Colloquium on the Geometry of Groups and Numbers

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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