Prof. D. Kotschick: Seminar on secondary characteristic classes

• Time (tentative): Thu 14--16
• Summary: Whereas the usual, or primary, characteristic classes are topological invariants of vector bundles, secondary characteristic classes are geometric invariants, which depend on the choice of a geometric structure, for example a connection. Secondary characteristic classes often arise from the vanishing of some primary class. Unlike primary classes, the secondary ones can have nontrivial continuous variations, or, if they do not, then their rigidity is in itself a non-trivial property.
  In this seminar we will discuss various examples of secondary characteristic classes, such as
  (1) Chern-Simons invariants,
  (2) Godbillon-Vey invariants of foliations,
  (3) Maslov classes from symplectic geometry, and
  (4) characteristic classes of surface bundles.
  We may also discuss
  (5) Bott-Chern classes
  and other invariants from complex or conformal geometry. The discussions of the different invariants share a common leitmotif, but are logically independent of each other.
• Intended audience: Master and PhD students of mathematics and/or physics.
• Prerequisites: Some knowledge of differential geometry and of algebraic topology, in particular cohomology theory and primary characteristic classes.
• References:
  General background, especially on primary characteristic classes and Chern-Weil theory:
  [MS] J.W. Milnor and J.D. Stasheff: Characteristic classes, Princeton University Press
  [Du] J. Dupont: Curvature and characteristic classes, Springer LNM
  References for talks in the seminar:
  [CS] S.S. Chern and J. Simons: Characteristic forms and geometric invariants, Annals of Math. 1974
  [Do] S.K. Donaldson: Floer homology groups in Yang-Mills theory, Cambridge UP
  [Ch] S.S. Chern Complex manifolds without potential theory, Springer Verlag
  [Pi] H.V. Pittie: Characteristic classes of foliations, Pitman Publishing
  [Mo] S. Morita: Geometry of characteristic classes, American Mathematical Society
  [Va] I. Vaisman: Symplectic Geometry and Secondary Characteristic Classes, Birkhäuser Verlag
  
• Special note because of Covid-19 restrictions: The time of meetings is still to be determined, and I will take into consideration participants' preferences. Talks will have to be given via zoom. To get access to information about the seminar, you need to sign up by email. To do so, please send me an email adhering closely to the following format:
  Recipient: D.Kotschick@lmu.de
  subject line: secondary invariants
  In the body of the message please write the following data, in the order given here:
  Last name, First name,
  Email address,
  Matriculation number,
  Course of study (e.g. master mathematics, or TMP).
  Please indicate which of the types of secondary characteristic classes you would like to talk about, referring to the list above.