K-theory for real C*-algebras

Prof. Bernd Ammann, Zimmer 119

Content of the lecture

In the lecture we develop and study K-theory and KK-theory for real C*-algebras, often called KO-theory and KKO-theory. We plan to cover the following topics. We are interested in the real (and not the complex) theory as this allows more refined applications to geometric problems. We will cover the following subjects
  1. (Real) C*-algebras
  2. Clifford algebras
  3. Crossed products
  4. KO-theory
  5. Real Hilbert modules
  6. Kasparov's KK- and KKO-theory
  7. intersection product and periodicity in KK-theory
  8. pseudodifferential operators
  9. index theorems for foliations


For parts 1.-6. of the lecture we do not require more specialized knowledge than functional analysis in order to follow the lecture itself. However to understand the motivation for studying KO-theory and some of the examples, knowledge about geometry and topology, in particular the Atiyah-Singer index theorem is very helpful. In the last part foliations and pseudo-differential operators will be used, which will be briefly recalled.

Time and Room

Wednesday, 8:30-10:00 in M101


Linked Websites

Kriterien für Leistungsnachweise

Siehe kommentiertes Vorlesungsverzeichnis.
Bernd Ammann, 23.1.2018 oder später