Seminar on Manifolds, SS 2003, Prof. D. Kotschick
Topology of Foliations
Time and place: Tuesdays, 4-6pm, HS 252
Information: http://129.187.111.185/lehrveranstaltungen/foliat.html,
Dr. Thilo Kuessner, Office 307, Tel.: 2180-4625
| Seminar 1
29.04.03 J.Kedra |
Construction of examples I (codimension one)
foliated bundles, suspension, gluing foliations, the Reeb foliation, turbulization (Sources: [CC] ch.3, [HH] ch.IV, 3-5) |
| Seminar 2
06.05.03 V.Strazdin |
Construction of examples II (codimension one)
open book decompositions, foliations on open books, some examples on spheres and on other manifolds (Source: [HH] ch.IV,6 ) |
| Seminar 3
13.05.03 S.Eberle |
Novikov's theorem
foliations of reducible 3-manifolds have a compact leaf, proof based on minimal surfaces (Source: [H], th.2.8 ) |
| Seminar 4
20.05.03 Th.Vogel |
Compact leaves in codimension one
Thurston's stability theorem; tautness of foliations of 3-manifolds without torus leaves (Source: [CC], ch.6 ) |
| Seminar 5
27.05.03 E.Volkov |
Poincare-Bendixson theory and Haefliger's theorem
foliated Morse theory, non-existence of analytic foliations on the sphere (Source: [CC], ch.7 ) |
| Seminar 6
03.06.03 T.Moriyama |
Hector's theorem
existence of local minimal sets (Source: [CC], ch.8.1) |
| Seminar 6
17.06.03 T.Kuessner |
Sacksteder's theorem
exceptional local minimal sets contain resilient leaves (Source: [CC] ch.8.2) |
| Seminar 7
24.06.03 A.Stadelmaier |
Codimension one foliations without holonomy I
foliations without holonomy have a leaf-preserving flow (Source: [CC], ch.9.1,9.2 ) |
| Seminar 8
01.07.03 M.Hamilton |
Codimension one foliations without holonomy II
transverse measures and nonsingular 1-forms, Tischler's theorem (Source: [CC], ch.9.3,9.4) |
| Seminar 9
08.07.03 N.N. |
Construction of examples III (higher codimension)
foliated surgeries, some existence results for 2-dimensional foliations on 4-manifolds (Sources: [S], ex.7.1, sect.9.2; [CC], ch.3) |
ReferenceS:
| [CC] | A.Candel, L.Conlon: Foliations I, Graduate Studies in Mathematics, vol. 23, American Mathematical Society (2000) |
| [HH] | G.Hector, U.Hirsch: Introduction to the geometry of foliations, part B, Vieweg Verlag (1987). |
| [H] | J.Hass: Minimal surfaces in foliated 3-manifolds, Comment.Math.Helv. 61 (1986). |
| [S] | A. Scorpan: A quick survey of foliations on 4-manifolds, http://xxx.uni-augsburg.de/abs/math.GT/0302323 |