NMAK13010U  Introduction to Equivariant KK-theory and Baum-Connes Conjecture

Volume 2013/2014
Education
MSc programme in Mathematics
Content
Hilbert modules; Definition and basic properties of (equivariant) KK-theory for C*-algebras; The Kasparov product; Applications to K-theory (including the Baum-Connes conjecture).
Learning Outcome
Knowledge: By the end of the course, the student will be familiar with the basic definitions and properties of KK-theory, and its relationship to K-theory for C*-algebras.

Skills
: The student will be able to give precise statements of the main definitions, theorems and examples in the subject, and provide proofs of the standard properties of KK-theory.

Competences
: The student will use the basic results to construct classes in KK-theory, and to compute K- and KK-groups and Kasparov products, in particular cases. The student will apply these computations to a variety of problems in operator algebras, topology, and representation theory.
Topological K-theory for operator algebras.
5 hours of lectures and 3 hours of exercises per week.
Credit
7,5 ECTS
Type of assessment
Continuous assessment
The assessment will be via regular written assignments.
Marking scale
7-point grading scale
Censorship form
No external censorship
one internal examiner.
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.

  • Category
  • Hours
  • Lectures
  • 45
  • Theory exercises
  • 27
  • Preparation
  • 134
  • Total
  • 206