# 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
- (Real) C
^{*}-algebras
- Clifford algebras
- Crossed products
- KO-theory
- Real Hilbert modules
- Kasparov's KK- and KKO-theory
- intersection product and periodicity in KK-theory
- pseudodifferential operators
- index theorems for foliations

## Prerequisites

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
## Literature

- Herbert SchrÃ¶der, K-theory for real
C
^{*}-algebras and applications, Pitman Research Notes in Math. Series, Longman Scientific & Technical
- Bruce Blackadar, K-theory for operator algebras, MSRI Publications Vol. 5

## Linked Websites

## Kriterien für Leistungsnachweise

Siehe kommentiertes Vorlesungsverzeichnis.

Bernd Ammann, 23.1.2018 oder später