CRC 878 C03 - Baum-Connes conjecture and expanders

Basic data for this project

Description

We study C*-algebras constructed from locally compact (semi)groups or group actions, by means of topological invariants such as their K-theory groups. One major tool for this is given by (confirmed cases of) the Baum-Connes conjecture. Known counterexamples to the Baum-Connes conjecture involve groups (Gromov's monster groups) that admit coarse embeddings of expanders. We will study a new formulation of the conjecture that avoids the existing counterexamples, and we will study the relation between the coarse geometry of expanders and rigidity properties for groups and operator algebras.