The Baum-Connes conjecture for the dual of SU$_q$(2)
Seminar Room 1, Newton Institute
We describe the proof of an analogue of the Baum-Connes conjecture for the dual of the quantum SU(2) group of Woronowicz. Following the work of Meyer and Nest, the formulation of the conjecture is based on the use of triangulated categories arising from equivariant Kasparov theory. The main ingredient in the proof is an explicit analysis of the equivariant K-theory and K-homology of the standard Podles sphere. This involves the study of equivariant Fredholm modules representing twisted Dirac operators as well as Hopf-Galois theory and the equivariant Chern character.