K-theory for real C*-algebras
Prof. Bernd Ammann, Zimmer 119
Veranstaltungsnummer (LSF) 51097
Die Vorlesung wird auf das Wintersemester 2018/19 verschoben
The lecture will be pushed to the Winter term 2018/19
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 Schröder, 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