Index theory for (regular) foliations

This is the page of  my weekly seminar in the Athens math dept. for 2011-12. Announcements about this seminar will appear in this page -- lecture notes (in greek) will be posted here.

Next lecture: 11:15 a.m., Friday October 21, 2011. "The Dirac operator and the Euler characteristic of a compact manifold"

  1. Fredholm operators
  2. Pseudo-differential operators (definition, ellipticity, analytical index)
  3. K-theory of C*-algebras (definition and relation with topological K-theory, exact sequences, Bott periodicity)
  4. Topological index (definition, Chern character, characteristic classes)
  5. Equality of the two indices (Atiyah-Singer theorem)
  1. Introduction to (regular) foliations (definition, examples, the notion of holonomy, the holonomy groupoid and its C*-algebra)
  2. Transverse measures (holonomy invariant measures, Ruelle-Sullivan current)
  3. Locally traceable operators
  4. Connes' measured index theorem for foliations.