On Commensurability Invariance of the Farrell-Jones Conjecture

Kun Wang  (Vanderbilt University)

14:00 pm to 14:50 pm, June 5th, 2015   Science Building A1414

Abstract:

The Farrell-Jones conjecture in algebraic K- and L-theories is a cousin of the Baum-Connes conjecture in topological K-theory. As well as the Baum-Connes conjecture, the Farrell-Jones conjecture has many applications in geometry and topology. For example, it implies the Borel conjecture on topological rigidity of closed aspherical manifolds and the Novikov conjecture on homotopy invariance of higher signatures. From the viewpoint of coarse geometry, it's a natural question that whether the conjecture is coarsely in- variant. In this talk, I will present some recent progress on the following weaker problem: whether the conjecture is commensurably invariant, i.e. if two groups have isomorphic subgroups of nite indices and if one of the groups satisfies the conjecture, whether the other group also satisfies the conjecture.