423 3032 l 6481 3025 l 6539 3019 l 6596 3012 l 6652 3005 l 6709 2998 l 6764 2991 l 6820 2983 l 6875 2975 l 6929 2967 l 6983 2958 l 7037 2950 l 7091 2941 l 7144 2932 l 7197 2922 l 7250 2913 l 7301 2903 l 7352 2893 l 7403 2882 l 7454 2872 l 7506 2860 l 7557 2849 l 7610 2837 l 7663 2824 l 7716 2811 l 7771 2797 l 7827 2783 l 7883 2768 l 7941 2752 l 8001 2736 l 8061 2719 l 8124 2701 l 8188 2683 l 8253 2663 l 8321 2643 l 8390 2622 l 8461 2600 l 8534 2578 l 8608 2555 l 8684 2531 l 8762 2506 l 8841 2480 l 8921 2455 l 9002 2428 l 9084 2402 l 9165 2375 l 9247 2348 l 9328 2321 l 9408 2294 l 9487 2268 l 9563 2242 l 9637 2217 l 9707 2194 l 9774 2171 l 9836 2150 l 9894 2130 l 9947 2112 l 9995 2096 l 10038 2081 l 10075 2068 l 10106 2057 l 10132 2048 l 10154 2041 l 10170 2035 l 10182 2031 l 10191 2028 l 10196 2026 l 10199 2025 l 10200 2025 l gs col-1 s gr % Polyline n 1200 7350 m 1202 7349 l 1205 7348 l 1213 7345 l 1224 7340 l 1240 7333 l 1261 7324 l 1288 7313 l 1321 7300 l 1360 7284 l 1404 7265 l 1453 7245 l 1507 7223 l 1565 7199 l 1626 7173 l 1689 7147 l 1755 7120 l 1821 7093 l 1888 7066 l 1954 7039 l 2020 7012 l 2084 6986 l 2147 6960 l 2208 6936 l 2267 6912 l 2323 6890 l 2378 6868 l 2430 6848 l 2480 6828 l 2528 6809 l 2574 6792 l 2617 6775 l 2659 6760 l 2699 6745 l 2738 6731 l 2775 6717 l 2811 6705 l 2845 6693 l 2879 6681 l 2912 6670 l 2944 6660 l 2975 6650 l 3013 6638 l 3050 6627 l 3087 6616 l 3124 6606 l 3160 6596 l 3197 6586 l 3233 6577 l 3269 6568 l 3305 6560 l 3341 6551 l 3378 6544 l 3414 6536 l 3451 6529 l 3487 6523 l 3524 6516 l 3560 6510 l 3597 6505 l 3633 6500 l 3669 6495 l 3705 6490 l 3741 6486 l 3777 6482 l 3813 6478 l 3848 6475 l 3884 6471 l 3919 6468 l 3954 6466 l 3988 6463 l 4023 6461 l 4058 6458 l 4093 6456 l 4128 6454 l 4164 6452 l 4200 6450 l 4231 6448 l 4263 6447 l 4295 6445 l 4329 6443 l 4363 6441 l 4397 6440 l 4433 6438 l 4470 6436 l 4507 6435 l 4546 6433 l 4585 6431 l 4625 6430 l 4666 6428 l 4708 6427 l 4751 6425 l 4795 6424 l 4839 6423 l 4883 6422 l 4929 6420 l 4974 6419 l 5020 6419 l 5066 6418 l 5113 6417 l 5159 6416 l 5206 6416 l 5252 6416 l 5299 6415 l 5345 6415 l 5391 6415 l 5436 6415 l 5482 6416 l 5526 6416 l 5571 6417 l 5615 6418 l 5659 6418 l 5703 6419 l 5746 6421 l 5789 6422 l 5832 6423 l 5875 6425 l 5916 6427 l 5957 6429 l 5999 6431 l 6040 6433 l 6082 6435 l 6125 6438 l 6168 6440 l 6211 6443 l 6255 6446 l 6300 6450 l 6344 6453 l 6390 6457 l 6435 6461 l 6481 6465 l 6528 6469 l 6574 6473 l 6621 6478 l 6668 6483 l 6714 6488 l 6761 6493 l 6808 6498 l 6854 6503 l 6900 6509 l 6946 6514 l 6991 6520 l 7036 6526 l 7080 6532 l 7123 6538 l 7166 6543 l 7208 6550 l 7249 6556 l 7290 6562 l 7329 6568 l 7368 6574 l 7406 6580 l 7443 6587 l 7479 6593 l 7515 6599 l 7549 6606 l 7584 6612 l 7617 6618 l 7650 6625 l 7690 6633 l 7730 6641 l 7769 6650 l 7808 6659 l 7847 6667 l 7886 6676 l 7924 6686 l 7963 6695 l 8002 6705 l 8041 6715 l 8079 6725 l 8118 6735 l 8157 6745 l 8196 6756 l 8234 6766 l 8273 6777 l 8311 6788 l 8349 6798 l 8387 6809 l 8424 6819 l 8461 6830 l 8497 6840 l 8533 6850 l 8569 6860 l 8603 6870 l 8638 6880 l 8672 6889 l 8705 6899 l 8738 6908 l 8771 6916 l 8803 6925 l 8836 6934 l 8868 6942 l 8900 6950 l 8931 6958 l 8962 6965 l 8993 6973 l 9025 6980 l 9058 6987 l 9092 6995 l 9126 7002 l 9163 7010 l 9200 7018 l 9239 7026 l 9280 7034 l 9323 7042 l 9368 7051 l 9415 7060 l 9464 7069 l 9514 7078 l 9567 7088 l 9620 7098 l 9675 7108 l 9730 7117 l 9786 7127 l 9840 7137 l 9893 7146 l 9943 7155 l 9991 7164 l 10034 7171 l 10073 7178 l 10107 7184 l 10135 7189 l 10157 7193 l 10174 7196 l 10186 7198 l 10194 7199 l 10198 7200 l 10200 7200 l gs col-1 s gr % Polyline n 5100 3150 m 5101 3151 l 5104 3154 l 5112 3162 l 5123 3173 l 5135 3185 l 5147 3197 l 5158 3208 l 5168 3218 l 5177 3227 l 5188 3238 l 5196 3246 l 5206 3256 l 5216 3266 l 5227 3278 l 5238 3290 l 5250 3303 l 5262 3317 l 5273 3331 l 5284 3345 l 5294 3359 l 5304 3373 l 5313 3388 l 5320 3400 l 5327 3413 l 5334 3427 l 5340 3442 l 5347 3458 l 5354 3474 l 5360 3491 l 5366 3509 l 5372 3527 l 5377 3545 l 5382 3562 l 5387 3580 l 5391 3597 l 5395 3615 l 5398 3631 l 5402 3647 l 5405 3664 l 5408 3682 l 5412 3701 l 5415 3721 l 5418 3741 l 5421 3762 l 5425 3784 l 5428 3806 l 5430 3828 l 5433 3849 l 5436 3871 l 5438 3892 l 5440 3914 l 5443 3935 l 5444 3954 l 5446 3974 l 5448 3995 l 5450 4016 l 5452 4038 l 5454 4060 l 5455 4084 l 5457 4107 l 5459 4130 l 5461 4154 l 5462 4177 l 5464 4199 l 5465 4221 l 5466 4241 l 5467 4261 l 5468 4280 l 5469 4298 l 5470 4315 l 5471 4334 l 5472 4352 l 5472 4370 l 5473 4388 l 5473 4405 l 5474 4423 l 5474 4441 l 5474 4458 l 5475 4474 l 5475 4491 l 5475 4506 l 5475 4521 l 5475 4535 l 5475 4549 l 5475 4562 l 5475 4575 l 5475 4590 l 5475 4605 l 5475 4620 l 5475 4637 l 5475 4653 l 5475 4670 l 5475 4688 l 5475 4705 l 5475 4722 l 5475 4738 l 5475 4755 l 5475 4770 l 5475 4785 l 5475 4800 l 5475 4815 l 5475 4830 l 5475 4846 l 5475 4862 l 5475 4880 l 5475 4898 l 5474 4916 l 5474 4935 l 5474 4955 l 5473 4974 l 5472 4994 l 5472 5013 l 5471 5033 l 5470 5053 l 5469 5068 l 5468 5085 l 5467 5102 l 5466 5120 l 5465 5139 l 5464 5159 l 5462 5179 l 5461 5200 l 5460 5221 l 5458 5242 l 5457 5263 l 5455 5284 l 5454 5304 l 5452 5323 l 5451 5342 l 5450 5360 l 5449 5378 l 5448 5395 l 5446 5414 l 5445 5432 l 5444 5451 l 5442 5470 l 5441 5490 l 5440 5509 l 5438 5529 l 5436 5549 l 5435 5569 l 5433 5588 l 5431 5607 l 5429 5626 l 5427 5644 l 5425 5662 l 5422 5680 l 5420 5698 l 5417 5715 l 5414 5734 l 5411 5753 l 5408 5772 l 5404 5792 l 5400 5813 l 5395 5834 l 5390 5856 l 5386 5877 l 5381 5898 l 5375 5918 l 5370 5937 l 5365 5955 l 5360 5973 l 5355 5989 l 5350 6005 l 5344 6022 l 5338 6039 l 5331 6056 l 5324 6073 l 5317 6090 l 5309 6107 l 5301 6123 l 5292 6139 l 5284 6154 l 5276 6168 l 5267 6181 l 5259 6194 l 5251 6206 l 5243 6218 l 5234 6229 l 5225 6240 l 5215 6252 l 5205 6264 l 5193 6278 l 5179 6292 l 5164 6308 l 5148 6325 l 5133 6341 l 5120 6355 l 5109 6365 l 5103 6372 l 5100 6375 l gs col-1 s gr % Polyline [120] 0 sd n 5100 3150 m 5097 3153 l 5091 3160 l 5081 3171 l 5067 3185 l 5052 3202 l 5037 3220 l 5022 3237 l 5009 3253 l 4997 3268 l 4987 3283 l 4978 3297 l 4970 3311 l 4963 3325 l 4956 3338 l 4950 3352 l 4944 3367 l 4938 3383 l 4932 3400 l 4926 3417 l 4920 3436 l 4914 3455 l 4908 3475 l 4903 3495 l 4897 3515 l 4892 3535 l 4887 3555 l 4882 3574 l 4877 3593 l 4873 3613 l 4868 3630 l 4864 3648 l 4860 3666 l 4855 3685 l 4850 3705 l 4845 3726 l 4840 3747 l 4835 3769 l 4830 3791 l 4825 3813 l 4820 3836 l 4816 3859 l 4811 3881 l 4806 3903 l 4802 3924 l 4798 3946 l 4794 3967 l 4790 3988 l 4787 4007 l 4783 4026 l 4780 4046 l 4776 4066 l 4773 4088 l 4770 4110 l 4766 4132 l 4763 4155 l 4760 4179 l 4756 4203 l 4753 4227 l 4750 4251 l 4747 4275 l 4744 4298 l 4742 4322 l 4739 4345 l 4737 4367 l 4734 4389 l 4732 4411 l 4730 4433 l 4728 4454 l 4726 4476 l 4724 4499 l 4722 4522 l 4720 4546 l 4719 4570 l 4717 4595 l 4715 4620 l 4714 4646 l 4712 4671 l 4711 4697 l 4710 4722 l 4708 4747 l 4708 4772 l 4707 4796 l 4706 4819 l 4706 4841 l 4705 4863 l 4705 4884 l 4705 4905 l 4705 4926 l 4705 4946 l 4706 4967 l 4706 4988 l 4707 5009 l 4708 5031 l 4708 5053 l 4710 5076 l 4711 5098 l 4712 5120 l 4714 5143 l 4715 5165 l 4717 5187 l 4719 5208 l 4720 5229 l 4722 5249 l 4724 5268 l 4726 5288 l 4728 5306 l 4730 5325 l 4732 5346 l 4735 5367 l 4737 5388 l 4740 5410 l 4743 5432 l 4746 5455 l 4749 5478 l 4753 5501 l 4756 5524 l 4760 5547 l 4763 5570 l 4767 5592 l 4770 5613 l 4774 5634 l 4777 5653 l 4781 5672 l 4784 5690 l 4788 5708 l 4791 5727 l 4795 5746 l 4800 5765 l 4804 5784 l 4809 5803 l 4813 5822 l 4818 5841 l 4823 5860 l 4828 5879 l 4833 5896 l 4838 5914 l 4843 5930 l 4848 5945 l 4853 5960 l 4858 5974 l 4863 5988 l 4868 6003 l 4874 6018 l 4879 6033 l 4886 6048 l 4892 6064 l 4898 6080 l 4905 6095 l 4912 6111 l 4918 6126 l 4924 6140 l 4931 6154 l 4936 6167 l 4942 6180 l 4948 6193 l 4954 6207 l 4960 6221 l 4967 6236 l 4973 6252 l 4980 6267 l 4987 6282 l 4994 6297 l 5001 6311 l 5007 6324 l 5013 6336 l 5019 6347 l 5025 6358 l 5032 6369 l 5039 6380 l 5047 6390 l 5057 6402 l 5067 6414 l 5079 6427 l 5089 6438 l 5096 6446 l 5099 6449 l 5100 6450 l gs col-1 s gr [] 0 sd % Polyline n 16200 2700 m 16202 2700 l 16206 2701 l 16213 2703 l 16225 2705 l 16242 2709 l 16265 2713 l 16294 2719 l 16328 2726 l 16369 2734 l 16415 2744 l 16465 2754 l 16521 2765 l 16580 2777 l 16642 2790 l 16706 2803 l 16771 2816 l 16837 2829 l 16902 2842 l 16967 2855 l 17031 2867 l 17093 2880 l 17154 2892 l 17212 2903 l 17268 2914 l 17322 2924 l 17374 2934 l 17424 2943 l 17472 2952 l 17517 2961 l 17561 2969 l 17603 2976 l 17644 2983 l 17683 2990 l 17722 2997 l 17759 3003 l 17795 3009 l 17830 3014 l 17865 3020 l 17900 3025 l 17934 3030 l 17968 3035 l 18002 3040 l 18036 3044 l 18070 3049 l 18105 3053 l 18139 3058 l 18174 3062 l 18209 3066 l 18245 3070 l 18281 3074 l 18318 3077 l 18355 3081 l 18393 3084 l 18431 3088 l 18470 3091 l 18509 3094 l 18549 3097 l 18589 3099 l 18629 3102 l 18671 3105 l 18712 3107 l 18754 3109 l 18796 3111 l 18838 3113 l 18881 3115 l 18924 3116 l 18967 3118 l 19011 3119 l 19055 3120 l 19099 3121 l 19143 3122 l 19187 3123 l 19232 3123 l 19278 3124 l 19323 3124 l 19370 3125 l 19416 3125 l 19464 3125 l 19513 3125 l 19550 3125 l 19589 3125 l 19629 3125 l 19669 3125 l 19710 3124 l 19752 3124 l 19794 3123 l 19838 3123 l 19883 3122 l 19929 3121 l 19975 3120 l 20023 3119 l 20071 3118 l 20121 3117 l 20171 3115 l 20222 3114 l 20275 3112 l 20328 3110 l 20382 3108 l 20436 3105 l 20492 3103 l 20548 3100 l 20604 3097 l 20662 3094 l 20719 3090 l 20777 3087 l 20836 3083 l 20894 3079 l 20953 3074 l 21012 3070 l 21071 3065 l 21130 3060 l 21189 3055 l 21248 3049 l 21307 3044 l 21365 3038 l 21423 3032 l 21481 3025 l 21539 3019 l 21596 3012 l 21652 3005 l 21709 2998 l 21764 2991 l 21820 2983 l 21875 2975 l 21929 2967 l 21983 2958 l 22037 2950 l 22091 2941 l 22144 2932 l 22197 2922 l 22250 2913 l 22301 2903 l 22352 2893 l 22403 2882 l 22454 2872 l 22506 2860 l 22557 2849 l 22610 2837 l 22663 2824 l 22716 2811 l 22771 2797 l 22827 2783 l 22883 2768 l 22941 2752 l 23001 2736 l 23061 2719 l 23124 2701 l 23188 2683 l 23253 2663 l 23321 2643 l 23390 2622 l 23461 2600 l 23534 2578 l 23608 2555 l 23684 2531 l 23762 2506 l 23841 2480 l 23921 2455 l 24002 2428 l 24084 2402 l 24165 2375 l 24247 2348 l 24328 2321 l 24408 2294 l 24487 2268 l 24563 2242 l 24637 2217 l 24707 2194 l 24774 2171 l 24836 2150 l 24894 2130 l 24947 2112 l 24995 2096 l 25038 2081 l 25075 2068 l 25106 2057 l 25132 2048 l 25154 2041 l 25170 2035 l 25182 2031 l 25191 2028 l 25196 2026 l 25199 2025 l 25200 2025 l gs col-1 s gr % Polyline n 16200 7350 m 16202 7349 l 16205 7348 l 16213 7345 l 16224 7340 l 16240 7333 l 16261 7324 l 16288 7313 l 16321 7300 l 16360 7284 l 16404 7265 l 16453 7245 l 16507 7223 l 16565 7199 l 16626 7173 l 16689 7147 l 16755 7120 l 16821 7093 l 16888 7066 l 16954 7039 l 17020 7012 l 17084 6986 l 17147 6960 l 17208 6936 l 17267 6912 l 17323 6890 l 17378 6868 l 17430 6848 l 17480 6828 l 17528 6809 l 17574 6792 l 17617 6775 l 17659 6760 l 17699 6745 l 17738 6731 l 17775 6717 l 17811 6705 l 17845 6693 l 17879 6681 l 17912 6670 l 17944 6660 l 17975 6650 l 18013 6638 l 18050 6627 l 18087 6616 l 18124 6606 l 18160 6596 l 18197 6586 l 18233 6577 l 18269 6568 l 18305 6560 l 18341 6551 l 18378 6544 l 18414 6536 l 18451 6529 l 18487 6523 l 18524 6516 l 18560 6510 l 18597 6505 l 18633 6500 l 18669 6495 l 18705 6490 l 18741 6486 l 18777 6482 l 18813 6478 l 18848 6475 l 18884 6471 l 18919 6468 l 18954 6466 l 18988 6463 l 19023 6461 l 19058 6458 l 19093 6456 l 19128 6454 l 19164 6452 l 19200 6450 l 19231 6448 l 19263 6447 l 19295 6445 l 19329 6443 l 19363 6441 l 19397 6440 l 19433 6438 l 19470 6436 l 19507 6435 l 19546 6433 l 19585 6431 l 19625 6430 l 19666 6428 l 19708 6427 l 19751 6425 l 19795 6424 l 19839 6423 l 19883 6422 l 19929 6420 l 19974 6419 l 20020 6419 l 20066 6418 l 20113 6417 l 20159 6416 l 20206 6416 l 20252 6416 l 20299 6415 l 20345 6415 l 20391 6415 l 20436 6415 l 20482 6416 l 20526 6416 l 20571 6417 l 20615 6418 l 20659 6418 l 20703 6419 l 20746 6421 l 20789 6422 l 20832 6423 l 20875 6425 l 20916 6427 l 20957 6429 l 20999 6431 l 21040 6433 l 21082 6435 l 21125 6438 l 21168 6440 l 21211 6443 l 21255 6446 l 21300 6450 l 21344 6453 l 21390 6457 l 21435 6461 l 21481 6465 l 21528 6469 l 21574 6473 l 21621 6478 l 21668 6483 l 21714 6488 l 21761 6493 l 21808 6498 l 21854 6503 l 21900 6509 l 21946 6514 l 21991 6520 l 22036 6526 l 22080 6532 l 22123 6538 l 22166 6543 l 22208 6550 l 22249 6556 l 22290 6562 l 22329 6568 l 22368 6574 l 22406 6580 l 22443 6587 l 22479 6593 l 22515 6599 l 22549 6606 l 22584 6612 l 22617 6618 l 22650 6625 l 22690 6633 l 22730 6641 l 22769 6650 l 22808 6659 l 22847 6667 l 22886 6676 l 22924 6686 l 22963 6695 l 23002 6705 l 23041 6715 l 23079 6725 l 23118 6735 l 23157 6745 l 23196 6756 l 23234 6766 l 23273 6777 l 23311 6788 l 23349 6798 l 23387 6809 l 23424 6819 l 23461 6830 l 23497 6840 l 23533 6850 l 23569 6860 l 23603 6870 l 23638 6880 l 23672 6889 l 23705 6899 l 23738 6908 l 23771 6916 l 23803 6925 l 23836 6934 l 23868 6942 l 23900 6950 l 23931 6958 l 23962 6965 l 23993 6973 l 24025 6980 l 24058 6987 l 24092 6995 l 24126 7002 l 24163 7010 l 24200 7018 l 24239 7026 l 24280 7034 l 24323 7042 l 24368 7051 l 24415 7060 l 24464 7069 l 24514 7078 l 24567 7088 l 24620 7098 l 24675 7108 l 24730 7117 l 24786 7127 l 24840 7137 l 24893 7146 l 24943 7155 l 24991 7164 l 25034 7171 l 25073 7178 l 25107 7184 l 25135 7189 l 25157 7193 l 25174 7196 l 25186 7198 l 25194 7199 l 25198 7200 l 25200 7200 l gs col-1 s gr % Ellipse n 5475 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline n 16125 3525 m 16127 3525 l 16131 3526 l 16139 3527 l 16151 3529 l 16168 3531 l 16190 3535 l 16218 3539 l 16251 3544 l 16289 3549 l 16331 3556 l 16377 3563 l 16425 3570 l 16476 3578 l 16527 3586 l 16579 3595 l 16630 3603 l 16681 3612 l 16731 3620 l 16779 3629 l 16826 3637 l 16872 3645 l 16916 3654 l 16958 3662 l 16999 3670 l 17039 3678 l 17078 3686 l 17116 3695 l 17153 3703 l 17190 3712 l 17227 3721 l 17263 3730 l 17300 3740 l 17338 3750 l 17373 3760 l 17409 3770 l 17446 3780 l 17483 3791 l 17520 3802 l 17559 3814 l 17598 3826 l 17637 3838 l 17678 3851 l 17719 3865 l 17760 3878 l 17802 3892 l 17844 3907 l 17886 3922 l 17929 3937 l 17971 3952 l 18014 3968 l 18056 3984 l 18098 4000 l 18139 4016 l 18180 4032 l 18220 4048 l 18260 4064 l 18298 4080 l 18336 4096 l 18372 4112 l 18408 4128 l 18442 4144 l 18475 4159 l 18507 4174 l 18538 4190 l 18568 4204 l 18596 4219 l 18623 4234 l 18650 4248 l 18675 4263 l 18706 4281 l 18736 4299 l 18765 4318 l 18792 4337 l 18819 4356 l 18844 4375 l 18868 4395 l 18892 4415 l 18914 4436 l 18935 4457 l 18955 4478 l 18974 4500 l 18992 4522 l 19008 4544 l 19024 4567 l 19038 4590 l 19051 4612 l 19063 4635 l 19073 4658 l 19083 4681 l 19091 4703 l 19098 4726 l 19105 4749 l 19110 4771 l 19115 4794 l 19119 4817 l 19122 4839 l 19125 4863 l 19127 4884 l 19129 4907 l 19130 4930 l 19130 4953 l 19130 4978 l 19129 5002 l 19128 5028 l 19126 5054 l 19123 5080 l 19119 5107 l 19115 5135 l 19109 5162 l 19103 5190 l 19095 5218 l 19087 5247 l 19078 5275 l 19067 5302 l 19056 5330 l 19044 5357 l 19031 5384 l 19017 5410 l 19002 5435 l 18986 5460 l 18969 5484 l 18952 5507 l 18933 5530 l 18914 5551 l 18894 5572 l 18872 5593 l 18850 5613 l 18829 5629 l 18808 5646 l 18785 5663 l 18761 5679 l 18736 5695 l 18709 5710 l 18682 5726 l 18653 5742 l 18623 5757 l 18591 5772 l 18559 5787 l 18525 5802 l 18490 5817 l 18454 5831 l 18417 5846 l 18379 5860 l 18340 5874 l 18301 5887 l 18261 5900 l 18221 5913 l 18180 5926 l 18139 5938 l 18098 5950 l 18056 5962 l 18015 5973 l 17974 5984 l 17933 5995 l 17892 6005 l 17852 6015 l 17811 6025 l 17771 6035 l 17731 6044 l 17690 6053 l 17650 6063 l 17616 6070 l 17581 6078 l 17546 6086 l 17510 6093 l 17474 6101 l 17437 6109 l 17399 6117 l 17360 6125 l 17319 6133 l 17277 6142 l 17234 6150 l 17189 6159 l 17142 6169 l 17093 6178 l 17042 6188 l 16989 6198 l 16934 6209 l 16878 6220 l 16820 6231 l 16760 6242 l 16700 6254 l 16639 6265 l 16578 6277 l 16518 6288 l 16458 6299 l 16401 6310 l 16346 6320 l 16295 6330 l 16248 6338 l 16206 6346 l 16168 6353 l 16136 6359 l 16110 6364 l 16089 6368 l 16073 6371 l 16062 6373 l 16055 6374 l 16052 6375 l 16050 6375 l gs col-1 s gr /Times-Italic ff 750.00 scf sf 5775 4920 m gs 1 -1 sc (p) col-1 sh gr % Polyline n 25125 3000 m 25123 3001 l 25120 3002 l 25113 3004 l 25103 3008 l 25088 3013 l 25067 3020 l 25042 3028 l 25012 3039 l 24976 3051 l 24935 3065 l 24890 3080 l 24841 3097 l 24789 3115 l 24733 3134 l 24677 3154 l 24618 3174 l 24560 3194 l 24501 3215 l 24443 3235 l 24386 3255 l 24330 3275 l 24275 3295 l 24222 3313 l 24171 3332 l 24122 3349 l 24075 3367 l 24029 3384 l 23985 3400 l 23943 3416 l 23902 3431 l 23862 3446 l 23824 3461 l 23787 3476 l 23750 3490 l 23714 3505 l 23679 3519 l 23644 3533 l 23609 3548 l 23575 3563 l 23537 3579 l 23499 3595 l 23460 3612 l 23422 3629 l 23383 3647 l 23344 3664 l 23305 3682 l 23266 3701 l 23226 3719 l 23187 3739 l 23147 3758 l 23107 3778 l 23067 3798 l 23027 3818 l 22987 3838 l 22948 3859 l 22909 3879 l 22870 3900 l 22832 3921 l 22795 3941 l 22759 3962 l 22723 3982 l 22688 4002 l 22655 4022 l 22622 4042 l 22590 4061 l 22560 4081 l 22531 4099 l 22503 4118 l 22476 4136 l 22450 4153 l 22425 4171 l 22402 4188 l 22379 4205 l 22358 4221 l 22338 4238 l 22312 4258 l 22289 4279 l 22266 4300 l 22245 4320 l 22224 4341 l 22205 4363 l 22187 4384 l 22169 4406 l 22153 4428 l 22138 4451 l 22124 4474 l 22111 4497 l 22099 4521 l 22088 4544 l 22078 4568 l 22070 4593 l 22062 4617 l 22056 4641 l 22051 4665 l 22046 4690 l 22042 4714 l 22040 4739 l 22038 4763 l 22037 4788 l 22036 4812 l 22036 4837 l 22036 4862 l 22038 4888 l 22039 4910 l 22040 4934 l 22042 4958 l 22045 4982 l 22048 5007 l 22052 5033 l 22056 5060 l 22061 5087 l 22067 5114 l 22074 5143 l 22082 5171 l 22090 5200 l 22100 5230 l 22110 5259 l 22122 5289 l 22134 5318 l 22148 5347 l 22163 5377 l 22178 5405 l 22195 5433 l 22213 5461 l 22231 5488 l 22251 5514 l 22272 5540 l 22294 5565 l 22316 5588 l 22340 5611 l 22365 5633 l 22391 5654 l 22418 5674 l 22446 5694 l 22475 5713 l 22501 5728 l 22528 5742 l 22556 5757 l 22585 5770 l 22616 5784 l 22647 5797 l 22680 5810 l 22714 5823 l 22750 5835 l 22786 5847 l 22824 5859 l 22863 5871 l 22903 5882 l 22945 5893 l 22987 5904 l 23029 5914 l 23073 5924 l 23117 5934 l 23162 5943 l 23207 5953 l 23252 5962 l 23298 5970 l 23343 5979 l 23389 5987 l 23434 5994 l 23479 6002 l 23523 6009 l 23567 6016 l 23611 6023 l 23654 6029 l 23696 6035 l 23738 6041 l 23779 6047 l 23819 6053 l 23859 6059 l 23898 6064 l 23937 6070 l 23975 6075 l 24015 6081 l 24054 6086 l 24094 6092 l 24133 6098 l 24173 6104 l 24213 6110 l 24253 6116 l 24294 6123 l 24336 6129 l 24379 6136 l 24424 6143 l 24470 6151 l 24517 6159 l 24566 6167 l 24617 6175 l 24669 6184 l 24723 6193 l 24777 6202 l 24832 6211 l 24888 6221 l 24943 6230 l 24997 6239 l 25049 6248 l 25099 6257 l 25146 6265 l 25188 6272 l 25226 6279 l 25259 6284 l 25287 6289 l 25308 6293 l 25325 6296 l 25337 6298 l 25344 6299 l 25348 6300 l 25350 6300 l gs col-1 s gr /Times-Roman ff 600.00 scf sf 12180 4635 m gs 1 -1 sc (cut) col-1 sh gr /Times-Italic ff 750.00 scf sf 19125 4350 m gs 1 -1 sc (V) col-1 sh gr /Times-Italic ff 525.00 scf sf 21900 4170 m gs 1 -1 sc (*) col-1 sh gr /Times-Italic ff 750.00 scf sf 21300 4350 m gs 1 -1 sc (V) col-1 sh gr /Symbol ff 900.00 scf sf 450 3150 m gs 1 -1 sc (S) col-1 sh gr /Symbol ff 900.00 scf sf 15000 2850 m gs 1 -1 sc (S) col-1 sh gr /Symbol ff 900.00 scf sf 15000 3975 m gs 1 -1 sc (S) col-1 sh gr /Times-Italic ff 750.00 scf sf 18375 4920 m gs 1 -1 sc (p) col-1 sh gr /Times-Italic ff 750.00 scf sf 22425 4920 m gs 1 -1 sc (p) col-1 sh gr /Times-Roman ff 450.00 scf sf 18675 5175 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 450.00 scf sf 22725 5175 m gs 1 -1 sc (2) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1710 4375 a FP(Figure)32 b(5.21)605 4543 y FQ(Then)24 b(w)n(e)f(\\\014ll)g(in)h(the)f(space)g(b)r(et)n(w)n(een)g (\006)h(and)f(\006)2159 4513 y FE(00)2201 4543 y FQ(",)h(i.e.,)h(w)n(e) e(consider)f(a)h(3-manifold)g FJ(M)456 4643 y FQ(with)k(b)r(oundary)f FJ(@)5 b(M)31 b FQ(=)23 b(\006)16 b FL(t)p 1414 4576 103 4 v 17 w FQ(\006)1474 4619 y FE(00)1543 4643 y FQ(\(see)27 b(Figure)f(5.22\).)36 b(This)26 b FJ(M)36 b FQ(is)26 b(a)g FL(C)5 b FQ(-mark)n(ed)25 b(3-manifold,)456 4742 y(hence)i(it)h(giv)n(es)f(a)g(v)n(ector)1259 4877 y FJ(\034)9 b FQ(\()p FJ(M)g FQ(\))24 b FL(2)f FJ(\034)9 b FQ(\()p FJ(@)c(M)k FQ(\))24 b FL(')f FQ(Hom)2093 4889 y FI(k)2133 4877 y FQ(\()p FJ(\034)9 b FQ(\(\006)2302 4842 y FE(0)r(0)2346 4877 y FQ(\))p FJ(;)14 b(\034)9 b FQ(\(\006\)\))p FJ(:)456 5016 y FQ(Considered)33 b(as)h(a)g(map)g FJ(\034)9 b FQ(\(\006)1405 4986 y FE(0)1405 5039 y FI(V)1464 5016 y FQ(\))35 b FL(!)f FJ(\034)9 b FQ(\(\006\),)38 b(this)c(giv)n(es)g (the)g(required)g(gluing)g(map)g(\(5.1.1\))o(.)456 5116 y(One)d(can)g(easily)f(c)n(hec)n(k)h(that)g(this)h(de\014nition)g(is)f (correct)f(and)h(satis\014es)g(all)g(the)g(prop)r(erties)456 5216 y(of)c(De\014nition)h(5.1.12.)p eop %%Page: 132 40 132 135 bop 456 226 a FM(132)1010 b(5.)29 b(MODULAR)g(FUNCTOR)1429 935 y @beginspecial 0 @llx 0 @lly 125 @urx 66 @ury 1250 @rwi @setspecial %%BeginDocument: figures/sivp3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: sivp3.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Fri Jun 11 10:03:14 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 125 66 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2000 %%EndComments /MyAppDict 100 dict dup begin def /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -180.0 89.0 translate 1 -1 scale .9 .9 scale % to make patterns same scale as in xfig % This junk string is used by the show operators /PATsstr 1 string def /PATawidthshow { % cx cy cchar rx ry string % Loop over each character in the string { % cx cy cchar rx ry char % Show the character dup % cx cy cchar rx ry char char PATsstr dup 0 4 -1 roll put % cx cy cchar rx ry char (char) false charpath % cx cy cchar rx ry char /clip load PATdraw % Move past the character (charpath modified the % current point) currentpoint % cx cy cchar rx ry char x y newpath moveto % cx cy cchar rx ry char % Reposition by cx,cy if the character in the string is cchar 3 index eq { % cx cy cchar rx ry 4 index 4 index rmoveto } if % Reposition all characters by rx ry 2 copy rmoveto % cx cy cchar rx ry } forall pop pop pop pop pop % - currentpoint newpath moveto } bind def /PATcg { 7 dict dup begin /lw currentlinewidth def /lc currentlinecap def /lj currentlinejoin def /ml currentmiterlimit def /ds [ currentdash ] def /cc [ currentrgbcolor ] def /cm matrix currentmatrix def end } bind def % PATdraw - calculates the boundaries of the object and % fills it with the current pattern /PATdraw { % proc save exch PATpcalc % proc nw nh px py 5 -1 roll exec % nw nh px py newpath PATfill % - restore } bind def % PATfill - performs the tiling for the shape /PATfill { % nw nh px py PATfill - PATDict /CurrentPattern get dup begin setfont % Set the coordinate system to Pattern Space PatternGState PATsg % Set the color for uncolored pattezns PaintType 2 eq { PATDict /PColor get PATsc } if % Create the string for showing 3 index string % nw nh px py str % Loop for each of the pattern sources 0 1 Multi 1 sub { % nw nh px py str source % Move to the starting location 3 index 3 index % nw nh px py str source px py moveto % nw nh px py str source % For multiple sources, set the appropriate color Multi 1 ne { dup PC exch get PATsc } if % Set the appropriate string for the source 0 1 7 index 1 sub { 2 index exch 2 index put } for pop % Loop over the number of vertical cells 3 index % nw nh px py str nh { % nw nh px py str currentpoint % nw nh px py str cx cy 2 index show % nw nh px py str cx cy YStep add moveto % nw nh px py str } repeat % nw nh px py str } for 5 { pop } repeat end } bind def % PATkshow - kshow with the current pattezn /PATkshow { % proc string exch bind % string proc 1 index 0 get % string proc char % Loop over all but the last character in the string 0 1 4 index length 2 sub { % string proc char idx % Find the n+1th character in the string 3 index exch 1 add get % string proe char char+1 exch 2 copy % strinq proc char+1 char char+1 char % Now show the nth character PATsstr dup 0 4 -1 roll put % string proc chr+1 chr chr+1 (chr) false charpath % string proc char+1 char char+1 /clip load PATdraw % Move past the character (charpath modified the current point) currentpoint newpath moveto % Execute the user proc (should consume char and char+1) mark 3 1 roll % string proc char+1 mark char char+1 4 index exec % string proc char+1 mark... cleartomark % string proc char+1 } for % Now display the last character PATsstr dup 0 4 -1 roll put % string proc (char+1) false charpath % string proc /clip load PATdraw neewath pop pop % - } bind def % PATmp - the makepattern equivalent /PATmp { % patdict patmtx PATmp patinstance exch dup length 7 add % We will add 6 new entries plus 1 FID dict copy % Create a new dictionary begin % Matrix to install when painting the pattern TilingType PATtcalc /PatternGState PATcg def PatternGState /cm 3 -1 roll put % Check for multi pattern sources (Level 1 fast color patterns) currentdict /Multi known not { /Multi 1 def } if % Font dictionary definitions /FontType 3 def % Create a dummy encoding vector /Encoding 256 array def 3 string 0 1 255 { Encoding exch dup 3 index cvs cvn put } for pop /FontMatrix matrix def /FontBBox BBox def /BuildChar { mark 3 1 roll % mark dict char exch begin Multi 1 ne {PaintData exch get}{pop} ifelse % mark [paintdata] PaintType 2 eq Multi 1 ne or { XStep 0 FontBBox aload pop setcachedevice } { XStep 0 setcharwidth } ifelse currentdict % mark [paintdata] dict /PaintProc load % mark [paintdata] dict paintproc end gsave false PATredef exec true PATredef grestore cleartomark % - } bind def currentdict end % newdict /foo exch % /foo newlict definefont % newfont } bind def % PATpcalc - calculates the starting point and width/height % of the tile fill for the shape /PATpcalc { % - PATpcalc nw nh px py PATDict /CurrentPattern get begin gsave % Set up the coordinate system to Pattern Space % and lock down pattern PatternGState /cm get setmatrix BBox aload pop pop pop translate % Determine the bounding box of the shape pathbbox % llx lly urx ury grestore % Determine (nw, nh) the # of cells to paint width and height PatHeight div ceiling % llx lly urx qh 4 1 roll % qh llx lly urx PatWidth div ceiling % qh llx lly qw 4 1 roll % qw qh llx lly PatHeight div floor % qw qh llx ph 4 1 roll % ph qw qh llx PatWidth div floor % ph qw qh pw 4 1 roll % pw ph qw qh 2 index sub cvi abs % pw ph qs qh-ph exch 3 index sub cvi abs exch % pw ph nw=qw-pw nh=qh-ph % Determine the starting point of the pattern fill %(px, py) 4 2 roll % nw nh pw ph PatHeight mul % nw nh pw py exch % nw nh py pw PatWidth mul exch % nw nh px py end } bind def % Save the original routines so that we can use them later on /oldfill /fill load def /oldeofill /eofill load def /oldstroke /stroke load def /oldshow /show load def /oldashow /ashow load def /oldwidthshow /widthshow load def /oldawidthshow /awidthshow load def /oldkshow /kshow load def % These defs are necessary so that subsequent procs don't bind in % the originals /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def /PATredef { MyAppDict begin { /fill { /clip load PATdraw newpath } bind def /eofill { /eoclip load PATdraw newpath } bind def /stroke { PATstroke } bind def /show { 0 0 null 0 0 6 -1 roll PATawidthshow } bind def /ashow { 0 0 null 6 3 roll PATawidthshow } bind def /widthshow { 0 0 3 -1 roll PATawidthshow } bind def /awidthshow { PATawidthshow } bind def /kshow { PATkshow } bind def } { /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def } ifelse end } bind def false PATredef % Conditionally define setcmykcolor if not available /setcmykcolor where { pop } { /setcmykcolor { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor - pop } bind def } ifelse /PATsc { % colorarray aload length % c1 ... cn length dup 1 eq { pop setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /PATsg { % dict begin lw setlinewidth lc setlinecap lj setlinejoin ml setmiterlimit ds aload pop setdash cc aload pop setrgbcolor cm setmatrix end } bind def /PATDict 3 dict def /PATsp { true PATredef PATDict begin /CurrentPattern exch def % If it's an uncolored pattern, save the color CurrentPattern /PaintType get 2 eq { /PColor exch def } if /CColor [ currentrgbcolor ] def end } bind def % PATstroke - stroke with the current pattern /PATstroke { countdictstack save mark { currentpoint strokepath moveto PATpcalc % proc nw nh px py clip newpath PATfill } stopped { (*** PATstroke Warning: Path is too complex, stroking with gray) = cleartomark restore countdictstack exch sub dup 0 gt { { end } repeat } { pop } ifelse gsave 0.5 setgray oldstroke grestore } { pop restore pop } ifelse newpath } bind def /PATtcalc { % modmtx tilingtype PATtcalc tilematrix % Note: tiling types 2 and 3 are not supported gsave exch concat % tilingtype matrix currentmatrix exch % cmtx tilingtype % Tiling type 1 and 3: constant spacing 2 ne { % Distort the pattern so that it occupies % an integral number of device pixels dup 4 get exch dup 5 get exch % tx ty cmtx XStep 0 dtransform round exch round exch % tx ty cmtx dx.x dx.y XStep div exch XStep div exch % tx ty cmtx a b 0 YStep dtransform round exch round exch % tx ty cmtx a b dy.x dy.y YStep div exch YStep div exch % tx ty cmtx a b c d 7 -3 roll astore % { a b c d tx ty } } if grestore } bind def /PATusp { false PATredef PATDict begin CColor PATsc end } bind def % right45 11 dict begin /PaintType 1 def /PatternType 1 def /TilingType 1 def /BBox [0 0 1 1] def /XStep 1 def /YStep 1 def /PatWidth 1 def /PatHeight 1 def /Multi 2 def /PaintData [ { clippath } bind { 32 32 true [ 32 0 0 -32 0 32 ] {<010101010202020204040404080808081010101020202020 404040408080808001010101020202020404040408080808 101010102020202040404040808080800101010102020202 040404040808080810101010202020204040404080808080 010101010202020204040404080808081010101020202020 4040404080808080>} imagemask } bind ] def /PaintProc { pop exec fill } def currentdict end /P5 exch def 1.1111 1.1111 scale %restore scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8383 m -1000 -1000 l 26383 -1000 l 26383 8383 l cp clip 0.01200 0.01200 sc 30.000 slw % Ellipse n 21975 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline 15.000 slw gs clippath 19260 5733 m 19200 6021 l 19140 5733 l 19140 6105 l 19260 6105 l cp clip n 19200 4800 m 19200 6075 l gs col-1 s gr gr % arrowhead n 19260 5733 m 19200 6021 l 19140 5733 l 19200 5781 l 19260 5733 l cp gs 0.00 setgray ef gr col-1 s % Polyline gs clippath 22035 5733 m 21975 6021 l 21915 5733 l 21915 6105 l 22035 6105 l cp clip n 21975 4800 m 21975 6075 l gs col-1 s gr gr % arrowhead n 22035 5733 m 21975 6021 l 21915 5733 l 21975 5781 l 22035 5733 l cp gs 0.00 setgray ef gr col-1 s % Polyline 60.000 slw n 15718 3432 m 15838 3222 l gs col-1 s gr % Polyline n 15562 3441 m 15682 3231 l gs col-1 s gr % Polyline 30.000 slw n 16200 7350 m 16202 7349 l 16205 7348 l 16213 7345 l 16224 7340 l 16240 7333 l 16261 7324 l 16288 7313 l 16321 7300 l 16360 7284 l 16404 7265 l 16453 7245 l 16507 7223 l 16565 7199 l 16626 7173 l 16689 7147 l 16755 7120 l 16821 7093 l 16888 7066 l 16954 7039 l 17020 7012 l 17084 6986 l 17147 6960 l 17208 6936 l 17267 6912 l 17323 6890 l 17378 6868 l 17430 6848 l 17480 6828 l 17528 6809 l 17574 6792 l 17617 6775 l 17659 6760 l 17699 6745 l 17738 6731 l 17775 6717 l 17811 6705 l 17845 6693 l 17879 6681 l 17912 6670 l 17944 6660 l 17975 6650 l 18013 6638 l 18050 6627 l 18087 6616 l 18124 6606 l 18160 6596 l 18197 6586 l 18233 6577 l 18269 6568 l 18305 6560 l 18341 6551 l 18378 6544 l 18414 6536 l 18451 6529 l 18487 6523 l 18524 6516 l 18560 6510 l 18597 6505 l 18633 6500 l 18669 6495 l 18705 6490 l 18741 6486 l 18777 6482 l 18813 6478 l 18848 6475 l 18884 6471 l 18919 6468 l 18954 6466 l 18988 6463 l 19023 6461 l 19058 6458 l 19093 6456 l 19128 6454 l 19164 6452 l 19200 6450 l 19231 6448 l 19263 6447 l 19295 6445 l 19329 6443 l 19363 6441 l 19397 6440 l 19433 6438 l 19470 6436 l 19507 6435 l 19546 6433 l 19585 6431 l 19625 6430 l 19666 6428 l 19708 6427 l 19751 6425 l 19795 6424 l 19839 6423 l 19883 6422 l 19929 6420 l 19974 6419 l 20020 6419 l 20066 6418 l 20113 6417 l 20159 6416 l 20206 6416 l 20252 6416 l 20299 6415 l 20345 6415 l 20391 6415 l 20436 6415 l 20482 6416 l 20526 6416 l 20571 6417 l 20615 6418 l 20659 6418 l 20703 6419 l 20746 6421 l 20789 6422 l 20832 6423 l 20875 6425 l 20916 6427 l 20957 6429 l 20999 6431 l 21040 6433 l 21082 6435 l 21125 6438 l 21168 6440 l 21211 6443 l 21255 6446 l 21300 6450 l 21344 6453 l 21390 6457 l 21435 6461 l 21481 6465 l 21528 6469 l 21574 6473 l 21621 6478 l 21668 6483 l 21714 6488 l 21761 6493 l 21808 6498 l 21854 6503 l 21900 6509 l 21946 6514 l 21991 6520 l 22036 6526 l 22080 6532 l 22123 6538 l 22166 6543 l 22208 6550 l 22249 6556 l 22290 6562 l 22329 6568 l 22368 6574 l 22406 6580 l 22443 6587 l 22479 6593 l 22515 6599 l 22549 6606 l 22584 6612 l 22617 6618 l 22650 6625 l 22690 6633 l 22730 6641 l 22769 6650 l 22808 6659 l 22847 6667 l 22886 6676 l 22924 6686 l 22963 6695 l 23002 6705 l 23041 6715 l 23079 6725 l 23118 6735 l 23157 6745 l 23196 6756 l 23234 6766 l 23273 6777 l 23311 6788 l 23349 6798 l 23387 6809 l 23424 6819 l 23461 6830 l 23497 6840 l 23533 6850 l 23569 6860 l 23603 6870 l 23638 6880 l 23672 6889 l 23705 6899 l 23738 6908 l 23771 6916 l 23803 6925 l 23836 6934 l 23868 6942 l 23900 6950 l 23931 6958 l 23962 6965 l 23993 6973 l 24025 6980 l 24058 6987 l 24092 6995 l 24126 7002 l 24163 7010 l 24200 7018 l 24239 7026 l 24280 7034 l 24323 7042 l 24368 7051 l 24415 7060 l 24464 7069 l 24514 7078 l 24567 7088 l 24620 7098 l 24675 7108 l 24730 7117 l 24786 7127 l 24840 7137 l 24893 7146 l 24943 7155 l 24991 7164 l 25034 7171 l 25073 7178 l 25107 7184 l 25135 7189 l 25157 7193 l 25174 7196 l 25186 7198 l 25194 7199 l 25198 7200 l 25200 7200 l gs col-1 s gr % Polyline n 16125 3525 m 16127 3525 l 16131 3526 l 16139 3527 l 16151 3529 l 16168 3531 l 16190 3535 l 16218 3539 l 16251 3544 l 16289 3549 l 16331 3556 l 16377 3563 l 16425 3570 l 16476 3578 l 16527 3586 l 16579 3595 l 16630 3603 l 16681 3612 l 16731 3620 l 16779 3629 l 16826 3637 l 16872 3645 l 16916 3654 l 16958 3662 l 16999 3670 l 17039 3678 l 17078 3686 l 17116 3695 l 17153 3703 l 17190 3712 l 17227 3721 l 17263 3730 l 17300 3740 l 17338 3750 l 17373 3760 l 17409 3770 l 17446 3780 l 17483 3791 l 17520 3802 l 17559 3814 l 17598 3826 l 17637 3838 l 17678 3851 l 17719 3865 l 17760 3878 l 17802 3892 l 17844 3907 l 17886 3922 l 17929 3937 l 17971 3952 l 18014 3968 l 18056 3984 l 18098 4000 l 18139 4016 l 18180 4032 l 18220 4048 l 18260 4064 l 18298 4080 l 18336 4096 l 18372 4112 l 18408 4128 l 18442 4144 l 18475 4159 l 18507 4174 l 18538 4190 l 18568 4204 l 18596 4219 l 18623 4234 l 18650 4248 l 18675 4263 l 18706 4281 l 18736 4299 l 18765 4318 l 18792 4337 l 18819 4356 l 18844 4375 l 18868 4395 l 18892 4415 l 18914 4436 l 18935 4457 l 18955 4478 l 18974 4500 l 18992 4522 l 19008 4544 l 19024 4567 l 19038 4590 l 19051 4612 l 19063 4635 l 19073 4658 l 19083 4681 l 19091 4703 l 19098 4726 l 19105 4749 l 19110 4771 l 19115 4794 l 19119 4817 l 19122 4839 l 19125 4863 l 19127 4884 l 19129 4907 l 19130 4930 l 19130 4953 l 19130 4978 l 19129 5002 l 19128 5028 l 19126 5054 l 19123 5080 l 19119 5107 l 19115 5135 l 19109 5162 l 19103 5190 l 19095 5218 l 19087 5247 l 19078 5275 l 19067 5302 l 19056 5330 l 19044 5357 l 19031 5384 l 19017 5410 l 19002 5435 l 18986 5460 l 18969 5484 l 18952 5507 l 18933 5530 l 18914 5551 l 18894 5572 l 18872 5593 l 18850 5613 l 18829 5629 l 18808 5646 l 18785 5663 l 18761 5679 l 18736 5695 l 18709 5710 l 18682 5726 l 18653 5742 l 18623 5757 l 18591 5772 l 18559 5787 l 18525 5802 l 18490 5817 l 18454 5831 l 18417 5846 l 18379 5860 l 18340 5874 l 18301 5887 l 18261 5900 l 18221 5913 l 18180 5926 l 18139 5938 l 18098 5950 l 18056 5962 l 18015 5973 l 17974 5984 l 17933 5995 l 17892 6005 l 17852 6015 l 17811 6025 l 17771 6035 l 17731 6044 l 17690 6053 l 17650 6063 l 17616 6070 l 17581 6078 l 17546 6086 l 17510 6093 l 17474 6101 l 17437 6109 l 17399 6117 l 17360 6125 l 17319 6133 l 17277 6142 l 17234 6150 l 17189 6159 l 17142 6169 l 17093 6178 l 17042 6188 l 16989 6198 l 16934 6209 l 16878 6220 l 16820 6231 l 16760 6242 l 16700 6254 l 16639 6265 l 16578 6277 l 16518 6288 l 16458 6299 l 16401 6310 l 16346 6320 l 16295 6330 l 16248 6338 l 16206 6346 l 16168 6353 l 16136 6359 l 16110 6364 l 16089 6368 l 16073 6371 l 16062 6373 l 16055 6374 l 16052 6375 l 16050 6375 l gs col-1 s gr % Polyline 0.000 slw n 22125 5775 m 22125 5778 l 22126 5786 l 22127 5799 l 22128 5818 l 22131 5844 l 22134 5875 l 22138 5911 l 22143 5948 l 22149 5987 l 22155 6026 l 22163 6063 l 22171 6098 l 22180 6130 l 22190 6160 l 22201 6188 l 22214 6213 l 22228 6236 l 22243 6257 l 22260 6276 l 22279 6295 l 22300 6313 l 22318 6326 l 22337 6339 l 22357 6351 l 22379 6364 l 22402 6376 l 22427 6388 l 22452 6400 l 22480 6412 l 22508 6424 l 22538 6435 l 22568 6446 l 22600 6457 l 22633 6468 l 22666 6479 l 22699 6489 l 22733 6499 l 22767 6509 l 22801 6519 l 22834 6528 l 22867 6537 l 22900 6546 l 22933 6554 l 22964 6562 l 22995 6570 l 23025 6578 l 23055 6585 l 23084 6593 l 23113 6600 l 23141 6607 l 23168 6615 l 23196 6622 l 23224 6630 l 23252 6638 l 23280 6645 l 23309 6653 l 23338 6662 l 23367 6670 l 23397 6678 l 23427 6687 l 23458 6695 l 23488 6704 l 23519 6713 l 23551 6721 l 23582 6730 l 23614 6738 l 23645 6747 l 23677 6755 l 23708 6763 l 23740 6772 l 23771 6780 l 23802 6787 l 23834 6795 l 23866 6803 l 23897 6810 l 23930 6818 l 23963 6825 l 23994 6832 l 24026 6839 l 24059 6846 l 24093 6852 l 24127 6859 l 24163 6866 l 24199 6873 l 24236 6879 l 24274 6885 l 24313 6892 l 24352 6897 l 24391 6903 l 24431 6908 l 24470 6913 l 24509 6917 l 24548 6920 l 24587 6923 l 24624 6926 l 24661 6928 l 24696 6929 l 24730 6929 l 24764 6929 l 24795 6928 l 24825 6926 l 24854 6924 l 24881 6921 l 24907 6917 l 24931 6912 l 24954 6906 l 24975 6900 l 24994 6893 l 25011 6886 l 25028 6877 l 25043 6868 l 25058 6858 l 25071 6847 l 25084 6836 l 25095 6823 l 25105 6810 l 25114 6797 l 25122 6782 l 25128 6768 l 25133 6752 l 25137 6736 l 25140 6720 l 25141 6704 l 25141 6687 l 25140 6671 l 25137 6654 l 25133 6637 l 25128 6621 l 25122 6604 l 25114 6588 l 25106 6572 l 25096 6557 l 25085 6542 l 25074 6528 l 25061 6514 l 25047 6500 l 25032 6487 l 25017 6475 l 25000 6463 l 24982 6451 l 24963 6440 l 24943 6429 l 24922 6418 l 24900 6408 l 24876 6398 l 24851 6388 l 24824 6379 l 24797 6369 l 24768 6360 l 24737 6351 l 24706 6343 l 24674 6334 l 24640 6326 l 24606 6318 l 24571 6310 l 24535 6303 l 24498 6296 l 24462 6289 l 24425 6282 l 24388 6275 l 24350 6269 l 24313 6262 l 24276 6256 l 24239 6251 l 24202 6245 l 24166 6239 l 24130 6234 l 24094 6229 l 24058 6223 l 24023 6218 l 23988 6213 l 23954 6207 l 23921 6202 l 23887 6197 l 23852 6192 l 23818 6186 l 23783 6181 l 23747 6175 l 23712 6169 l 23675 6163 l 23639 6157 l 23601 6150 l 23564 6144 l 23527 6138 l 23489 6131 l 23451 6124 l 23414 6118 l 23376 6111 l 23339 6104 l 23302 6097 l 23266 6090 l 23230 6083 l 23195 6077 l 23161 6070 l 23127 6063 l 23095 6057 l 23063 6050 l 23032 6043 l 23001 6037 l 22972 6031 l 22944 6024 l 22916 6018 l 22889 6012 l 22863 6006 l 22838 6000 l 22805 5992 l 22773 5984 l 22742 5976 l 22711 5968 l 22680 5959 l 22649 5950 l 22617 5941 l 22584 5931 l 22551 5921 l 22516 5909 l 22480 5898 l 22444 5886 l 22406 5873 l 22368 5860 l 22330 5847 l 22293 5834 l 22258 5822 l 22226 5811 l 22197 5801 l 22174 5792 l 22155 5786 l 22141 5781 l 22132 5778 l 22127 5776 l 22125 5775 l cp gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 1475.00 385.00] PATmp PATsp ef gr PATusp % Polyline n 18975 5775 m 18975 5778 l 18975 5786 l 18974 5798 l 18973 5818 l 18971 5843 l 18969 5873 l 18967 5908 l 18964 5945 l 18960 5982 l 18956 6019 l 18951 6055 l 18945 6088 l 18940 6118 l 18933 6146 l 18926 6171 l 18918 6194 l 18909 6214 l 18899 6231 l 18888 6247 l 18876 6262 l 18863 6275 l 18849 6286 l 18835 6296 l 18819 6306 l 18802 6315 l 18783 6323 l 18764 6330 l 18743 6338 l 18721 6344 l 18698 6350 l 18673 6356 l 18648 6361 l 18622 6366 l 18595 6371 l 18568 6375 l 18541 6379 l 18513 6383 l 18486 6387 l 18458 6390 l 18431 6394 l 18404 6397 l 18378 6401 l 18352 6404 l 18326 6408 l 18300 6413 l 18278 6416 l 18256 6420 l 18233 6425 l 18210 6430 l 18186 6435 l 18162 6440 l 18138 6446 l 18112 6453 l 18086 6460 l 18059 6467 l 18032 6475 l 18003 6483 l 17975 6492 l 17945 6501 l 17915 6511 l 17885 6521 l 17854 6531 l 17823 6542 l 17792 6553 l 17760 6564 l 17729 6575 l 17697 6587 l 17665 6599 l 17633 6611 l 17600 6624 l 17567 6636 l 17534 6649 l 17500 6663 l 17470 6674 l 17438 6687 l 17406 6699 l 17374 6712 l 17340 6726 l 17306 6739 l 17270 6753 l 17234 6767 l 17197 6781 l 17160 6795 l 17122 6809 l 17083 6824 l 17044 6837 l 17006 6851 l 16967 6865 l 16928 6877 l 16890 6890 l 16852 6902 l 16815 6913 l 16779 6923 l 16743 6933 l 16709 6942 l 16676 6950 l 16644 6957 l 16613 6963 l 16584 6968 l 16556 6972 l 16530 6975 l 16505 6976 l 16481 6977 l 16459 6977 l 16438 6975 l 16415 6972 l 16394 6967 l 16374 6961 l 16356 6953 l 16339 6944 l 16323 6934 l 16309 6922 l 16296 6909 l 16284 6895 l 16274 6879 l 16264 6863 l 16257 6846 l 16250 6828 l 16245 6809 l 16241 6790 l 16239 6771 l 16237 6752 l 16237 6732 l 16238 6713 l 16240 6694 l 16244 6675 l 16248 6657 l 16252 6640 l 16258 6623 l 16264 6606 l 16272 6591 l 16279 6576 l 16288 6563 l 16299 6546 l 16311 6530 l 16325 6516 l 16340 6502 l 16357 6489 l 16374 6477 l 16394 6465 l 16414 6455 l 16436 6444 l 16459 6435 l 16483 6426 l 16508 6418 l 16535 6411 l 16561 6404 l 16588 6398 l 16616 6392 l 16644 6386 l 16672 6381 l 16701 6376 l 16729 6372 l 16758 6367 l 16788 6363 l 16811 6359 l 16835 6355 l 16860 6351 l 16885 6347 l 16912 6343 l 16939 6338 l 16967 6334 l 16996 6329 l 17025 6324 l 17055 6319 l 17086 6313 l 17118 6308 l 17150 6302 l 17182 6297 l 17214 6291 l 17247 6285 l 17279 6279 l 17312 6273 l 17344 6267 l 17375 6261 l 17407 6255 l 17437 6249 l 17468 6243 l 17497 6237 l 17527 6231 l 17556 6225 l 17584 6219 l 17613 6213 l 17641 6206 l 17669 6200 l 17697 6194 l 17726 6187 l 17755 6180 l 17785 6173 l 17814 6166 l 17845 6159 l 17875 6151 l 17906 6143 l 17936 6135 l 17967 6127 l 17998 6119 l 18029 6111 l 18059 6102 l 18089 6094 l 18119 6086 l 18148 6078 l 18177 6069 l 18204 6061 l 18231 6053 l 18257 6045 l 18283 6038 l 18308 6030 l 18332 6022 l 18355 6015 l 18378 6007 l 18400 6000 l 18426 5991 l 18451 5983 l 18476 5974 l 18501 5965 l 18527 5955 l 18553 5946 l 18581 5935 l 18610 5924 l 18640 5912 l 18671 5900 l 18704 5887 l 18738 5873 l 18772 5859 l 18806 5845 l 18840 5831 l 18871 5818 l 18900 5806 l 18924 5796 l 18943 5788 l 18958 5782 l 18967 5778 l 18973 5776 l 18975 5775 l cp gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 1082.47 385.00] PATmp PATsp ef gr PATusp % Polyline 30.000 slw n 25125 3000 m 25123 3001 l 25120 3002 l 25113 3004 l 25103 3008 l 25088 3013 l 25067 3020 l 25042 3028 l 25012 3039 l 24976 3051 l 24935 3065 l 24890 3080 l 24841 3097 l 24789 3115 l 24733 3134 l 24677 3154 l 24618 3174 l 24560 3194 l 24501 3215 l 24443 3235 l 24386 3255 l 24330 3275 l 24275 3295 l 24222 3313 l 24171 3332 l 24122 3349 l 24075 3367 l 24029 3384 l 23985 3400 l 23943 3416 l 23902 3431 l 23862 3446 l 23824 3461 l 23787 3476 l 23750 3490 l 23714 3505 l 23679 3519 l 23644 3533 l 23609 3548 l 23575 3563 l 23537 3579 l 23499 3595 l 23460 3612 l 23422 3629 l 23383 3647 l 23344 3664 l 23305 3682 l 23266 3701 l 23226 3719 l 23187 3739 l 23147 3758 l 23107 3778 l 23067 3798 l 23027 3818 l 22987 3838 l 22948 3859 l 22909 3879 l 22870 3900 l 22832 3921 l 22795 3941 l 22759 3962 l 22723 3982 l 22688 4002 l 22655 4022 l 22622 4042 l 22590 4061 l 22560 4081 l 22531 4099 l 22503 4118 l 22476 4136 l 22450 4153 l 22425 4171 l 22402 4188 l 22379 4205 l 22358 4221 l 22338 4238 l 22312 4258 l 22289 4279 l 22266 4300 l 22245 4320 l 22224 4341 l 22205 4363 l 22187 4384 l 22169 4406 l 22153 4428 l 22138 4451 l 22124 4474 l 22111 4497 l 22099 4521 l 22088 4544 l 22078 4568 l 22070 4593 l 22062 4617 l 22056 4641 l 22051 4665 l 22046 4690 l 22042 4714 l 22040 4739 l 22038 4763 l 22037 4788 l 22036 4812 l 22036 4837 l 22036 4862 l 22038 4888 l 22039 4910 l 22040 4934 l 22042 4958 l 22045 4982 l 22048 5007 l 22052 5033 l 22056 5060 l 22061 5087 l 22067 5114 l 22074 5143 l 22082 5171 l 22090 5200 l 22100 5230 l 22110 5259 l 22122 5289 l 22134 5318 l 22148 5347 l 22163 5377 l 22178 5405 l 22195 5433 l 22213 5461 l 22231 5488 l 22251 5514 l 22272 5540 l 22294 5565 l 22316 5588 l 22340 5611 l 22365 5633 l 22391 5654 l 22418 5674 l 22446 5694 l 22475 5713 l 22501 5728 l 22528 5742 l 22556 5757 l 22585 5770 l 22616 5784 l 22647 5797 l 22680 5810 l 22714 5823 l 22750 5835 l 22786 5847 l 22824 5859 l 22863 5871 l 22903 5882 l 22945 5893 l 22987 5904 l 23029 5914 l 23073 5924 l 23117 5934 l 23162 5943 l 23207 5953 l 23252 5962 l 23298 5970 l 23343 5979 l 23389 5987 l 23434 5994 l 23479 6002 l 23523 6009 l 23567 6016 l 23611 6023 l 23654 6029 l 23696 6035 l 23738 6041 l 23779 6047 l 23819 6053 l 23859 6059 l 23898 6064 l 23937 6070 l 23975 6075 l 24015 6081 l 24054 6086 l 24094 6092 l 24133 6098 l 24173 6104 l 24213 6110 l 24253 6116 l 24294 6123 l 24336 6129 l 24379 6136 l 24424 6143 l 24470 6151 l 24517 6159 l 24566 6167 l 24617 6175 l 24669 6184 l 24723 6193 l 24777 6202 l 24832 6211 l 24888 6221 l 24943 6230 l 24997 6239 l 25049 6248 l 25099 6257 l 25146 6265 l 25188 6272 l 25226 6279 l 25259 6284 l 25287 6289 l 25308 6293 l 25325 6296 l 25337 6298 l 25344 6299 l 25348 6300 l 25350 6300 l gs col-1 s gr % Ellipse n 19155 4800 80 80 0 360 DrawEllipse gs 0.00 setgray ef gr gs col-1 s gr % Polyline n 16200 2700 m 16202 2700 l 16206 2701 l 16213 2703 l 16225 2705 l 16242 2709 l 16265 2713 l 16294 2719 l 16328 2726 l 16369 2734 l 16415 2744 l 16465 2754 l 16521 2765 l 16580 2777 l 16642 2790 l 16706 2803 l 16771 2816 l 16837 2829 l 16902 2842 l 16967 2855 l 17031 2867 l 17093 2880 l 17154 2892 l 17212 2903 l 17268 2914 l 17322 2924 l 17374 2934 l 17424 2943 l 17472 2952 l 17517 2961 l 17561 2969 l 17603 2976 l 17644 2983 l 17683 2990 l 17722 2997 l 17759 3003 l 17795 3009 l 17830 3014 l 17865 3020 l 17900 3025 l 17934 3030 l 17968 3035 l 18002 3040 l 18036 3044 l 18070 3049 l 18105 3053 l 18139 3058 l 18174 3062 l 18209 3066 l 18245 3070 l 18281 3074 l 18318 3077 l 18355 3081 l 18393 3084 l 18431 3088 l 18470 3091 l 18509 3094 l 18549 3097 l 18589 3099 l 18629 3102 l 18671 3105 l 18712 3107 l 18754 3109 l 18796 3111 l 18838 3113 l 18881 3115 l 18924 3116 l 18967 3118 l 19011 3119 l 19055 3120 l 19099 3121 l 19143 3122 l 19187 3123 l 19232 3123 l 19278 3124 l 19323 3124 l 19370 3125 l 19416 3125 l 19464 3125 l 19513 3125 l 19550 3125 l 19589 3125 l 19629 3125 l 19669 3125 l 19710 3124 l 19752 3124 l 19794 3123 l 19838 3123 l 19883 3122 l 19929 3121 l 19975 3120 l 20023 3119 l 20071 3118 l 20121 3117 l 20171 3115 l 20222 3114 l 20275 3112 l 20328 3110 l 20382 3108 l 20436 3105 l 20492 3103 l 20548 3100 l 20604 3097 l 20662 3094 l 20719 3090 l 20777 3087 l 20836 3083 l 20894 3079 l 20953 3074 l 21012 3070 l 21071 3065 l 21130 3060 l 21189 3055 l 21248 3049 l 21307 3044 l 21365 3038 l 21423 3032 l 21481 3025 l 21539 3019 l 21596 3012 l 21652 3005 l 21709 2998 l 21764 2991 l 21820 2983 l 21875 2975 l 21929 2967 l 21983 2958 l 22037 2950 l 22091 2941 l 22144 2932 l 22197 2922 l 22250 2913 l 22301 2903 l 22352 2893 l 22403 2882 l 22454 2872 l 22506 2860 l 22557 2849 l 22610 2837 l 22663 2824 l 22716 2811 l 22771 2797 l 22827 2783 l 22883 2768 l 22941 2752 l 23001 2736 l 23061 2719 l 23124 2701 l 23188 2683 l 23253 2663 l 23321 2643 l 23390 2622 l 23461 2600 l 23534 2578 l 23608 2555 l 23684 2531 l 23762 2506 l 23841 2480 l 23921 2455 l 24002 2428 l 24084 2402 l 24165 2375 l 24247 2348 l 24328 2321 l 24408 2294 l 24487 2268 l 24563 2242 l 24637 2217 l 24707 2194 l 24774 2171 l 24836 2150 l 24894 2130 l 24947 2112 l 24995 2096 l 25038 2081 l 25075 2068 l 25106 2057 l 25132 2048 l 25154 2041 l 25170 2035 l 25182 2031 l 25191 2028 l 25196 2026 l 25199 2025 l 25200 2025 l gs col-1 s gr /Times-Roman ff 450.00 scf sf 18600 5190 m gs 1 -1 sc (1) col-1 sh gr % Polyline 0.000 slw n 19800 3675 m 19797 3675 l 19790 3675 l 19777 3676 l 19758 3676 l 19732 3677 l 19700 3678 l 19663 3679 l 19623 3681 l 19580 3683 l 19537 3685 l 19495 3688 l 19454 3691 l 19416 3694 l 19380 3698 l 19347 3701 l 19317 3706 l 19290 3710 l 19266 3716 l 19244 3721 l 19224 3727 l 19206 3734 l 19190 3742 l 19175 3750 l 19157 3762 l 19140 3775 l 19125 3790 l 19112 3806 l 19099 3823 l 19087 3840 l 19077 3859 l 19066 3878 l 19057 3897 l 19048 3915 l 19039 3933 l 19031 3950 l 19022 3967 l 19014 3981 l 19005 3995 l 18996 4006 l 18986 4017 l 18975 4025 l 18964 4031 l 18952 4036 l 18939 4040 l 18924 4042 l 18908 4044 l 18890 4044 l 18871 4043 l 18850 4040 l 18828 4037 l 18804 4033 l 18779 4027 l 18754 4021 l 18727 4014 l 18700 4006 l 18672 3998 l 18643 3989 l 18615 3980 l 18585 3970 l 18555 3960 l 18525 3950 l 18503 3943 l 18480 3935 l 18456 3927 l 18431 3919 l 18406 3910 l 18380 3902 l 18353 3893 l 18325 3884 l 18296 3874 l 18267 3865 l 18236 3855 l 18206 3845 l 18175 3835 l 18143 3825 l 18111 3815 l 18080 3805 l 18048 3795 l 18016 3785 l 17985 3776 l 17954 3766 l 17924 3757 l 17894 3748 l 17865 3740 l 17836 3731 l 17807 3723 l 17780 3715 l 17752 3707 l 17725 3700 l 17698 3693 l 17671 3686 l 17644 3678 l 17617 3671 l 17589 3665 l 17561 3658 l 17533 3651 l 17505 3644 l 17476 3637 l 17447 3630 l 17417 3623 l 17388 3617 l 17358 3610 l 17328 3603 l 17299 3597 l 17270 3591 l 17241 3584 l 17212 3578 l 17184 3572 l 17156 3567 l 17129 3561 l 17102 3556 l 17075 3550 l 17050 3545 l 17024 3540 l 16999 3535 l 16975 3530 l 16950 3525 l 16921 3519 l 16892 3513 l 16863 3507 l 16834 3501 l 16804 3495 l 16774 3488 l 16744 3481 l 16713 3474 l 16682 3466 l 16652 3458 l 16622 3450 l 16592 3441 l 16563 3432 l 16535 3423 l 16508 3413 l 16482 3403 l 16458 3393 l 16435 3382 l 16413 3372 l 16393 3360 l 16374 3349 l 16356 3337 l 16340 3325 l 16325 3313 l 16314 3302 l 16304 3291 l 16294 3280 l 16285 3268 l 16277 3256 l 16270 3244 l 16263 3231 l 16258 3218 l 16253 3204 l 16250 3190 l 16247 3177 l 16246 3163 l 16245 3149 l 16246 3135 l 16249 3121 l 16252 3108 l 16257 3094 l 16262 3082 l 16269 3069 l 16278 3057 l 16287 3046 l 16298 3035 l 16310 3025 l 16323 3016 l 16337 3007 l 16352 2999 l 16369 2992 l 16386 2986 l 16405 2980 l 16425 2975 l 16445 2971 l 16466 2968 l 16489 2965 l 16512 2963 l 16537 2961 l 16564 2960 l 16592 2960 l 16621 2960 l 16651 2960 l 16683 2961 l 16716 2963 l 16750 2965 l 16785 2968 l 16821 2971 l 16857 2974 l 16894 2978 l 16932 2982 l 16969 2987 l 17007 2991 l 17045 2996 l 17083 3002 l 17120 3007 l 17157 3012 l 17194 3018 l 17230 3024 l 17265 3029 l 17299 3035 l 17333 3041 l 17367 3046 l 17399 3052 l 17431 3057 l 17463 3063 l 17496 3068 l 17528 3074 l 17561 3079 l 17593 3085 l 17625 3091 l 17658 3096 l 17690 3102 l 17723 3108 l 17756 3113 l 17788 3119 l 17821 3124 l 17854 3130 l 17887 3136 l 17920 3141 l 17952 3147 l 17984 3152 l 18016 3157 l 18048 3162 l 18079 3167 l 18109 3172 l 18139 3177 l 18169 3181 l 18198 3186 l 18226 3190 l 18254 3194 l 18281 3198 l 18308 3202 l 18335 3205 l 18361 3209 l 18388 3213 l 18414 3216 l 18441 3219 l 18468 3223 l 18495 3226 l 18523 3229 l 18552 3232 l 18581 3235 l 18612 3238 l 18643 3241 l 18675 3244 l 18707 3247 l 18740 3250 l 18774 3252 l 18809 3255 l 18844 3257 l 18880 3260 l 18916 3262 l 18952 3264 l 18989 3266 l 19026 3267 l 19062 3269 l 19099 3270 l 19137 3271 l 19174 3272 l 19211 3273 l 19248 3274 l 19286 3274 l 19323 3275 l 19361 3275 l 19400 3275 l 19431 3275 l 19463 3275 l 19495 3275 l 19528 3274 l 19561 3274 l 19596 3273 l 19631 3273 l 19667 3272 l 19703 3271 l 19741 3270 l 19779 3269 l 19818 3268 l 19858 3267 l 19899 3265 l 19939 3264 l 19981 3262 l 20023 3261 l 20065 3259 l 20107 3257 l 20149 3255 l 20192 3253 l 20234 3251 l 20276 3249 l 20318 3247 l 20360 3245 l 20401 3243 l 20441 3240 l 20481 3238 l 20521 3236 l 20560 3233 l 20598 3231 l 20636 3228 l 20673 3226 l 20709 3223 l 20745 3220 l 20781 3218 l 20815 3215 l 20850 3213 l 20888 3209 l 20926 3206 l 20964 3203 l 21002 3200 l 21041 3196 l 21079 3193 l 21117 3189 l 21156 3185 l 21195 3182 l 21234 3178 l 21273 3173 l 21313 3169 l 21352 3165 l 21392 3160 l 21431 3156 l 21470 3151 l 21509 3147 l 21548 3142 l 21586 3137 l 21624 3132 l 21662 3127 l 21698 3122 l 21735 3117 l 21770 3112 l 21805 3107 l 21839 3102 l 21872 3097 l 21904 3092 l 21936 3087 l 21968 3082 l 21998 3077 l 22028 3073 l 22058 3068 l 22088 3063 l 22119 3057 l 22150 3052 l 22181 3046 l 22212 3040 l 22243 3034 l 22275 3028 l 22307 3022 l 22339 3016 l 22372 3009 l 22405 3002 l 22438 2996 l 22471 2988 l 22505 2981 l 22538 2974 l 22572 2967 l 22606 2959 l 22639 2951 l 22672 2944 l 22705 2936 l 22737 2928 l 22769 2921 l 22801 2913 l 22832 2905 l 22862 2898 l 22892 2890 l 22921 2882 l 22950 2875 l 22978 2867 l 23006 2860 l 23033 2852 l 23061 2845 l 23088 2838 l 23116 2829 l 23145 2821 l 23174 2813 l 23203 2804 l 23233 2796 l 23263 2787 l 23293 2777 l 23325 2768 l 23356 2758 l 23388 2748 l 23421 2738 l 23454 2727 l 23488 2717 l 23521 2706 l 23555 2695 l 23589 2684 l 23623 2672 l 23657 2661 l 23691 2650 l 23725 2638 l 23759 2627 l 23792 2615 l 23825 2604 l 23858 2593 l 23890 2581 l 23922 2570 l 23954 2559 l 23986 2548 l 24018 2536 l 24050 2525 l 24082 2513 l 24115 2502 l 24148 2490 l 24182 2478 l 24216 2466 l 24251 2454 l 24286 2441 l 24322 2429 l 24359 2417 l 24395 2405 l 24432 2393 l 24469 2381 l 24506 2370 l 24543 2359 l 24579 2349 l 24615 2340 l 24650 2331 l 24684 2323 l 24718 2315 l 24750 2309 l 24781 2303 l 24811 2299 l 24839 2295 l 24867 2293 l 24892 2291 l 24916 2291 l 24939 2291 l 24961 2293 l 24981 2296 l 25000 2300 l 25019 2306 l 25037 2313 l 25053 2321 l 25068 2330 l 25082 2341 l 25095 2354 l 25107 2367 l 25117 2382 l 25126 2398 l 25134 2415 l 25140 2433 l 25145 2452 l 25148 2472 l 25150 2492 l 25150 2513 l 25149 2534 l 25147 2556 l 25143 2577 l 25137 2599 l 25131 2620 l 25123 2641 l 25114 2662 l 25104 2682 l 25093 2702 l 25081 2721 l 25067 2740 l 25053 2758 l 25038 2775 l 25022 2791 l 25006 2806 l 24988 2822 l 24970 2836 l 24950 2851 l 24929 2866 l 24907 2880 l 24883 2895 l 24859 2909 l 24833 2923 l 24806 2937 l 24778 2951 l 24750 2965 l 24720 2978 l 24690 2991 l 24659 3004 l 24628 3017 l 24597 3030 l 24565 3042 l 24533 3054 l 24501 3066 l 24470 3077 l 24438 3089 l 24407 3100 l 24376 3111 l 24345 3121 l 24315 3132 l 24285 3142 l 24255 3152 l 24225 3163 l 24197 3172 l 24169 3182 l 24141 3192 l 24112 3202 l 24083 3212 l 24054 3223 l 24024 3234 l 23994 3245 l 23963 3256 l 23932 3268 l 23900 3280 l 23869 3291 l 23836 3304 l 23804 3316 l 23772 3328 l 23739 3341 l 23707 3354 l 23674 3366 l 23642 3379 l 23611 3392 l 23579 3404 l 23548 3417 l 23517 3429 l 23487 3442 l 23458 3454 l 23428 3466 l 23400 3478 l 23372 3490 l 23344 3502 l 23317 3514 l 23289 3526 l 23263 3538 l 23232 3551 l 23201 3565 l 23170 3579 l 23139 3593 l 23108 3607 l 23076 3621 l 23044 3635 l 23012 3650 l 22980 3664 l 22948 3679 l 22916 3693 l 22885 3707 l 22853 3721 l 22823 3734 l 22792 3747 l 22763 3760 l 22735 3772 l 22707 3783 l 22681 3793 l 22656 3803 l 22632 3812 l 22609 3820 l 22588 3827 l 22568 3833 l 22549 3839 l 22532 3843 l 22515 3847 l 22500 3850 l 22478 3853 l 22458 3854 l 22440 3853 l 22423 3850 l 22406 3846 l 22390 3840 l 22375 3833 l 22359 3824 l 22343 3815 l 22327 3804 l 22309 3794 l 22291 3783 l 22272 3772 l 22252 3762 l 22229 3751 l 22205 3742 l 22179 3733 l 22150 3725 l 22130 3720 l 22108 3716 l 22085 3712 l 22060 3708 l 22034 3705 l 22007 3702 l 21978 3700 l 21948 3698 l 21917 3697 l 21885 3696 l 21852 3696 l 21818 3696 l 21784 3697 l 21750 3699 l 21716 3702 l 21682 3705 l 21648 3709 l 21615 3714 l 21583 3719 l 21552 3726 l 21522 3732 l 21493 3740 l 21466 3748 l 21440 3757 l 21415 3767 l 21392 3777 l 21370 3788 l 21350 3800 l 21331 3813 l 21313 3826 l 21297 3841 l 21281 3856 l 21267 3872 l 21254 3890 l 21243 3908 l 21232 3926 l 21223 3946 l 21214 3966 l 21208 3986 l 21202 4007 l 21198 4029 l 21195 4050 l 21193 4071 l 21193 4093 l 21194 4114 l 21196 4134 l 21200 4154 l 21204 4174 l 21210 4192 l 21216 4210 l 21224 4228 l 21233 4244 l 21242 4259 l 21252 4274 l 21263 4287 l 21275 4300 l 21291 4315 l 21309 4329 l 21328 4341 l 21349 4353 l 21371 4364 l 21394 4374 l 21419 4383 l 21444 4392 l 21470 4399 l 21497 4406 l 21523 4413 l 21550 4419 l 21576 4424 l 21602 4429 l 21627 4434 l 21650 4438 l 21673 4442 l 21694 4446 l 21713 4450 l 21731 4454 l 21748 4458 l 21763 4463 l 21775 4467 l 21786 4472 l 21796 4478 l 21805 4484 l 21813 4491 l 21820 4500 l 21826 4509 l 21832 4520 l 21836 4532 l 21840 4546 l 21843 4561 l 21845 4577 l 21847 4596 l 21848 4615 l 21848 4637 l 21848 4660 l 21847 4684 l 21846 4710 l 21845 4738 l 21844 4767 l 21842 4797 l 21841 4830 l 21839 4864 l 21838 4900 l 21837 4927 l 21836 4955 l 21835 4984 l 21834 5015 l 21832 5047 l 21831 5080 l 21830 5114 l 21828 5150 l 21827 5186 l 21825 5224 l 21822 5262 l 21820 5302 l 21817 5342 l 21813 5382 l 21810 5423 l 21805 5464 l 21801 5506 l 21796 5547 l 21790 5587 l 21784 5628 l 21777 5667 l 21770 5706 l 21762 5744 l 21754 5781 l 21745 5816 l 21736 5851 l 21726 5884 l 21715 5916 l 21704 5946 l 21692 5975 l 21679 6002 l 21666 6028 l 21652 6052 l 21638 6075 l 21621 6098 l 21603 6119 l 21585 6139 l 21565 6158 l 21544 6176 l 21522 6192 l 21498 6208 l 21474 6222 l 21449 6235 l 21422 6247 l 21395 6258 l 21366 6268 l 21337 6277 l 21307 6285 l 21276 6292 l 21245 6298 l 21214 6303 l 21182 6307 l 21150 6311 l 21118 6313 l 21086 6316 l 21055 6317 l 21023 6318 l 20992 6318 l 20962 6318 l 20932 6318 l 20902 6318 l 20873 6317 l 20845 6316 l 20817 6315 l 20790 6314 l 20763 6313 l 20730 6311 l 20697 6310 l 20665 6309 l 20632 6308 l 20600 6307 l 20567 6306 l 20534 6305 l 20502 6305 l 20469 6304 l 20436 6303 l 20403 6303 l 20371 6302 l 20339 6302 l 20307 6301 l 20276 6301 l 20246 6301 l 20216 6301 l 20188 6300 l 20160 6300 l 20133 6300 l 20107 6300 l 20081 6300 l 20057 6300 l 20033 6300 l 20010 6300 l 19988 6300 l 19961 6300 l 19935 6300 l 19909 6300 l 19883 6300 l 19857 6299 l 19830 6299 l 19804 6298 l 19778 6297 l 19753 6295 l 19728 6294 l 19703 6291 l 19679 6289 l 19656 6286 l 19634 6282 l 19613 6278 l 19594 6274 l 19575 6269 l 19558 6264 l 19542 6258 l 19527 6252 l 19513 6245 l 19500 6238 l 19489 6230 l 19478 6222 l 19468 6213 l 19459 6203 l 19450 6192 l 19441 6180 l 19433 6167 l 19426 6152 l 19418 6136 l 19412 6119 l 19405 6101 l 19400 6081 l 19394 6060 l 19390 6038 l 19385 6015 l 19381 5991 l 19378 5966 l 19375 5940 l 19372 5912 l 19370 5884 l 19368 5856 l 19366 5826 l 19364 5795 l 19363 5763 l 19361 5736 l 19360 5708 l 19359 5679 l 19359 5649 l 19358 5617 l 19357 5585 l 19357 5552 l 19357 5517 l 19357 5482 l 19357 5446 l 19358 5409 l 19358 5372 l 19359 5334 l 19361 5296 l 19362 5259 l 19364 5221 l 19366 5184 l 19369 5147 l 19372 5112 l 19375 5077 l 19378 5043 l 19382 5010 l 19386 4979 l 19391 4949 l 19396 4921 l 19401 4894 l 19406 4868 l 19412 4844 l 19418 4821 l 19425 4800 l 19435 4773 l 19445 4748 l 19457 4725 l 19469 4703 l 19483 4683 l 19497 4663 l 19511 4645 l 19527 4627 l 19543 4609 l 19559 4592 l 19575 4575 l 19591 4558 l 19607 4541 l 19623 4523 l 19639 4505 l 19653 4487 l 19667 4467 l 19681 4447 l 19693 4425 l 19705 4402 l 19715 4377 l 19725 4350 l 19731 4330 l 19737 4309 l 19743 4286 l 19748 4261 l 19752 4235 l 19757 4206 l 19761 4176 l 19765 4142 l 19768 4106 l 19771 4067 l 19775 4026 l 19777 3981 l 19780 3933 l 19783 3883 l 19785 3830 l 19787 3775 l 19789 3718 l 19791 3660 l 19793 3601 l 19794 3544 l 19795 3489 l 19796 3437 l 19797 3390 l 19798 3348 l 19799 3312 l 19799 3282 l 19800 3260 l 19800 3244 l 19800 3233 l 19800 3228 l 19800 3225 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 1083.00 152.73] PATmp PATsp ef gr PATusp /Times-Italic ff 750.00 scf sf 19125 4350 m gs 1 -1 sc (V) col-1 sh gr /Times-Italic ff 525.00 scf sf 21900 4170 m gs 1 -1 sc (*) col-1 sh gr /Times-Italic ff 750.00 scf sf 21300 4350 m gs 1 -1 sc (V) col-1 sh gr /Symbol ff 900.00 scf sf 15000 2850 m gs 1 -1 sc (S) col-1 sh gr /Symbol ff 900.00 scf sf 15000 3975 m gs 1 -1 sc (S) col-1 sh gr /Times-Italic ff 750.00 scf sf 20325 5775 m gs 1 -1 sc (M) col-1 sh gr /Times-Italic ff 750.00 scf sf 18300 4920 m gs 1 -1 sc (p) col-1 sh gr /Times-Italic ff 750.00 scf sf 22350 4920 m gs 1 -1 sc (p) col-1 sh gr /Times-Roman ff 450.00 scf sf 22650 5175 m gs 1 -1 sc (2) col-1 sh gr $F2psEnd rs end %%EndDocument @endspecial 1710 1135 a FP(Figure)j(5.22)605 1333 y FK(2D)g(MF)g FL(!)h FK(3D)f(TQFT.)54 b FQ(This)34 b(implication)f(is)g (m)n(uc)n(h)g(more)g(di\016cult)h(and,)h(to)e(the)456 1432 y(b)r(est)27 b(of)g(our)g(kno)n(wledge,)f(no)h(complete)g (construction)g(of)g(it)g(is)h(kno)n(wn.)36 b(There)26 b(are)h(t)n(w)n(o)f(ap-)456 1532 y(proac)n(hes:)31 b(the)20 b(\014rst)f(one,)i(due)f(to)g(L.)g(Crane)f([)p FK(C)p FQ(])h(\(see)f(also)g([)p FK(Ko)p FQ(]\),)j(is)d(based)g(on)h(the)g (Heegaard)456 1632 y(splitting;)27 b(the)h(second)e(one,)h(due)g(to)g (M.)h(Kon)n(tsevic)n(h)d(and)i(to)g(I.)h(F)-7 b(renk)n(el)26 b(\(unpublished\),)j(is)456 1731 y(based)e(on)g(Morse)f(theory)-7 b(.)605 1831 y(F)g(ollo)n(wing)22 b(Crane)g([)p FK(C)p FQ(],)i(w)n(e)f(will)h(construct)e(\(non-extended\))i(3D)f(TQFT)g (starting)f(from)456 1931 y(a)35 b FL(C)5 b FQ(-extended)36 b(2D)g(MF.)g(W)-7 b(e)36 b(do)g(not)g(kno)n(w)f(ho)n(w)g(to)h(extend)g (this)h(construction)e(to)h(a)f FL(C)5 b FQ(-)456 2030 y(extended)27 b(3D)h(TQFT.)605 2130 y(W)-7 b(e)32 b(will)f(use)g(the)g (follo)n(wing)f(w)n(ell-kno)n(wn)g(theorem)h(in)g(top)r(ology)f(\(for)h (references,)g(see)456 2229 y([)p FK(Cr)p FQ(]\).)605 2374 y FP(Theorem)h FQ(5.8.1)e(\(Reidemeister{Singer\))p FP(.)40 b FO(L)l(et)32 b FJ(M)42 b FO(b)l(e)33 b(a)g(c)l(onne)l(cte)l (d)g(close)l(d)h(oriente)l(d)456 2474 y(3-manifold.)40 b(Then)6 b FQ(:)605 2573 y(\(i\))30 b FJ(M)39 b FO(c)l(an)29 b(b)l(e)h(pr)l(esente)l(d)g(as)g(a)g(r)l(esult)f(of)i(gluing)f(of)h (two)e(solid)j(hand)t(leb)l(o)l(dies)7 b FQ(:)1536 2708 y FJ(M)31 b FQ(=)23 b FJ(M)1817 2720 y FI(')1887 2708 y FQ(=)g FJ(H)2044 2720 y FM(1)2100 2708 y FL(t)2155 2720 y FI(')2221 2708 y FJ(H)2290 2720 y FM(2)2328 2708 y FJ(;)456 2863 y FO(wher)l(e)30 b FJ(')9 b FQ(:)28 b FJ(@)5 b(H)922 2875 y FM(1)1011 2816 y FE(\030)982 2863 y FL(\000)-39 b(!)p 1114 2795 155 4 v 23 w FJ(@)5 b(H)1232 2875 y FM(2)1269 2863 y FO(.)39 b(Such)29 b(a)h(pr)l(esentation)g(is)g (c)l(al)t(le)l(d)i(a)e FQ(Heegaard)c(splitting)p FO(.)605 2965 y FQ(\(ii\))43 b FO(Two)h(such)e FJ(M)1240 2977 y FI(')1330 2965 y FO(and)h FJ(M)1585 2977 y FI(')1629 2961 y Fx(0)1697 2965 y FO(ar)l(e)g(home)l(omorphic)i(i\013)e FJ(')9 b FQ(:)33 b FJ(@)5 b(H)2772 2977 y FM(1)2883 2918 y FE(\030)2855 2965 y FL(\000)-40 b(!)p 3009 2897 V 46 w FJ(@)5 b(H)3127 2977 y FM(2)3207 2965 y FO(c)l(an)42 b(b)l(e)456 3075 y(obtaine)l(d)30 b(fr)l(om)h FJ(')1035 3045 y FE(0)1068 3075 y FQ(:)c FJ(@)5 b(H)1243 3045 y FE(0)1236 3095 y FM(1)1325 3028 y FE(\030)1296 3075 y FL(\000)-39 b(!)p 1428 3004 V 23 w FJ(@)5 b(H)1553 3046 y FE(0)1546 3097 y FM(2)1613 3075 y FO(by)30 b(a)g(se)l(quenc)l(e)f(of) i(the)f(fol)t(lowing)i(moves)7 b FQ(:)605 3174 y(\(a\))30 b FJ(H)810 3186 y FM(1)870 3174 y FQ(=)23 b FJ(H)1034 3144 y FE(0)1027 3195 y FM(1)1064 3174 y FO(,)30 b FJ(H)1188 3186 y FM(2)1249 3174 y FQ(=)22 b FJ(H)1412 3144 y FE(0)1405 3195 y FM(2)1442 3174 y FO(,)31 b FJ(')1552 3144 y FE(0)1605 3174 y FO(is)f(isotopic)i(to)d FJ(')p FO(.)605 3274 y FQ(\(b\))h FJ(H)814 3286 y FM(1)875 3274 y FQ(=)22 b FJ(H)1038 3244 y FE(0)1031 3295 y FM(1)1069 3274 y FO(,)30 b FJ(H)1193 3286 y FM(2)1253 3274 y FQ(=)23 b FJ(H)1417 3244 y FE(0)1410 3295 y FM(2)1447 3274 y FO(,)30 b FJ(')1556 3244 y FE(0)1603 3274 y FQ(=)22 b FJ(y)g FL(\016)c FJ(')g FL(\016)g FJ(x)p FO(,)31 b(wher)l(e)f FJ(x)24 b FL(2)f FJ(N)2498 3286 y FI(H)2552 3294 y FF(1)2589 3274 y FO(,)30 b FJ(y)c FL(2)d FJ(N)2856 3286 y FI(H)2910 3294 y FF(2)2977 3274 y FO(and)979 3408 y FJ(N)1046 3420 y FI(H)1132 3408 y FQ(:=)g FL(f)p FO(home)l(omorphisms)31 b(of)g FJ(@)5 b(H)36 b FO(which)c(extend)d(to)h FJ(H)6 b FL(g)p FJ(:)605 3548 y FQ(\(c\))30 b(Stabilization)p FO(.)39 b(L)l(et)30 b FJ(H)1477 3518 y FE(0)1470 3569 y FM(1)1530 3548 y FQ(=)23 b FJ(H)1687 3560 y FM(1)1725 3548 y FQ(#)p FJ(T)12 b FO(,)29 b FJ(H)1985 3518 y FE(0)1978 3569 y FM(2)2039 3548 y FQ(=)23 b FJ(H)2196 3560 y FM(2)2233 3548 y FQ(#)p FJ(T)12 b FO(,)30 b(wher)l(e)g FJ(T)41 b FO(is)31 b(a)f(solid)h(torus)f (and)456 3648 y FQ(#)g FO(denotes)g(a)g(c)l(onne)l(cte)l(d)f(sum)h(of)g (top)l(olo)l(gic)l(al)i(sp)l(ac)l(es)37 b FQ(\()p FO(se)l(e)30 b(Figur)l(e)h FQ(5.23)d FO(b)l(elow)9 b FQ(\))p FO(.)40 b(L)l(et)29 b FJ(')3333 3618 y FE(0)3380 3648 y FQ(=)456 3754 y FJ(')p FQ(#)p FJ(s)p FO(,)g(wher)l(e)g FJ(s)9 b FQ(:)28 b FJ(@)5 b(T)1164 3707 y FE(\030)1135 3754 y FL(\000)-39 b(!)23 b FJ(@)5 b(T)39 b FO(is)28 b(the)h(home)l (omorphism)h(of)f(the)g(2-torus)e(which)j(has)f(a)g(matrix)456 3782 y Fy(\022)517 3849 y FQ(0)82 b FL(\000)p FQ(1)517 3948 y(1)115 b(0)747 3782 y Fy(\023)838 3899 y FO(in)29 b(the)h(standar)l(d)g(b)l(asis)g FL(f)p FJ(\013;)14 b(\014)t FL(g)29 b FO(of)48 b FQ(H)2045 3911 y FM(1)2083 3899 y FQ(\()p FJ(@)5 b(T)i(;)14 b FH(R)p FQ(\))p FO(.)44 b(Then)30 b FJ(M)2709 3911 y FI(')2753 3895 y Fx(0)2802 3899 y FL(')22 b FJ(M)2970 3911 y FI(')3018 3899 y FQ(#)p FJ(S)3143 3869 y FM(3)3203 3899 y FL(')h FJ(M)3372 3911 y FI(')3419 3899 y FO(.)588 4613 y @beginspecial 0 @llx 0 @lly 327 @urx 48 @ury 3270 @rwi @setspecial %%BeginDocument: figures/consum.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: consum.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Fri Jun 11 10:06:11 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 327 48 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -28.0 81.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7744 m -1000 -1000 l 30570 -1000 l 30570 7744 l cp clip 0.01200 0.01200 sc % Polyline 30.000 slw n 23400 4575 m 23401 4577 l 23403 4580 l 23407 4587 l 23412 4597 l 23420 4611 l 23430 4629 l 23443 4650 l 23458 4675 l 23474 4703 l 23492 4732 l 23511 4763 l 23531 4793 l 23552 4824 l 23573 4853 l 23594 4881 l 23615 4907 l 23637 4931 l 23658 4953 l 23680 4972 l 23702 4988 l 23725 5003 l 23749 5015 l 23775 5025 l 23797 5032 l 23820 5038 l 23844 5043 l 23870 5048 l 23897 5052 l 23926 5055 l 23955 5058 l 23986 5060 l 24018 5062 l 24051 5064 l 24085 5065 l 24119 5066 l 24154 5067 l 24190 5067 l 24225 5067 l 24260 5067 l 24296 5067 l 24331 5066 l 24365 5065 l 24399 5064 l 24432 5062 l 24464 5060 l 24495 5058 l 24524 5055 l 24553 5052 l 24580 5048 l 24606 5043 l 24630 5038 l 24653 5032 l 24675 5025 l 24701 5015 l 24725 5003 l 24748 4988 l 24770 4972 l 24792 4953 l 24813 4931 l 24835 4907 l 24856 4881 l 24877 4853 l 24898 4824 l 24919 4793 l 24939 4762 l 24958 4732 l 24976 4703 l 24992 4675 l 25007 4650 l 25020 4629 l 25030 4611 l 25038 4597 l 25043 4587 l 25047 4580 l 25049 4577 l 25050 4575 l gs col-1 s gr % Polyline n 26325 4725 m 26327 4723 l 26330 4720 l 26336 4713 l 26345 4703 l 26357 4691 l 26372 4675 l 26389 4658 l 26409 4639 l 26429 4619 l 26451 4600 l 26473 4582 l 26496 4565 l 26519 4549 l 26543 4535 l 26568 4522 l 26595 4511 l 26625 4500 l 26646 4493 l 26668 4487 l 26691 4480 l 26716 4473 l 26742 4466 l 26769 4459 l 26797 4451 l 26826 4444 l 26855 4435 l 26886 4427 l 26917 4419 l 26949 4410 l 26981 4402 l 27013 4393 l 27045 4385 l 27078 4377 l 27110 4370 l 27143 4363 l 27175 4357 l 27207 4352 l 27238 4347 l 27270 4344 l 27300 4341 l 27331 4340 l 27361 4341 l 27391 4342 l 27421 4345 l 27450 4350 l 27478 4356 l 27505 4363 l 27534 4372 l 27564 4382 l 27594 4395 l 27626 4409 l 27660 4425 l 27695 4443 l 27731 4462 l 27769 4483 l 27809 4506 l 27849 4530 l 27890 4554 l 27931 4580 l 27973 4605 l 28013 4630 l 28052 4655 l 28089 4679 l 28124 4701 l 28155 4721 l 28183 4740 l 28207 4755 l 28228 4769 l 28244 4779 l 28256 4788 l 28265 4793 l 28271 4797 l 28274 4799 l 28275 4800 l gs col-1 s gr % Polyline n 26550 4500 m 26551 4502 l 26553 4506 l 26556 4513 l 26561 4524 l 26568 4539 l 26578 4558 l 26589 4582 l 26603 4610 l 26618 4642 l 26635 4676 l 26653 4712 l 26673 4750 l 26692 4788 l 26712 4826 l 26733 4862 l 26753 4897 l 26773 4930 l 26792 4961 l 26811 4989 l 26830 5014 l 26849 5036 l 26867 5056 l 26886 5073 l 26905 5088 l 26925 5100 l 26947 5111 l 26971 5121 l 26996 5129 l 27021 5135 l 27048 5140 l 27076 5144 l 27105 5147 l 27135 5149 l 27165 5150 l 27196 5150 l 27227 5150 l 27259 5149 l 27291 5148 l 27322 5146 l 27353 5144 l 27384 5142 l 27414 5139 l 27443 5136 l 27472 5132 l 27499 5127 l 27526 5122 l 27551 5116 l 27576 5109 l 27600 5100 l 27623 5090 l 27646 5078 l 27668 5063 l 27691 5047 l 27715 5028 l 27739 5006 l 27764 4982 l 27790 4956 l 27816 4928 l 27843 4899 l 27870 4868 l 27896 4837 l 27922 4807 l 27947 4778 l 27969 4750 l 27990 4725 l 28007 4704 l 28021 4686 l 28033 4672 l 28041 4662 l 28046 4655 l 28049 4652 l 28050 4650 l gs col-1 s gr % Polyline n 25813 6125 m 25833 6136 l 25854 6148 l 25876 6160 l 25899 6173 l 25922 6187 l 25946 6202 l 25971 6217 l 25997 6233 l 26023 6249 l 26050 6266 l 26078 6283 l 26107 6301 l 26137 6319 l 26167 6338 l 26197 6356 l 26228 6375 l 26259 6394 l 26291 6412 l 26323 6431 l 26355 6449 l 26386 6467 l 26418 6484 l 26450 6501 l 26481 6517 l 26512 6533 l 26543 6548 l 26574 6563 l 26605 6577 l 26635 6590 l 26665 6602 l 26695 6614 l 26725 6625 l 26755 6635 l 26786 6645 l 26816 6654 l 26848 6663 l 26880 6671 l 26912 6678 l 26945 6685 l 26979 6691 l 27013 6696 l 27048 6700 l 27084 6704 l 27120 6707 l 27157 6709 l 27194 6710 l 27232 6711 l 27269 6710 l 27307 6709 l 27345 6706 l 27383 6703 l 27421 6699 l 27459 6694 l 27496 6688 l 27533 6682 l 27570 6674 l 27606 6666 l 27642 6657 l 27677 6647 l 27712 6637 l 27747 6626 l 27781 6614 l 27816 6601 l 27850 6588 l 27881 6575 l 27911 6561 l 27943 6547 l 27974 6532 l 28006 6516 l 28038 6500 l 28071 6482 l 28104 6464 l 28137 6445 l 28171 6426 l 28205 6405 l 28239 6384 l 28274 6362 l 28309 6339 l 28344 6316 l 28379 6292 l 28414 6268 l 28449 6243 l 28483 6218 l 28517 6193 l 28551 6168 l 28584 6142 l 28617 6117 l 28649 6091 l 28681 6066 l 28711 6040 l 28741 6015 l 28770 5990 l 28798 5966 l 28826 5941 l 28853 5917 l 28878 5893 l 28904 5869 l 28928 5846 l 28952 5823 l 28975 5800 l 29002 5773 l 29029 5745 l 29055 5718 l 29080 5690 l 29105 5662 l 29130 5634 l 29154 5605 l 29178 5576 l 29202 5547 l 29224 5517 l 29247 5488 l 29269 5458 l 29290 5428 l 29310 5398 l 29330 5368 l 29348 5338 l 29366 5308 l 29383 5279 l 29399 5250 l 29414 5221 l 29428 5193 l 29441 5166 l 29453 5139 l 29464 5112 l 29474 5086 l 29484 5061 l 29492 5036 l 29500 5011 l 29506 4987 l 29513 4963 l 29519 4935 l 29524 4907 l 29528 4879 l 29532 4850 l 29535 4822 l 29536 4793 l 29537 4763 l 29537 4733 l 29536 4702 l 29533 4672 l 29530 4641 l 29526 4610 l 29521 4578 l 29514 4548 l 29507 4517 l 29499 4486 l 29490 4456 l 29480 4427 l 29469 4398 l 29458 4370 l 29446 4342 l 29433 4315 l 29419 4289 l 29405 4263 l 29390 4238 l 29375 4213 l 29361 4191 l 29346 4169 l 29331 4147 l 29315 4125 l 29298 4102 l 29280 4080 l 29261 4057 l 29241 4033 l 29221 4010 l 29200 3986 l 29178 3961 l 29155 3937 l 29131 3912 l 29107 3887 l 29083 3862 l 29058 3838 l 29032 3813 l 29007 3788 l 28981 3764 l 28955 3739 l 28929 3715 l 28903 3692 l 28877 3668 l 28852 3645 l 28826 3623 l 28801 3600 l 28775 3578 l 28750 3556 l 28725 3534 l 28700 3513 l 28676 3492 l 28652 3471 l 28628 3451 l 28603 3430 l 28578 3408 l 28553 3387 l 28526 3365 l 28500 3343 l 28472 3321 l 28444 3299 l 28416 3277 l 28387 3254 l 28358 3232 l 28328 3209 l 28298 3187 l 28268 3166 l 28238 3144 l 28207 3123 l 28177 3103 l 28147 3083 l 28116 3063 l 28086 3045 l 28057 3027 l 28027 3009 l 27998 2993 l 27969 2977 l 27940 2963 l 27912 2949 l 27884 2935 l 27856 2923 l 27828 2911 l 27800 2900 l 27770 2889 l 27740 2879 l 27709 2869 l 27678 2860 l 27647 2851 l 27615 2843 l 27582 2836 l 27549 2830 l 27515 2824 l 27481 2819 l 27446 2815 l 27411 2811 l 27376 2808 l 27340 2806 l 27305 2804 l 27270 2804 l 27235 2804 l 27201 2805 l 27167 2806 l 27133 2808 l 27100 2811 l 27068 2815 l 27037 2819 l 27006 2823 l 26976 2829 l 26947 2834 l 26919 2841 l 26891 2847 l 26864 2855 l 26838 2863 l 26809 2871 l 26782 2881 l 26754 2891 l 26726 2902 l 26699 2913 l 26671 2925 l 26643 2938 l 26616 2951 l 26588 2965 l 26560 2979 l 26532 2993 l 26504 3008 l 26477 3023 l 26450 3038 l 26423 3052 l 26396 3067 l 26370 3082 l 26345 3096 l 26320 3110 l 26296 3124 l 26273 3137 l 26250 3150 l 26228 3162 l 26206 3173 l 26185 3184 l 26165 3194 l 26145 3204 l 26125 3213 l 26102 3222 l 26079 3231 l 26056 3239 l 26033 3246 l 26009 3253 l 25985 3259 l 25960 3264 l 25935 3268 l 25909 3271 l 25883 3273 l 25856 3274 l 25829 3274 l 25801 3273 l 25773 3271 l 25745 3268 l 25717 3264 l 25689 3259 l 25661 3253 l 25632 3247 l 25604 3239 l 25575 3230 l 25546 3221 l 25517 3211 l 25488 3200 l 25465 3191 l 25441 3182 l 25417 3172 l 25393 3161 l 25367 3150 l 25341 3139 l 25314 3127 l 25286 3115 l 25257 3102 l 25228 3089 l 25198 3075 l 25167 3061 l 25135 3047 l 25103 3033 l 25071 3019 l 25038 3005 l 25005 2991 l 24971 2978 l 24938 2964 l 24905 2951 l 24871 2938 l 24838 2926 l 24805 2914 l 24773 2903 l 24741 2892 l 24709 2883 l 24678 2873 l 24646 2865 l 24616 2857 l 24585 2850 l 24555 2843 l 24525 2838 l 24495 2832 l 24465 2828 l 24434 2825 l 24403 2822 l 24372 2819 l 24340 2818 l 24308 2817 l 24275 2816 l 24242 2817 l 24208 2818 l 24174 2819 l 24140 2821 l 24105 2824 l 24069 2828 l 24034 2832 l 23998 2837 l 23963 2842 l 23927 2848 l 23892 2854 l 23856 2861 l 23821 2868 l 23787 2875 l 23753 2883 l 23719 2891 l 23685 2899 l 23652 2908 l 23620 2916 l 23588 2925 l 23556 2934 l 23525 2944 l 23494 2953 l 23463 2963 l 23431 2972 l 23400 2982 l 23368 2993 l 23336 3003 l 23304 3014 l 23271 3025 l 23238 3036 l 23204 3048 l 23170 3060 l 23136 3072 l 23101 3084 l 23067 3097 l 23032 3110 l 22997 3123 l 22963 3135 l 22928 3148 l 22894 3161 l 22860 3174 l 22827 3186 l 22795 3199 l 22763 3211 l 22732 3223 l 22703 3235 l 22674 3246 l 22645 3257 l 22618 3268 l 22592 3278 l 22567 3288 l 22543 3298 l 22519 3307 l 22497 3316 l 22475 3325 l 22447 3336 l 22420 3347 l 22393 3358 l 22367 3368 l 22342 3378 l 22316 3387 l 22291 3396 l 22266 3405 l 22242 3413 l 22217 3421 l 22193 3428 l 22169 3434 l 22146 3440 l 22123 3446 l 22100 3450 l 22077 3454 l 22054 3458 l 22032 3460 l 22010 3462 l 21988 3464 l 21967 3464 l 21945 3464 l 21923 3464 l 21900 3463 l 21879 3461 l 21856 3459 l 21833 3456 l 21809 3453 l 21785 3450 l 21759 3446 l 21732 3441 l 21705 3436 l 21677 3430 l 21647 3424 l 21618 3418 l 21588 3411 l 21557 3404 l 21527 3396 l 21496 3389 l 21466 3381 l 21435 3373 l 21405 3365 l 21376 3356 l 21347 3348 l 21319 3340 l 21292 3332 l 21265 3324 l 21239 3316 l 21213 3308 l 21188 3300 l 21160 3291 l 21133 3283 l 21107 3274 l 21079 3265 l 21052 3256 l 21024 3247 l 20997 3238 l 20969 3229 l 20940 3220 l 20912 3212 l 20883 3203 l 20855 3194 l 20827 3186 l 20799 3178 l 20772 3171 l 20745 3164 l 20719 3157 l 20693 3151 l 20668 3145 l 20644 3140 l 20620 3136 l 20596 3132 l 20573 3128 l 20550 3125 l 20527 3122 l 20504 3120 l 20480 3119 l 20457 3117 l 20432 3117 l 20407 3117 l 20382 3118 l 20356 3119 l 20330 3122 l 20304 3125 l 20277 3129 l 20250 3133 l 20223 3139 l 20196 3145 l 20170 3152 l 20144 3160 l 20118 3169 l 20092 3178 l 20068 3188 l 20043 3199 l 20020 3211 l 19996 3223 l 19973 3236 l 19950 3250 l 19930 3263 l 19911 3276 l 19891 3290 l 19871 3305 l 19850 3321 l 19830 3338 l 19809 3356 l 19788 3375 l 19767 3395 l 19746 3416 l 19725 3438 l 19704 3461 l 19683 3484 l 19662 3508 l 19642 3533 l 19622 3558 l 19603 3584 l 19584 3610 l 19566 3636 l 19549 3663 l 19532 3689 l 19516 3715 l 19501 3742 l 19487 3768 l 19474 3795 l 19461 3821 l 19449 3848 l 19438 3875 l 19427 3902 l 19417 3930 l 19407 3958 l 19398 3987 l 19389 4017 l 19381 4047 l 19373 4079 l 19366 4111 l 19359 4143 l 19353 4177 l 19348 4210 l 19343 4245 l 19339 4279 l 19335 4314 l 19332 4349 l 19330 4384 l 19328 4418 l 19327 4453 l 19327 4486 l 19327 4520 l 19328 4552 l 19330 4584 l 19332 4616 l 19334 4646 l 19338 4676 l 19341 4705 l 19345 4734 l 19350 4763 l 19355 4791 l 19361 4819 l 19367 4847 l 19374 4875 l 19382 4903 l 19390 4932 l 19399 4960 l 19408 4989 l 19418 5018 l 19429 5047 l 19440 5076 l 19452 5105 l 19465 5134 l 19478 5163 l 19492 5191 l 19506 5219 l 19520 5246 l 19534 5273 l 19549 5299 l 19564 5324 l 19579 5349 l 19594 5372 l 19610 5395 l 19625 5418 l 19640 5439 l 19656 5460 l 19672 5480 l 19688 5500 l 19705 5521 l 19723 5542 l 19741 5562 l 19760 5583 l 19779 5603 l 19799 5623 l 19820 5643 l 19841 5662 l 19863 5682 l 19886 5701 l 19908 5720 l 19932 5738 l 19955 5756 l 19979 5773 l 20003 5789 l 20026 5805 l 20050 5820 l 20073 5834 l 20097 5847 l 20120 5859 l 20142 5870 l 20164 5880 l 20186 5889 l 20208 5898 l 20229 5906 l 20250 5913 l 20273 5919 l 20296 5925 l 20320 5931 l 20343 5935 l 20368 5939 l 20393 5942 l 20418 5945 l 20445 5946 l 20471 5948 l 20498 5948 l 20526 5948 l 20553 5947 l 20581 5945 l 20609 5943 l 20637 5941 l 20664 5938 l 20692 5934 l 20719 5930 l 20745 5926 l 20772 5921 l 20798 5916 l 20824 5911 l 20849 5906 l 20875 5900 l 20899 5895 l 20923 5889 l 20948 5883 l 20973 5877 l 20999 5871 l 21025 5864 l 21052 5858 l 21080 5851 l 21108 5844 l 21136 5837 l 21165 5830 l 21194 5823 l 21223 5816 l 21252 5809 l 21281 5802 l 21310 5796 l 21338 5790 l 21365 5784 l 21392 5778 l 21418 5773 l 21444 5768 l 21469 5764 l 21493 5760 l 21517 5756 l 21540 5753 l 21563 5750 l 21587 5747 l 21611 5745 l 21635 5743 l 21659 5742 l 21684 5741 l 21708 5741 l 21733 5741 l 21759 5742 l 21784 5743 l 21810 5745 l 21836 5747 l 21863 5750 l 21889 5753 l 21915 5756 l 21941 5760 l 21966 5765 l 21992 5770 l 22017 5775 l 22041 5781 l 22066 5786 l 22090 5792 l 22114 5799 l 22138 5806 l 22163 5813 l 22185 5819 l 22208 5826 l 22232 5834 l 22256 5842 l 22281 5850 l 22307 5859 l 22333 5868 l 22360 5878 l 22388 5888 l 22416 5898 l 22445 5909 l 22474 5920 l 22503 5932 l 22533 5944 l 22562 5956 l 22592 5968 l 22621 5980 l 22650 5992 l 22678 6004 l 22706 6016 l 22733 6028 l 22760 6040 l 22786 6052 l 22812 6064 l 22837 6076 l 22863 6088 l 22888 6099 l 22913 6112 l 22938 6124 l 22964 6136 l 22990 6149 l 23016 6162 l 23043 6176 l 23070 6189 l 23097 6203 l 23124 6216 l 23152 6230 l 23180 6244 l 23207 6257 l 23235 6271 l 23262 6284 l 23289 6297 l 23315 6309 l 23341 6321 l 23366 6333 l 23390 6344 l 23414 6355 l 23437 6365 l 23460 6374 l 23482 6383 l 23504 6392 l 23525 6400 l 23548 6408 l 23571 6416 l 23594 6424 l 23617 6431 l 23640 6438 l 23664 6445 l 23688 6451 l 23713 6458 l 23738 6463 l 23763 6469 l 23789 6474 l 23814 6479 l 23840 6483 l 23866 6487 l 23891 6491 l 23917 6495 l 23942 6498 l 23967 6501 l 23992 6503 l 24016 6506 l 24040 6508 l 24064 6509 l 24088 6511 l 24113 6513 l 24137 6514 l 24162 6515 l 24188 6516 l 24214 6517 l 24241 6518 l 24269 6518 l 24298 6518 l 24327 6517 l 24357 6517 l 24387 6515 l 24418 6513 l 24448 6511 l 24479 6508 l 24509 6505 l 24539 6501 l 24568 6496 l 24597 6491 l 24625 6485 l 24652 6479 l 24678 6472 l 24704 6464 l 24728 6456 l 24752 6447 l 24775 6438 l 24798 6427 l 24820 6416 l 24842 6404 l 24865 6391 l 24887 6377 l 24909 6362 l 24932 6347 l 24954 6331 l 24976 6314 l 24999 6297 l 25021 6280 l 25043 6262 l 25065 6245 l 25086 6228 l 25107 6211 l 25128 6194 l 25148 6178 l 25167 6163 l 25186 6148 l 25205 6134 l 25223 6121 l 25240 6109 l 25258 6098 l 25275 6088 l 25292 6078 l 25310 6069 l 25327 6061 l 25345 6054 l 25364 6047 l 25383 6042 l 25403 6037 l 25424 6033 l 25445 6031 l 25467 6029 l 25489 6029 l 25512 6029 l 25536 6031 l 25559 6034 l 25584 6039 l 25608 6044 l 25633 6050 l 25658 6058 l 25683 6067 l 25708 6076 l 25734 6087 l 25759 6099 l 25786 6111 l cp gs col-1 s gr % Polyline n 20025 4650 m 20027 4649 l 20033 4645 l 20042 4639 l 20057 4630 l 20076 4618 l 20101 4603 l 20131 4585 l 20164 4565 l 20200 4544 l 20237 4522 l 20275 4501 l 20313 4480 l 20349 4460 l 20384 4441 l 20418 4424 l 20449 4409 l 20478 4396 l 20506 4385 l 20532 4375 l 20556 4367 l 20579 4361 l 20601 4356 l 20622 4353 l 20642 4351 l 20663 4350 l 20686 4351 l 20709 4354 l 20732 4358 l 20755 4365 l 20779 4374 l 20804 4386 l 20830 4400 l 20857 4416 l 20886 4435 l 20916 4456 l 20947 4480 l 20979 4505 l 21011 4530 l 21042 4556 l 21071 4580 l 21095 4601 l 21116 4619 l 21131 4633 l 21142 4642 l 21147 4648 l 21150 4650 l gs col-1 s gr % Polyline n 23250 4725 m 23251 4724 l 23254 4720 l 23258 4715 l 23266 4706 l 23276 4693 l 23289 4677 l 23305 4657 l 23325 4633 l 23348 4606 l 23373 4576 l 23400 4544 l 23429 4510 l 23459 4475 l 23490 4440 l 23521 4405 l 23552 4370 l 23582 4338 l 23612 4306 l 23641 4277 l 23670 4250 l 23697 4225 l 23724 4203 l 23750 4183 l 23775 4165 l 23800 4150 l 23825 4137 l 23850 4125 l 23876 4115 l 23902 4106 l 23929 4099 l 23957 4093 l 23985 4087 l 24015 4082 l 24044 4079 l 24075 4075 l 24106 4072 l 24137 4070 l 24169 4068 l 24201 4067 l 24234 4066 l 24266 4065 l 24298 4065 l 24331 4065 l 24363 4066 l 24394 4067 l 24425 4069 l 24456 4071 l 24486 4074 l 24516 4078 l 24544 4083 l 24572 4089 l 24599 4096 l 24625 4104 l 24651 4114 l 24675 4125 l 24699 4138 l 24722 4153 l 24745 4170 l 24768 4190 l 24792 4213 l 24815 4238 l 24840 4266 l 24865 4296 l 24890 4329 l 24916 4364 l 24943 4401 l 24969 4440 l 24996 4479 l 25023 4519 l 25048 4558 l 25073 4596 l 25096 4633 l 25117 4666 l 25136 4697 l 25153 4723 l 25167 4746 l 25178 4764 l 25187 4778 l 25193 4788 l 25197 4795 l 25199 4798 l 25200 4800 l gs col-1 s gr % Polyline n 15600 3225 m 15560 3209 l 15518 3195 l 15476 3182 l 15432 3170 l 15388 3159 l 15342 3149 l 15295 3140 l 15248 3132 l 15199 3124 l 15149 3118 l 15098 3112 l 15046 3107 l 14993 3103 l 14940 3099 l 14886 3096 l 14831 3094 l 14775 3091 l 14719 3090 l 14662 3088 l 14605 3088 l 14547 3087 l 14489 3087 l 14431 3087 l 14373 3088 l 14315 3089 l 14257 3090 l 14199 3091 l 14141 3093 l 14084 3095 l 14027 3098 l 13970 3101 l 13914 3104 l 13858 3107 l 13804 3111 l 13749 3115 l 13696 3120 l 13643 3125 l 13592 3131 l 13541 3137 l 13491 3143 l 13442 3151 l 13394 3159 l 13347 3168 l 13301 3177 l 13255 3188 l 13211 3199 l 13168 3212 l 13125 3225 l 13079 3241 l 13035 3258 l 12990 3277 l 12946 3297 l 12903 3318 l 12859 3341 l 12815 3365 l 12772 3389 l 12728 3415 l 12684 3442 l 12640 3470 l 12595 3498 l 12551 3528 l 12506 3558 l 12461 3589 l 12416 3620 l 12371 3652 l 12326 3685 l 12281 3718 l 12236 3751 l 12192 3785 l 12148 3819 l 12104 3853 l 12061 3888 l 12019 3922 l 11978 3957 l 11938 3992 l 11899 4026 l 11861 4061 l 11825 4096 l 11791 4130 l 11758 4165 l 11727 4199 l 11698 4233 l 11671 4267 l 11647 4301 l 11625 4335 l 11606 4369 l 11589 4403 l 11575 4437 l 11564 4472 l 11556 4506 l 11552 4540 l 11550 4575 l 11551 4607 l 11555 4640 l 11562 4673 l 11571 4707 l 11583 4741 l 11597 4776 l 11613 4811 l 11632 4848 l 11652 4884 l 11675 4922 l 11700 4960 l 11726 4999 l 11754 5039 l 11784 5079 l 11815 5120 l 11848 5161 l 11881 5202 l 11916 5244 l 11952 5287 l 11989 5329 l 12027 5372 l 12065 5415 l 12104 5458 l 12144 5501 l 12184 5543 l 12225 5586 l 12265 5628 l 12306 5670 l 12347 5711 l 12389 5752 l 12430 5792 l 12471 5831 l 12512 5869 l 12553 5907 l 12594 5943 l 12635 5979 l 12675 6013 l 12716 6046 l 12756 6078 l 12797 6108 l 12837 6137 l 12877 6165 l 12918 6191 l 12958 6216 l 12999 6239 l 13041 6261 l 13082 6281 l 13125 6300 l 13167 6317 l 13209 6332 l 13252 6346 l 13297 6359 l 13342 6370 l 13388 6381 l 13435 6391 l 13483 6400 l 13532 6408 l 13582 6415 l 13633 6421 l 13685 6427 l 13738 6431 l 13791 6436 l 13845 6439 l 13900 6443 l 13956 6445 l 14012 6447 l 14068 6449 l 14125 6450 l 14183 6451 l 14240 6452 l 14298 6452 l 14356 6452 l 14414 6451 l 14472 6450 l 14530 6449 l 14588 6448 l 14645 6446 l 14702 6444 l 14759 6441 l 14815 6438 l 14871 6435 l 14925 6432 l 14980 6428 l 15033 6424 l 15086 6419 l 15137 6414 l 15188 6408 l 15238 6402 l 15286 6395 l 15334 6388 l 15381 6380 l 15426 6371 l 15470 6362 l 15513 6351 l 15555 6340 l 15596 6328 l 15636 6314 l 15675 6300 l 15718 6282 l 15760 6263 l 15800 6242 l 15840 6220 l 15879 6196 l 15918 6170 l 15956 6144 l 15994 6116 l 16031 6087 l 16068 6056 l 16105 6025 l 16141 5992 l 16178 5958 l 16214 5924 l 16250 5888 l 16286 5852 l 16321 5815 l 16357 5778 l 16392 5740 l 16427 5702 l 16461 5663 l 16495 5624 l 16529 5585 l 16562 5545 l 16594 5506 l 16626 5466 l 16656 5427 l 16686 5388 l 16715 5349 l 16742 5310 l 16769 5271 l 16794 5233 l 16817 5195 l 16839 5158 l 16860 5121 l 16878 5084 l 16895 5047 l 16910 5011 l 16922 4976 l 16933 4940 l 16941 4905 l 16946 4870 l 16950 4835 l 16950 4800 l 16948 4765 l 16943 4730 l 16936 4694 l 16926 4659 l 16914 4622 l 16899 4586 l 16883 4549 l 16864 4511 l 16844 4473 l 16821 4434 l 16797 4395 l 16771 4355 l 16744 4315 l 16716 4275 l 16686 4234 l 16655 4193 l 16623 4151 l 16590 4109 l 16556 4068 l 16522 4026 l 16487 3984 l 16451 3942 l 16415 3901 l 16378 3859 l 16341 3818 l 16304 3778 l 16266 3738 l 16229 3699 l 16191 3660 l 16153 3623 l 16115 3586 l 16077 3550 l 16039 3516 l 16000 3482 l 15962 3450 l 15923 3419 l 15885 3389 l 15846 3361 l 15806 3335 l 15766 3310 l 15726 3286 l 15685 3264 l 15643 3244 l cp gs col-1 s gr % Polyline n 20250 4575 m 20253 4577 l 20259 4582 l 20270 4590 l 20286 4601 l 20307 4616 l 20332 4633 l 20360 4651 l 20389 4670 l 20418 4689 l 20446 4706 l 20473 4721 l 20499 4734 l 20523 4746 l 20546 4755 l 20568 4763 l 20589 4768 l 20609 4772 l 20630 4774 l 20650 4775 l 20669 4774 l 20688 4773 l 20708 4769 l 20730 4765 l 20752 4759 l 20776 4751 l 20802 4742 l 20830 4731 l 20860 4718 l 20892 4704 l 20926 4689 l 20960 4672 l 20995 4655 l 21029 4638 l 21061 4622 l 21089 4607 l 21112 4595 l 21129 4586 l 21141 4580 l 21147 4577 l 21150 4575 l gs col-1 s gr % Polyline n 12900 4725 m 12901 4724 l 12904 4723 l 12910 4721 l 12919 4717 l 12932 4711 l 12948 4704 l 12969 4695 l 12994 4684 l 13023 4672 l 13057 4657 l 13093 4642 l 13133 4625 l 13175 4607 l 13219 4588 l 13265 4569 l 13311 4549 l 13358 4530 l 13404 4511 l 13449 4493 l 13493 4475 l 13536 4459 l 13577 4443 l 13617 4428 l 13654 4414 l 13690 4402 l 13724 4391 l 13757 4381 l 13788 4371 l 13818 4363 l 13847 4356 l 13875 4350 l 13907 4344 l 13939 4338 l 13970 4334 l 14001 4330 l 14031 4326 l 14061 4323 l 14091 4321 l 14121 4318 l 14150 4317 l 14179 4315 l 14208 4314 l 14237 4313 l 14266 4312 l 14295 4311 l 14323 4311 l 14352 4311 l 14380 4311 l 14409 4312 l 14438 4313 l 14466 4315 l 14495 4316 l 14524 4319 l 14553 4322 l 14582 4326 l 14612 4331 l 14641 4336 l 14671 4343 l 14700 4350 l 14728 4358 l 14755 4367 l 14784 4378 l 14814 4390 l 14844 4403 l 14876 4418 l 14910 4435 l 14945 4453 l 14981 4473 l 15019 4494 l 15059 4516 l 15099 4539 l 15140 4563 l 15181 4588 l 15223 4613 l 15263 4637 l 15302 4661 l 15339 4684 l 15374 4705 l 15405 4725 l 15433 4742 l 15457 4757 l 15478 4770 l 15494 4780 l 15506 4788 l 15515 4794 l 15521 4797 l 15524 4799 l 15525 4800 l gs col-1 s gr /Times-Italic ff 1125.00 scf sf 10050 5175 m gs 1 -1 sc (#) col-1 sh gr % Polyline n 13125 4575 m 13126 4577 l 13128 4580 l 13133 4586 l 13139 4596 l 13148 4609 l 13160 4626 l 13175 4647 l 13193 4671 l 13213 4699 l 13235 4729 l 13258 4761 l 13284 4794 l 13310 4827 l 13337 4860 l 13364 4892 l 13392 4923 l 13419 4951 l 13446 4978 l 13474 5003 l 13501 5025 l 13529 5044 l 13558 5061 l 13587 5076 l 13618 5089 l 13650 5100 l 13676 5107 l 13703 5114 l 13732 5119 l 13762 5124 l 13793 5129 l 13826 5132 l 13860 5135 l 13895 5138 l 13932 5140 l 13969 5142 l 14008 5143 l 14047 5145 l 14088 5145 l 14129 5146 l 14170 5146 l 14212 5146 l 14254 5146 l 14295 5145 l 14337 5145 l 14378 5144 l 14419 5143 l 14459 5141 l 14499 5140 l 14537 5138 l 14574 5136 l 14610 5134 l 14645 5131 l 14679 5128 l 14711 5125 l 14742 5121 l 14771 5117 l 14799 5112 l 14825 5106 l 14850 5100 l 14883 5090 l 14914 5078 l 14943 5063 l 14971 5047 l 14998 5028 l 15024 5006 l 15050 4982 l 15075 4956 l 15100 4928 l 15125 4899 l 15149 4868 l 15173 4837 l 15195 4807 l 15215 4778 l 15234 4750 l 15251 4725 l 15265 4704 l 15277 4686 l 15286 4672 l 15293 4662 l 15297 4655 l 15299 4652 l 15300 4650 l gs col-1 s gr % Polyline n 9081 4750 m 9081 4709 l 9080 4668 l 9079 4626 l 9076 4584 l 9073 4542 l 9068 4499 l 9063 4456 l 9056 4413 l 9049 4369 l 9040 4324 l 9031 4280 l 9020 4235 l 9009 4189 l 8996 4144 l 8983 4098 l 8968 4053 l 8953 4007 l 8937 3962 l 8919 3917 l 8901 3872 l 8882 3827 l 8863 3783 l 8842 3740 l 8821 3697 l 8799 3656 l 8777 3615 l 8754 3575 l 8730 3536 l 8706 3498 l 8682 3461 l 8657 3425 l 8632 3391 l 8607 3357 l 8582 3325 l 8556 3295 l 8530 3265 l 8503 3237 l 8477 3210 l 8450 3184 l 8423 3159 l 8396 3135 l 8368 3113 l 8337 3089 l 8305 3066 l 8273 3045 l 8240 3024 l 8207 3005 l 8172 2986 l 8137 2969 l 8101 2952 l 8063 2937 l 8025 2923 l 7987 2909 l 7947 2897 l 7907 2886 l 7865 2875 l 7823 2866 l 7781 2858 l 7738 2850 l 7695 2844 l 7651 2839 l 7607 2835 l 7562 2832 l 7518 2830 l 7474 2828 l 7429 2828 l 7385 2829 l 7341 2830 l 7298 2832 l 7254 2835 l 7211 2839 l 7169 2844 l 7127 2849 l 7085 2854 l 7044 2861 l 7003 2868 l 6963 2875 l 6923 2883 l 6883 2891 l 6843 2900 l 6803 2909 l 6763 2919 l 6723 2929 l 6683 2940 l 6642 2951 l 6601 2963 l 6559 2975 l 6517 2988 l 6475 3001 l 6432 3014 l 6389 3028 l 6346 3043 l 6302 3057 l 6258 3072 l 6214 3088 l 6170 3103 l 6126 3119 l 6082 3134 l 6039 3150 l 5996 3166 l 5953 3181 l 5910 3197 l 5869 3212 l 5828 3228 l 5787 3243 l 5748 3257 l 5709 3272 l 5671 3286 l 5634 3299 l 5598 3312 l 5564 3325 l 5529 3337 l 5496 3349 l 5464 3360 l 5433 3371 l 5402 3381 l 5372 3391 l 5343 3400 l 5309 3410 l 5276 3420 l 5243 3429 l 5210 3438 l 5177 3446 l 5145 3454 l 5113 3460 l 5080 3467 l 5048 3472 l 5016 3477 l 4983 3481 l 4950 3485 l 4918 3488 l 4885 3490 l 4852 3491 l 4820 3492 l 4787 3492 l 4754 3491 l 4722 3490 l 4690 3488 l 4657 3485 l 4625 3481 l 4593 3477 l 4561 3472 l 4530 3467 l 4498 3461 l 4466 3454 l 4435 3447 l 4403 3439 l 4371 3431 l 4338 3422 l 4306 3413 l 4276 3404 l 4245 3394 l 4214 3385 l 4182 3375 l 4149 3364 l 4115 3354 l 4081 3343 l 4045 3332 l 4009 3320 l 3972 3309 l 3934 3298 l 3896 3286 l 3857 3275 l 3817 3265 l 3777 3254 l 3737 3244 l 3696 3235 l 3655 3226 l 3615 3217 l 3574 3210 l 3534 3203 l 3494 3197 l 3454 3192 l 3415 3189 l 3377 3186 l 3339 3184 l 3302 3184 l 3266 3184 l 3230 3186 l 3196 3190 l 3162 3194 l 3129 3200 l 3097 3207 l 3066 3216 l 3035 3226 l 3006 3238 l 2978 3250 l 2950 3264 l 2923 3279 l 2897 3296 l 2871 3315 l 2845 3335 l 2819 3356 l 2794 3379 l 2769 3404 l 2744 3430 l 2720 3458 l 2697 3487 l 2673 3518 l 2651 3550 l 2629 3583 l 2608 3617 l 2587 3653 l 2567 3689 l 2548 3727 l 2530 3765 l 2513 3804 l 2497 3844 l 2482 3884 l 2468 3925 l 2455 3966 l 2443 4006 l 2432 4048 l 2422 4088 l 2413 4129 l 2405 4170 l 2398 4211 l 2393 4251 l 2388 4291 l 2385 4331 l 2382 4370 l 2381 4410 l 2380 4449 l 2381 4488 l 2382 4526 l 2384 4565 l 2388 4604 l 2392 4644 l 2397 4683 l 2404 4723 l 2411 4762 l 2420 4803 l 2429 4843 l 2440 4883 l 2451 4924 l 2464 4964 l 2477 5005 l 2492 5045 l 2508 5085 l 2524 5125 l 2542 5164 l 2560 5203 l 2579 5241 l 2599 5278 l 2620 5315 l 2641 5350 l 2663 5385 l 2685 5418 l 2708 5451 l 2731 5482 l 2755 5512 l 2779 5540 l 2803 5567 l 2828 5593 l 2852 5617 l 2877 5640 l 2902 5662 l 2928 5682 l 2953 5701 l 2979 5719 l 3004 5735 l 3031 5750 l 3060 5765 l 3090 5779 l 3121 5792 l 3152 5804 l 3184 5814 l 3217 5823 l 3250 5830 l 3285 5837 l 3320 5843 l 3355 5847 l 3392 5851 l 3429 5853 l 3466 5854 l 3504 5855 l 3542 5854 l 3581 5853 l 3620 5851 l 3658 5848 l 3697 5845 l 3736 5841 l 3774 5837 l 3812 5832 l 3849 5826 l 3886 5821 l 3922 5815 l 3958 5809 l 3992 5803 l 4027 5797 l 4060 5791 l 4093 5785 l 4125 5779 l 4157 5773 l 4187 5768 l 4218 5763 l 4250 5757 l 4282 5752 l 4314 5748 l 4345 5744 l 4377 5740 l 4409 5736 l 4442 5733 l 4475 5731 l 4507 5728 l 4541 5727 l 4574 5725 l 4608 5725 l 4643 5725 l 4677 5725 l 4712 5726 l 4746 5728 l 4781 5730 l 4816 5733 l 4851 5736 l 4886 5741 l 4920 5745 l 4955 5751 l 4989 5757 l 5023 5763 l 5057 5770 l 5091 5778 l 5124 5787 l 5158 5796 l 5191 5805 l 5225 5815 l 5259 5826 l 5293 5838 l 5322 5848 l 5352 5858 l 5382 5870 l 5413 5881 l 5444 5894 l 5476 5907 l 5509 5920 l 5542 5934 l 5576 5948 l 5611 5963 l 5647 5979 l 5683 5994 l 5720 6011 l 5758 6027 l 5796 6044 l 5834 6061 l 5873 6078 l 5912 6095 l 5952 6113 l 5991 6130 l 6031 6147 l 6070 6164 l 6110 6181 l 6149 6198 l 6188 6214 l 6227 6231 l 6265 6246 l 6303 6262 l 6340 6277 l 6377 6291 l 6413 6305 l 6449 6318 l 6485 6331 l 6520 6344 l 6554 6355 l 6588 6367 l 6622 6377 l 6656 6388 l 6698 6400 l 6740 6411 l 6782 6422 l 6824 6432 l 6867 6442 l 6909 6451 l 6951 6459 l 6993 6467 l 7035 6474 l 7077 6481 l 7117 6487 l 7158 6492 l 7197 6497 l 7235 6502 l 7272 6506 l 7307 6510 l 7340 6513 l 7372 6515 l 7402 6518 l 7430 6519 l 7455 6521 l 7479 6522 l 7500 6523 l 7518 6524 l 7534 6524 l 7548 6525 l 7560 6525 l 7569 6525 l 7576 6525 l 7581 6525 l 7583 6525 l 7576 6525 l 7561 6525 l 7539 6525 l 7511 6525 l 7481 6525 l 7448 6525 l 7416 6525 l 7387 6525 l 7363 6525 l 7345 6525 l 7335 6525 l 7334 6525 l 7343 6525 l 7351 6525 l 7360 6525 l 7372 6525 l 7386 6524 l 7403 6524 l 7421 6523 l 7442 6522 l 7465 6520 l 7490 6518 l 7517 6515 l 7546 6512 l 7576 6508 l 7609 6504 l 7643 6498 l 7678 6492 l 7715 6485 l 7752 6477 l 7791 6468 l 7830 6459 l 7870 6448 l 7910 6436 l 7950 6423 l 7990 6410 l 8029 6395 l 8069 6379 l 8108 6362 l 8146 6345 l 8184 6326 l 8222 6305 l 8259 6284 l 8295 6261 l 8331 6238 l 8359 6217 l 8387 6196 l 8415 6174 l 8442 6150 l 8470 6126 l 8497 6100 l 8524 6073 l 8551 6045 l 8578 6015 l 8605 5984 l 8631 5953 l 8657 5919 l 8683 5885 l 8709 5850 l 8734 5813 l 8758 5775 l 8782 5737 l 8805 5697 l 8828 5657 l 8850 5616 l 8871 5574 l 8892 5532 l 8911 5489 l 8929 5445 l 8947 5402 l 8963 5358 l 8979 5314 l 8993 5270 l 9006 5226 l 9019 5182 l 9030 5138 l 9040 5095 l 9049 5051 l 9056 5008 l 9063 4965 l 9069 4922 l 9073 4879 l 9077 4836 l 9079 4793 l cp gs col-1 s gr % Polyline n 6075 4725 m 6076 4724 l 6079 4720 l 6083 4715 l 6091 4706 l 6101 4693 l 6114 4677 l 6130 4657 l 6150 4633 l 6173 4606 l 6198 4576 l 6225 4544 l 6254 4510 l 6284 4475 l 6315 4440 l 6346 4405 l 6377 4370 l 6407 4338 l 6437 4306 l 6466 4277 l 6495 4250 l 6522 4225 l 6549 4203 l 6575 4183 l 6600 4165 l 6625 4150 l 6650 4137 l 6675 4125 l 6701 4115 l 6727 4106 l 6754 4099 l 6782 4093 l 6810 4087 l 6840 4082 l 6869 4079 l 6900 4075 l 6931 4072 l 6962 4070 l 6994 4068 l 7026 4067 l 7059 4066 l 7091 4065 l 7123 4065 l 7156 4065 l 7188 4066 l 7219 4067 l 7250 4069 l 7281 4071 l 7311 4074 l 7341 4078 l 7369 4083 l 7397 4089 l 7424 4096 l 7450 4104 l 7476 4114 l 7500 4125 l 7524 4138 l 7547 4153 l 7570 4170 l 7593 4190 l 7617 4213 l 7640 4238 l 7665 4266 l 7690 4296 l 7715 4329 l 7741 4364 l 7768 4401 l 7794 4440 l 7821 4479 l 7848 4519 l 7873 4558 l 7898 4596 l 7921 4633 l 7942 4666 l 7961 4697 l 7978 4723 l 7992 4746 l 8003 4764 l 8012 4778 l 8018 4788 l 8022 4795 l 8024 4798 l 8025 4800 l gs col-1 s gr % Polyline n 6225 4575 m 6226 4577 l 6228 4580 l 6232 4587 l 6237 4597 l 6245 4611 l 6255 4629 l 6268 4650 l 6283 4675 l 6299 4703 l 6317 4732 l 6336 4763 l 6356 4793 l 6377 4824 l 6398 4853 l 6419 4881 l 6440 4907 l 6462 4931 l 6483 4953 l 6505 4972 l 6527 4988 l 6550 5003 l 6574 5015 l 6600 5025 l 6622 5032 l 6645 5038 l 6669 5043 l 6695 5048 l 6722 5052 l 6751 5055 l 6780 5058 l 6811 5060 l 6843 5062 l 6876 5064 l 6910 5065 l 6944 5066 l 6979 5067 l 7015 5067 l 7050 5067 l 7085 5067 l 7121 5067 l 7156 5066 l 7190 5065 l 7224 5064 l 7257 5062 l 7289 5060 l 7320 5058 l 7349 5055 l 7378 5052 l 7405 5048 l 7431 5043 l 7455 5038 l 7478 5032 l 7500 5025 l 7526 5015 l 7550 5003 l 7573 4988 l 7595 4972 l 7617 4953 l 7638 4931 l 7660 4907 l 7681 4881 l 7702 4853 l 7723 4824 l 7744 4793 l 7764 4762 l 7783 4732 l 7801 4703 l 7817 4675 l 7832 4650 l 7845 4629 l 7855 4611 l 7863 4597 l 7868 4587 l 7872 4580 l 7874 4577 l 7875 4575 l gs col-1 s gr % Polyline n 3300 4650 m 3302 4649 l 3308 4645 l 3317 4639 l 3332 4630 l 3351 4618 l 3376 4603 l 3406 4585 l 3439 4565 l 3475 4544 l 3512 4522 l 3550 4501 l 3588 4480 l 3624 4460 l 3659 4441 l 3693 4424 l 3724 4409 l 3753 4396 l 3781 4385 l 3807 4375 l 3831 4367 l 3854 4361 l 3876 4356 l 3897 4353 l 3917 4351 l 3938 4350 l 3961 4351 l 3984 4354 l 4007 4358 l 4030 4365 l 4054 4374 l 4079 4386 l 4105 4400 l 4132 4416 l 4161 4435 l 4191 4456 l 4222 4480 l 4254 4505 l 4286 4530 l 4317 4556 l 4346 4580 l 4370 4601 l 4391 4619 l 4406 4633 l 4417 4642 l 4422 4648 l 4425 4650 l gs col-1 s gr % Polyline n 3450 4575 m 3453 4577 l 3459 4582 l 3470 4590 l 3486 4601 l 3507 4616 l 3532 4633 l 3560 4651 l 3589 4670 l 3618 4689 l 3646 4706 l 3673 4721 l 3699 4734 l 3723 4746 l 3746 4755 l 3768 4763 l 3789 4768 l 3809 4772 l 3830 4774 l 3850 4775 l 3869 4774 l 3888 4773 l 3908 4769 l 3930 4765 l 3952 4759 l 3976 4751 l 4002 4742 l 4030 4731 l 4060 4718 l 4092 4704 l 4126 4689 l 4160 4672 l 4195 4655 l 4229 4638 l 4261 4622 l 4289 4607 l 4312 4595 l 4329 4586 l 4341 4580 l 4347 4577 l 4350 4575 l gs col-1 s gr /Times-Roman ff 1275.00 scf sf 17850 5100 m gs 1 -1 sc (=) col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 1115 4813 a FP(Figure)32 b(5.23.)40 b FQ(Connected)28 b(sum)g(of)f(3-manifolds.)605 5016 y(No)n(w)33 b(supp)r(ose)h(that)g(w) n(e)g(ha)n(v)n(e)e(a)i FL(C)5 b FQ(-extended)33 b(mo)r(dular)h (functor.)55 b(Let)34 b FJ(H)41 b FQ(b)r(e)34 b(a)g(solid)456 5116 y(handleb)r(o)r(dy)24 b(whose)f(b)r(oundary)h FJ(@)5 b(H)30 b FQ(is)25 b(a)e(surface)h(of)g(gen)n(us)f FJ(g)s FQ(.)35 b(W)-7 b(e)25 b(will)f(construct)g(a)g(v)n(ector)456 5216 y FJ(v)496 5228 y FM(0)533 5216 y FQ(\()p FJ(H)7 b FQ(\))23 b FL(2)h FJ(\034)9 b FQ(\()p FJ(@)c(H)i FQ(\))28 b(as)f(follo)n(ws.)p eop %%Page: 133 41 133 136 bop 1444 226 a FM(5.8.)29 b(FR)n(OM)g(2D)h(MF)e(TO)i(3D)f(TQFT) 867 b(133)605 425 y FQ(Cho)r(ose)38 b(some)h(non-in)n(tersecting)e (\\cuts",)k(i.e.,)h(disks)d(em)n(b)r(edded)g(in)g FJ(H)7 b FQ(,)42 b(whic)n(h)d(cut)456 525 y FJ(H)j FQ(in)n(to)36 b(con)n(tractible)e(pieces.)61 b(This)36 b(also)e(giv)n(es)h(a)g (system)g(of)h(cuts)g(on)f FJ(@)5 b(H)43 b FQ(and)35 b(th)n(us,)j(a)456 624 y(decomp)r(osition)32 b(of)g FJ(@)5 b(H)39 b FQ(in)n(to)32 b(spheres)g(with)h(holes:)46 b FJ(@)5 b(H)38 b FQ(=)2430 562 y Fy(S)2513 624 y FQ(\006)2573 636 y FI(a)2613 624 y FQ(.)52 b(Consider)32 b(all)g(p)r(ossible)456 724 y(lab)r(elings)18 b FJ(i)k FQ(:)h FL(f)p FQ(cuts)p FL(g)g(!)g FJ(I)i FQ(of)19 b(the)g(cutting)g(circles)e(b)n(y)i(simple)f (ob)5 b(jects)18 b(of)h FL(C)k FQ(\(see)c(Figure)e(5.24\).)1413 1578 y @beginspecial 0 @llx 0 @lly 129 @urx 81 @ury 1290 @rwi @setspecial %%BeginDocument: figures/cuttrin.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: cuttrin.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Fri Jun 11 10:25:14 1999 %%For: bakalov@rose (BAKALOV Bojko) %%Orientation: Portrait %%BoundingBox: 0 0 129 81 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 0.2200 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -173.0 104.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 8821 m -1000 -1000 l 23823 -1000 l 23823 8821 l cp clip 0.01320 0.01320 sc % Arc 15.000 slw gs [90] 0 sd n 14312.5 6487.5 3914.1 -19.6 19.6 arc gs col0 s gr gr [] 0 sd % Arc gs [90] 0 sd n 14712.5 3037.5 3512.7 -20.6 20.6 arc gs col0 s gr gr [] 0 sd % Arc gs n 19852.5 3037.5 2227.8 -146.3 146.3 arcn gs col0 s gr gr % Arc gs n 16687.5 4481.2 545.0 153.4 26.6 arcn gs col0 s gr gr % Arc gs [90] 0 sd n 16687.5 6262.5 1612.9 -107.6 -72.4 arc gs col0 s gr gr [] 0 sd % Arc gs n 19387.5 4593.8 432.9 162.3 17.7 arcn gs col0 s gr gr % Arc gs n 21975.0 6225.0 1651.7 -140.5 140.5 arcn gs col0 s gr gr % Arc gs [90] 0 sd n 19350.0 6000.0 1352.1 -109.4 -70.6 arc gs col0 s gr gr [] 0 sd % Arc gs n 16500.0 6225.0 1651.7 -140.5 140.5 arcn gs col0 s gr gr % Arc gs [90] 0 sd n 11643.8 6225.0 3732.0 -16.3 16.3 arc gs col0 s gr gr [] 0 sd % Arc gs [90] 0 sd n 17118.8 6225.0 3732.0 -16.3 16.3 arc gs col0 s gr gr [] 0 sd % Arc gs n 20092.5 6487.5 2470.1 -147.9 147.9 arcn gs col0 s gr gr /Times-Roman ff 330.00 scf sf 21570 6480 m gs 1 -1 sc (3) col-1 sh gr /Times-Italic ff 540.00 scf sf 18945 6405 m gs 1 -1 sc (i) col-1 sh gr /Times-Italic ff 750.00 scf sf 18600 6300 m gs 1 -1 sc (V) col-1 sh gr /Times-Roman ff 330.00 scf sf 19095 6480 m gs 1 -1 sc (2) col-1 sh gr /Times-Italic ff 540.00 scf sf 16095 6405 m gs 1 -1 sc (i) col-1 sh gr /Times-Italic ff 750.00 scf sf 15750 6300 m gs 1 -1 sc (V) col-1 sh gr /Times-Roman ff 330.00 scf sf 16245 6480 m gs 1 -1 sc (1) col-1 sh gr /Times-Italic ff 540.00 scf sf 19425 4155 m gs 1 -1 sc (i) col-1 sh gr /Times-Italic ff 750.00 scf sf 19080 4050 m gs 1 -1 sc (V) col-1 sh gr /Times-Roman ff 330.00 scf sf 19575 4230 m gs 1 -1 sc (6) col-1 sh gr /Times-Italic ff 540.00 scf sf 16695 4155 m gs 1 -1 sc (i) col-1 sh gr /Times-Italic ff 750.00 scf sf 21075 6300 m gs 1 -1 sc (V) col-1 sh gr /Times-Italic ff 750.00 scf sf 16350 4050 m gs 1 -1 sc (V) col-1 sh gr % Polyline 30.000 slw n 19725 4875 m 19726 4873 l 19728 4870 l 19732 4864 l 19737 4854 l 19745 4841 l 19756 4824 l 19769 4803 l 19784 4779 l 19802 4751 l 19821 4721 l 19842 4689 l 19864 4656 l 19887 4623 l 19910 4590 l 19933 4558 l 19957 4527 l 19981 4499 l 20004 4472 l 20028 4447 l 20051 4425 l 20074 4406 l 20098 4389 l 20123 4374 l 20148 4361 l 20175 4350 l 20199 4342 l 20225 4335 l 20252 4329 l 20280 4323 l 20310 4319 l 20341 4315 l 20373 4311 l 20406 4309 l 20441 4306 l 20476 4305 l 20512 4303 l 20549 4302 l 20587 4301 l 20625 4301 l 20663 4301 l 20700 4301 l 20738 4301 l 20776 4302 l 20813 4303 l 20849 4305 l 20884 4306 l 20919 4309 l 20952 4311 l 20984 4315 l 21015 4319 l 21045 4323 l 21073 4329 l 21100 4335 l 21126 4342 l 21150 4350 l 21177 4361 l 21202 4374 l 21227 4389 l 21251 4406 l 21274 4425 l 21297 4447 l 21321 4472 l 21344 4499 l 21368 4527 l 21392 4558 l 21415 4590 l 21438 4623 l 21461 4656 l 21483 4689 l 21504 4721 l 21523 4751 l 21541 4779 l 21556 4803 l 21569 4824 l 21580 4841 l 21588 4854 l 21593 4864 l 21597 4870 l 21599 4873 l 21600 4875 l gs col-1 s gr /Times-Roman ff 330.00 scf sf 16845 4230 m gs 1 -1 sc (4) col-1 sh gr /Times-Italic ff 540.00 scf sf 18900 2880 m gs 1 -1 sc (i) col-1 sh gr /Times-Italic ff 750.00 scf sf 18555 2775 m gs 1 -1 sc (V) col-1 sh gr /Times-Roman ff 330.00 scf sf 19050 2955 m gs 1 -1 sc (5) col-1 sh gr /Times-Italic ff 540.00 scf sf 21420 6405 m gs 1 -1 sc (i) col-1 sh gr % Ellipse n 18000 4800 4800 3000 0 360 DrawEllipse gs col-1 s gr % Polyline n 17100 4875 m 17101 4873 l 17103 4870 l 17107 4864 l 17112 4854 l 17120 4841 l 17131 4824 l 17144 4803 l 17159 4779 l 17177 4751 l 17196 4721 l 17217 4689 l 17239 4656 l 17262 4623 l 17285 4590 l 17308 4558 l 17332 4527 l 17356 4499 l 17379 4472 l 17403 4447 l 17426 4425 l 17449 4406 l 17473 4389 l 17498 4374 l 17523 4361 l 17550 4350 l 17574 4342 l 17600 4335 l 17627 4329 l 17655 4323 l 17685 4319 l 17716 4315 l 17748 4311 l 17781 4309 l 17816 4306 l 17851 4305 l 17887 4303 l 17924 4302 l 17962 4301 l 18000 4301 l 18038 4301 l 18075 4301 l 18113 4301 l 18151 4302 l 18188 4303 l 18224 4305 l 18259 4306 l 18294 4309 l 18327 4311 l 18359 4315 l 18390 4319 l 18420 4323 l 18448 4329 l 18475 4335 l 18501 4342 l 18525 4350 l 18552 4361 l 18577 4374 l 18602 4389 l 18626 4406 l 18649 4425 l 18672 4447 l 18696 4472 l 18719 4499 l 18743 4527 l 18767 4558 l 18790 4590 l 18813 4623 l 18836 4656 l 18858 4689 l 18879 4721 l 18898 4751 l 18916 4779 l 18931 4803 l 18944 4824 l 18955 4841 l 18963 4854 l 18968 4864 l 18972 4870 l 18974 4873 l 18975 4875 l gs col-1 s gr % Polyline n 17175 4725 m 17176 4727 l 17179 4731 l 17183 4738 l 17191 4748 l 17201 4763 l 17213 4781 l 17228 4803 l 17246 4827 l 17265 4854 l 17286 4881 l 17308 4909 l 17331 4937 l 17354 4964 l 17377 4988 l 17400 5011 l 17423 5032 l 17447 5050 l 17471 5066 l 17496 5079 l 17522 5091 l 17550 5100 l 17572 5106 l 17595 5111 l 17619 5115 l 17645 5119 l 17672 5122 l 17700 5125 l 17730 5128 l 17760 5129 l 17792 5131 l 17825 5132 l 17858 5133 l 17892 5134 l 17927 5135 l 17961 5135 l 17996 5135 l 18032 5135 l 18066 5135 l 18101 5134 l 18135 5133 l 18169 5132 l 18202 5131 l 18234 5129 l 18265 5128 l 18295 5125 l 18323 5122 l 18351 5119 l 18378 5115 l 18403 5111 l 18427 5106 l 18450 5100 l 18477 5091 l 18504 5081 l 18529 5069 l 18554 5056 l 18579 5040 l 18604 5022 l 18629 5002 l 18655 4980 l 18681 4957 l 18707 4932 l 18732 4907 l 18758 4881 l 18782 4856 l 18805 4831 l 18826 4808 l 18844 4788 l 18861 4770 l 18874 4755 l 18884 4743 l 18891 4735 l 18896 4729 l 18899 4726 l 18900 4725 l gs col-1 s gr % Polyline n 14400 4875 m 14401 4873 l 14403 4870 l 14407 4864 l 14412 4854 l 14420 4841 l 14431 4824 l 14444 4803 l 14459 4779 l 14477 4751 l 14496 4721 l 14517 4689 l 14539 4656 l 14562 4623 l 14585 4590 l 14608 4558 l 14632 4527 l 14656 4499 l 14679 4472 l 14703 4447 l 14726 4425 l 14749 4406 l 14773 4389 l 14798 4374 l 14823 4361 l 14850 4350 l 14874 4342 l 14900 4335 l 14927 4329 l 14955 4323 l 14985 4319 l 15016 4315 l 15048 4311 l 15081 4309 l 15116 4306 l 15151 4305 l 15187 4303 l 15224 4302 l 15262 4301 l 15300 4301 l 15338 4301 l 15375 4301 l 15413 4301 l 15451 4302 l 15488 4303 l 15524 4305 l 15559 4306 l 15594 4309 l 15627 4311 l 15659 4315 l 15690 4319 l 15720 4323 l 15748 4329 l 15775 4335 l 15801 4342 l 15825 4350 l 15852 4361 l 15877 4374 l 15902 4389 l 15926 4406 l 15949 4425 l 15972 4447 l 15996 4472 l 16019 4499 l 16043 4527 l 16067 4558 l 16090 4590 l 16113 4623 l 16136 4656 l 16158 4689 l 16179 4721 l 16198 4751 l 16216 4779 l 16231 4803 l 16244 4824 l 16255 4841 l 16263 4854 l 16268 4864 l 16272 4870 l 16274 4873 l 16275 4875 l gs col-1 s gr % Polyline n 14475 4725 m 14476 4727 l 14479 4731 l 14483 4738 l 14491 4748 l 14501 4763 l 14513 4781 l 14528 4803 l 14546 4827 l 14565 4854 l 14586 4881 l 14608 4909 l 14631 4937 l 14654 4964 l 14677 4988 l 14700 5011 l 14723 5032 l 14747 5050 l 14771 5066 l 14796 5079 l 14822 5091 l 14850 5100 l 14872 5106 l 14895 5111 l 14919 5115 l 14945 5119 l 14972 5122 l 15000 5125 l 15030 5128 l 15060 5129 l 15092 5131 l 15125 5132 l 15158 5133 l 15192 5134 l 15227 5135 l 15261 5135 l 15296 5135 l 15332 5135 l 15366 5135 l 15401 5134 l 15435 5133 l 15469 5132 l 15502 5131 l 15534 5129 l 15565 5128 l 15595 5125 l 15623 5122 l 15651 5119 l 15678 5115 l 15703 5111 l 15727 5106 l 15750 5100 l 15777 5091 l 15804 5081 l 15829 5069 l 15854 5056 l 15879 5040 l 15904 5022 l 15929 5002 l 15955 4980 l 15981 4957 l 16007 4932 l 16032 4907 l 16058 4881 l 16082 4856 l 16105 4831 l 16126 4808 l 16144 4788 l 16161 4770 l 16174 4755 l 16184 4743 l 16191 4735 l 16196 4729 l 16199 4726 l 16200 4725 l gs col-1 s gr % Polyline n 19800 4725 m 19801 4727 l 19804 4731 l 19808 4738 l 19816 4748 l 19826 4763 l 19838 4781 l 19853 4803 l 19871 4827 l 19890 4854 l 19911 4881 l 19933 4909 l 19956 4937 l 19979 4964 l 20002 4988 l 20025 5011 l 20048 5032 l 20072 5050 l 20096 5066 l 20121 5079 l 20147 5091 l 20175 5100 l 20197 5106 l 20220 5111 l 20244 5115 l 20270 5119 l 20297 5122 l 20325 5125 l 20355 5128 l 20385 5129 l 20417 5131 l 20450 5132 l 20483 5133 l 20517 5134 l 20552 5135 l 20586 5135 l 20621 5135 l 20657 5135 l 20691 5135 l 20726 5134 l 20760 5133 l 20794 5132 l 20827 5131 l 20859 5129 l 20890 5128 l 20920 5125 l 20948 5122 l 20976 5119 l 21003 5115 l 21028 5111 l 21052 5106 l 21075 5100 l 21102 5091 l 21129 5081 l 21154 5069 l 21179 5056 l 21204 5040 l 21229 5022 l 21254 5002 l 21280 4980 l 21306 4957 l 21332 4932 l 21357 4907 l 21383 4881 l 21407 4856 l 21430 4831 l 21451 4808 l 21469 4788 l 21486 4770 l 21499 4755 l 21509 4743 l 21516 4735 l 21521 4729 l 21524 4726 l 21525 4725 l gs col-1 s gr $F2psEnd rs %%EndDocument @endspecial 1710 1778 a FP(Figure)32 b(5.24)605 1972 y FQ(Then,)c(b)n(y)f(the)h(gluing)f(axiom,)1304 2130 y FJ(\034)9 b FQ(\()p FJ(@)c(H)i FQ(\))23 b FL(')1649 2051 y Fy(M)1700 2228 y FI(i)1788 2051 y Fy(O)1833 2225 y FI(a)1928 2130 y FJ(\034)9 b FQ(\(\006)2065 2142 y FI(a)2106 2130 y FQ(;)14 b FL(f)p FJ(V)2251 2096 y FI(")2233 2150 y(i)2256 2158 y FG(c)2291 2130 y FL(g)2333 2142 y FI(c)p FE(\032)p FI(@)t FM(\006)2501 2150 y FG(a)2541 2130 y FQ(\))p FJ(:)456 2348 y FQ(Here)28 b(\006)713 2360 y FI(a)782 2348 y FQ(are)f(the)i(comp)r(onen)n(ts)f(of)h FJ(@)5 b(H)i FQ(,)28 b(the)h(notation)f FJ(c)d FL(\032)f FJ(@)5 b FQ(\006)2531 2360 y FI(a)2600 2348 y FQ(means)28 b(that)h(the)g(cut)g FJ(c)g FQ(is)456 2448 y(one)i(of)g(the)h(b)r (oundary)f(comp)r(onen)n(ts)g(of)g(\006)1854 2460 y FI(a)1894 2448 y FQ(,)i(and)e FJ(V)2182 2418 y FI(")2249 2448 y FQ(is)h(either)f FJ(V)51 b FQ(or)30 b FJ(V)2847 2418 y FE(\003)2917 2448 y FQ(c)n(hosen)g(so)h(that)456 2547 y(ev)n(ery)26 b FJ(V)723 2559 y FI(i)746 2567 y FG(c)810 2547 y FQ(app)r(ears)g(in)i(the)g(tensor)f(pro)r(duct)g(once)g(as)g FJ(V)2257 2559 y FI(i)2280 2567 y FG(c)2344 2547 y FQ(and)h(once)f(as)g FJ(V)2864 2517 y FE(\003)2845 2569 y FI(i)2868 2577 y FG(c)2904 2547 y FQ(.)605 2648 y(Let)h(us)g(c)n(ho)r(ose)f(all)h FJ(i)1270 2660 y FI(c)1327 2648 y FQ(=)23 b(0,)28 b(i.e.,)g(all)g FJ(V)1829 2660 y FI(i)1852 2668 y FG(c)1912 2648 y FQ(=)23 b FK(1)p FQ(.)38 b(Then)28 b FJ(\034)9 b FQ(\(\006)2463 2660 y FI(a)2504 2648 y FQ(;)14 b FK(1)p FJ(;)g(:)g(:)g(:)g(;)g FK(1)p FQ(\))23 b(=)h FJ(k)s FQ(.)38 b(Therefore,)456 2747 y(this)27 b(giv)n(es)g(a)g(v)n(ector)1176 2905 y FJ(v)1216 2917 y FM(0)1253 2905 y FQ(\()p FJ(H)7 b FQ(\))24 b(=)1505 2826 y Fy(O)1549 3001 y FI(a)1630 2905 y FQ(\(1)f FL(2)g FJ(\034)9 b FQ(\(\006)1942 2917 y FI(a)1983 2905 y FQ(;)14 b FK(1)p FJ(;)g(:)g(:)g(:)g(;)g FK(1)p FQ(\)\))23 b FL(2)g FJ(\034)9 b FQ(\()p FJ(@)c(H)i FQ(\))p FJ(:)456 3125 y FQ(\(compare)26 b(with)i(Remark)f(4.5.4\).)605 3281 y FP(Theorem)32 b FQ(5.8.2)e(\(Crane)d([)p FK(C)p FQ(]\))p FP(.)41 b FO(The)31 b(ve)l(ctor)e FJ(v)2158 3293 y FM(0)2196 3281 y FQ(\()p FJ(H)7 b FQ(\))29 b FO(do)l(es)h(not)f (dep)l(end)h(on)f(the)h(choic)l(e)456 3381 y(of)g(the)g(cuts.)38 b(Mor)l(e)l(over,)32 b FJ(v)1330 3393 y FM(0)1367 3381 y FQ(\()p FJ(H)7 b FQ(\))30 b FO(is)g FJ(N)1693 3393 y FI(H)1756 3381 y FO(-invariant.)605 3537 y FP(Pr)n(oof.)41 b FQ(Ob)n(viously)-7 b(,)23 b(an)n(y)f(t)n(w)n(o)h(systems)f(of)h(cuts) h(of)f FJ(H)30 b FQ(in)n(to)23 b(a)g(union)g(of)g(solid)g(balls)g(can) 456 3636 y(b)r(e)28 b(related)f(to)g(one)g(another)g(b)n(y)g(a)g (sequence)g(of)h(the)g(follo)n(wing)f(mo)n(v)n(es:)605 3736 y(\(a\))h(the)g(action)f(of)g FJ(N)1292 3748 y FI(H)1355 3736 y FQ(,)h(and)f(\(b\))i(the)f(F-mo)n(v)n(e.)605 3835 y(It)k(is)f(easy)g(to)g(see)g(that)h FJ(v)1440 3847 y FM(0)1478 3835 y FQ(\()p FJ(H)7 b FQ(\))32 b(do)r(es)f(not)g(c)n(hange) g(under)g(the)h(mo)n(v)n(e)e(\(b\).)50 b(As)31 b(for)g(\(a\),)456 3935 y(one)39 b(needs)g(a)g(description)g(of)h(the)f(generators)e(of)j FJ(N)2225 3947 y FI(H)2288 3935 y FQ(.)72 b(Suc)n(h)40 b(a)f(description)g(is)g(kno)n(wn)456 4035 y([)p FK(Su)p FQ(].)j(Then)29 b(one)g(c)n(hec)n(ks)f(that)i FJ(v)1525 4047 y FM(0)1562 4035 y FQ(\()p FJ(H)7 b FQ(\))30 b(is)f(in)n(v)-5 b(arian)n(t)28 b(under)h(these)g(generators|this)e(is)i(not)456 4134 y(di\016cult|w)n(e)f(refer)e(to)i([)p FK(C)p FQ(],)g([)p FK(Ko)o FQ(])g(for)f(the)h(details.)605 4234 y(The)g(fact)f(that)h FJ(v)1159 4246 y FM(0)1197 4234 y FQ(\()p FJ(H)7 b FQ(\))28 b(is)f FJ(N)1515 4246 y FI(H)1578 4234 y FQ(-in)n(v)-5 b(arian)n(t)26 b(follo)n(ws)h(from)g(\(a\).)p 3384 4234 4 57 v 3388 4181 50 4 v 3388 4234 V 3437 4234 4 57 v 605 4399 a(No)n(w)38 b(w)n(e)f(will)i(use)f(Theorems)f(5.8.1)g(and)h (5.8.2)f(to)h(construct)f(in)n(v)-5 b(arian)n(ts)37 b(of)h(closed)456 4499 y(3-manifolds.)605 4599 y(Let)31 b FJ(M)37 b FQ(=)28 b FJ(M)1049 4611 y FI(')1125 4599 y FQ(=)g FJ(H)1287 4611 y FM(1)1345 4599 y FL(t)1400 4611 y FI(')1468 4599 y FJ(H)1537 4611 y FM(2)1605 4599 y FQ(b)r(e)k(as)e(in)h(5.8.1.)45 b(The)31 b(map)g FJ(')9 b FQ(:)29 b FJ(@)5 b(H)2762 4611 y FM(1)2856 4551 y FE(\030)2827 4599 y FL(\000)-39 b(!)p 2964 4531 155 4 v 28 w FJ(@)5 b(H)3082 4611 y FM(2)3150 4599 y FQ(giv)n(es)30 b(an)456 4708 y(isomorphism)c(of)i(v)n(ector)e (spaces)h FJ(')1594 4720 y FE(\003)1641 4708 y FQ(:)h FJ(\034)9 b FQ(\()p FJ(@)c(H)1887 4720 y FM(1)1925 4708 y FQ(\))2009 4661 y FE(\030)1980 4708 y FL(\000)-39 b(!)23 b FJ(\034)9 b FQ(\()p 2189 4641 V FJ(@)c(H)2307 4720 y FM(2)2345 4708 y FQ(\))23 b(=)g FJ(\034)9 b FQ(\()p FJ(@)c(H)2683 4720 y FM(2)2721 4708 y FQ(\))2753 4678 y FE(\003)2791 4708 y FQ(.)37 b(W)-7 b(e)28 b(de\014ne)1283 4855 y FJ(\034)9 b FQ(\()p FJ(M)g FQ(\))24 b(:=)f FJ(D)1688 4821 y FI(g)r FE(\000)p FM(1)1825 4855 y FQ(\()p FJ(')1911 4867 y FE(\003)1950 4855 y FQ(\()p FJ(v)2022 4867 y FM(0)2060 4855 y FQ(\()p FJ(H)2161 4867 y FM(1)2198 4855 y FQ(\)\))q FJ(;)14 b(v)2340 4867 y FM(0)2377 4855 y FQ(\()p FJ(H)2478 4867 y FM(2)2516 4855 y FQ(\)\))p FJ(;)-2147 b FQ(\(5.8.1\))456 5016 y(where)27 b FJ(D)e FQ(=)d FJ(s)916 4981 y FE(\000)p FM(1)916 5038 y(00)1033 5016 y FQ(is)28 b(de\014ned)g(b)n(y)g (\(3.1.15\))o(.)605 5116 y(The)e(prefactor)f FJ(D)1197 5086 y FI(g)r FE(\000)p FM(1)1347 5116 y FQ(is)g(c)n(hosen)g(in)i (order)d(that)j FJ(\034)9 b FQ(\()p FJ(M)g FQ(\))27 b(b)r(e)f(in)n(v)-5 b(arian)n(t)25 b(under)h(the)g(stabi-)456 5216 y(lization)h(mo)n(v)n(e) f(5.8.1\(c\).)36 b(Indeed,)28 b(let)g FJ(H)1786 5185 y FE(0)1832 5216 y FQ(=)22 b FJ(H)7 b FQ(#)p FJ(T)12 b FQ(.)36 b(Then)28 b FJ(@)5 b(H)2526 5185 y FE(0)2572 5216 y FQ(=)22 b FJ(@)5 b(H)i FQ(#)p FJ(@)e(T)12 b FQ(,)26 b(where)h FJ(@)5 b(T)39 b FQ(is)p eop %%Page: 134 42 134 137 bop 456 226 a FM(134)1010 b(5.)29 b(MODULAR)g(FUNCTOR)456 425 y FQ(the)f(2-torus.)35 b(By)27 b(the)h(construction)f(of)h FJ(v)1797 437 y FM(0)1834 425 y FQ(\()p FJ(H)1942 395 y FE(0)1965 425 y FQ(\))g(it)g(is)g(clear)e(that)1502 560 y FJ(v)1542 572 y FM(0)1579 560 y FQ(\()p FJ(H)1687 525 y FE(0)1711 560 y FQ(\))d(=)g FJ(v)1894 572 y FM(0)1931 560 y FQ(\()p FJ(H)7 b FQ(\))19 b FL(\012)f FJ(v)2213 572 y FM(0)2250 560 y FQ(\()p FJ(T)12 b FQ(\))p FJ(:)456 695 y FQ(Then)937 829 y FJ(\034)d FQ(\()p FJ(M)1104 795 y FE(0)1128 829 y FQ(\))23 b(=)g FJ(D)1342 795 y FI(g)1394 829 y FQ(\(\()p FJ(')p FQ(#)p FJ(s)p FQ(\))1652 841 y FE(\003)1692 829 y FQ(\()p FJ(v)1764 841 y FM(0)1802 829 y FQ(\()p FJ(H)1903 841 y FM(1)1940 829 y FQ(\))c FL(\012)f FJ(v)2114 841 y FM(0)2151 829 y FQ(\()p FJ(T)12 b FQ(\)\))p FJ(;)i(v)2385 841 y FM(0)2423 829 y FQ(\()p FJ(H)2531 795 y FE(0)2524 850 y FM(2)2561 829 y FQ(\))q(\))1183 959 y(=)23 b FJ(\034)9 b FQ(\()p FJ(M)g FQ(\))p FJ(D)17 b FQ(\()p FJ(s)1627 971 y FE(\003)1665 959 y FJ(v)1705 971 y FM(0)1743 959 y FQ(\()p FJ(T)12 b FQ(\))o FJ(;)i(v)1944 971 y FM(0)1982 959 y FQ(\()p FJ(T)e FQ(\))o(\))24 b(=)e FJ(\034)9 b FQ(\()p FJ(M)g FQ(\))p FJ(D)r(s)2558 971 y FM(00)2652 959 y FQ(=)23 b FJ(\034)9 b FQ(\()p FJ(M)g FQ(\))p FJ(:)605 1093 y FQ(Therefore,)31 b(w)n(e)g(ha)n(v)n(e)f (constructed)h(an)g(in)n(v)-5 b(arian)n(t)30 b FJ(\034)41 b FQ(of)32 b(closed)e(3-manifolds.)47 b(T)-7 b(o)31 b(con-)456 1193 y(struct)i(3D)h(TQFT,)f(w)n(e)h(ha)n(v)n(e)e(to)h(de\014ne)h FJ(\034)9 b FQ(\()p FJ(M)g FQ(\))35 b(for)e(an)n(y)g(3-manifold)g FJ(M)42 b FQ(with)34 b(b)r(oundary)-7 b(.)456 1293 y(T)g(o)30 b(do)h(so,)g(w)n(e)g(need)g(a)g(v)-5 b(arian)n(t)30 b(of)h(Heegaard)f (splitting)h(for)f(3-manifolds)h(with)g(b)r(oundary)-7 b(.)456 1392 y(There)27 b(is)h(suc)n(h)g(a)g(theorem,)g(due)g(to)g (Motto)g([)p FK(Mo)o FQ(].)39 b(His)28 b(result)g(is)g(similar)g(to)g (what)g(w)n(e)g(had)456 1492 y(b)r(efore,)36 b(only)f(one)g(has)f(to)h (consider)g(not)g(only)f(handleb)r(o)r(dies)h(but)h(also)e(\\hollo)n(w) g(handle-)456 1592 y(b)r(o)r(dies".)41 b(A)30 b(hollo)n(w)e(handleb)r (o)r(dy)h(is)g(a)g(handleb)r(o)r(dy)h(with)f(some)g(parts)f(of)i(its)f (in)n(terior)f(cut)456 1691 y(out.)47 b(Hence,)32 b(it)g(has)e(b)r(oth) i(\\inner")e(and)h(\\outer")e(b)r(oundary)-7 b(.)47 b(W)-7 b(e)32 b(glue)e(t)n(w)n(o)h(suc)n(h)f(hollo)n(w)456 1791 y(handleb)r(o)r(dies)23 b(b)n(y)g(iden)n(tifying)h(their)f(outer)g(b)r (oundaries,)g(the)h(remaining)e(inner)h(b)r(oundaries)456 1890 y(giv)n(e)j(the)i(b)r(oundary)f(of)h(the)g(resulting)f (3-manifold.)605 1990 y(Then)39 b(w)n(e)f(can)h(rep)r(eat)f(the)h(ab)r (o)n(v)n(e)f(construction)f(of)i FJ(\034)9 b FQ(\()p FJ(M)g FQ(\))40 b(for)e(manifolds)h FJ(M)47 b FQ(with)456 2090 y(b)r(oundary)-7 b(.)36 b(This)27 b(giv)n(es)g(the)h(implication) 1053 2224 y FL(C)5 b FQ(-extended)27 b(2D)h(MF)23 b FL(!)g FQ(\(non-extended\))28 b(3D)f(TQFT)p FJ(:)456 2359 y FQ(In)c(order)e(to)i(go)f(one)g(step)h(further,)h(i.e.,)g(to)f (construct)f(a)g FL(C)5 b FQ(-extended)23 b(3D)f(TQFT,)h(one)g(needs) 456 2459 y(an)18 b(analog)f(of)h(Heegaard)f(splitting)i(and)f (Reidemeister{Singer)f(theorem)h(for)g(manifolds)g(with)456 2558 y(b)r(oundary)31 b(and)h(mark)n(ed)f(p)r(oin)n(ts.)51 b(T)-7 b(o)32 b(the)g(b)r(est)h(of)f(our)g(kno)n(wledge,)g(suc)n(h)g(a) f(result)h(is)g(not)456 2658 y(a)n(v)-5 b(ailable)25 b(at)i(the)g(momen)n(t.)36 b(Hop)r(efully)-7 b(,)28 b(this)f(is)f(only) h(a)f(temp)r(orary)f(di\016cult)n(y)-7 b(.)37 b(Finally)-7 b(,)27 b(let)456 2758 y(us)34 b(note)f(that)i(if)f(w)n(e)g(start)f (with)i(a)e(non-extended)h(2D)g(MF,)g(without)h(gluing)e(axiom,)i(the) 456 2857 y(construction)26 b(of)i(3D)g(TQFT)f(w)n(ould)g(fail.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF