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.

Cited by in corpus (12)

• The Farrell-Jones Conjecture for virtually solvable groups
• Coarse flow spaces for relatively hyperbolic groups
• The Farrell-Jones conjecture for S-arithmetic groups
• The Farrell-Jones conjecture for hyperbolic and CAT(0)-groups revisited
• On the transfer reducibility of certain Farrell-Hsiang groups
• Long and thin covers for flow spaces
• K- and L-theory of group rings over GL_n(Z)
• The K-theoretic Farrell-Jones conjecture for CAT(0)-groups
• On the K-theory of subgroups of virtually connected Lie groups
• On equivariant asymptotic dimension
• The Farrell-Jones Conjecture for some nearly crystallographic groups
• On the Farrell-Jones conjecture for localising invariants