Taking place at Université Pierre et Marie Curie, 8th of June, 2017.

Alain Valette (Université de Neuchâtel)

## Explicit Baum-Connes for lamplighter groups over finite groups

We consider a lamplighter group *G*= wreath product of *F* and **Z**, with *F* a finite group. Although the Baum-Connes is known for *G* (because *G* is amenable), it does not allow for an explicit computation either of the left-hand side (the *G*-equivariant K-homology of the classifying space of *G*-proper actions) or the right-hand side (the analytical K-theory of the reduced *C^**-algebra of *G*). We provide an explicit proof of the Baum-Connes conjecture for *G*, by computing both sides and then the assembly map connecting them. We will focus in the talk on the left-hand side, where computation is made possible thanks to a 2-dimensional model for the classifying space.

This is joint work with Ramon Flores and Sanaz Pooya.

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