Geodesic flow for CAT(0)-groups

Abstract

We associate to a CAT(0)-space a flow space that can be used as the replacement for the geodesic flow on the sphere tangent bundle of a Riemannian manifold. We use this flow space to prove that CAT(0)-group are transfer reducible over the family of virtually cyclic groups. This result is an important ingredient in our proof of the Farrell-Jones Conjecture for these groups.