Sanaz Pooya: On the Baum–Connes assembly map for certain semi-direct products

Abstract: The Baum–Connes conjecture for a group G predicts that the assembly map \(\mu_i^G\colon K_i^G(\underline{E}G)\to K_i(C^*_rG)\) is an isomorphism for i = 0,1. A breakthrough result of Higson and Kasparov shows that a-T-menable groups satisfy the conjecture, hence the group \(G=F \wr \mathbb{F}_n\), where F is finite and \(\mathbb{F}_n\) is a free group. This result however does not describe the K-groups. In this talk, we shed light on the assembly map for this group and describe it explicitly. In doing so we reprove the conjecture for this group.