KK-theory with real coefficients, traces, and discrete group actions

Sara Azzali (University of Potsdam)

Thursday 21st February, 2019 16:00-17:00 Maths 311B

Abstract

The groups of KK-theory were introduced by Kasparov in the 1980’s and have important applications to many geometric and topological problems which are tackled by C*-algebraic techniques. Kasparov groups provide for instance a framework to understand and conceptualise the proofs of index theorems.In this talk, we investigate KK-theory groups with coefficients in R. By construction, the adding of real coefficients provides natural receptacles for classes coming from traces on C*-algebras.

We focus on two applications to the study of discrete groups actions on C*-algebras. One of them is the construction of R/Z-secondary classes associated to unitary representations of discrete groups.The second point is that in real equivariant KK-theory one can "localise at the unit element“ of the discrete group, and this procedure has interesting consequences on the Baum–Connes isomorphism conjecture.

Based on joint works with Paolo Antonini (Trieste) and Georges Skandalis (Paris 7).

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