#### Volume 16, issue 3 (2012)

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Geodesic flow for $\mathrm{CAT}(0)$–groups

### Arthur Bartels and Wolfgang Lück

Geometry & Topology 16 (2012) 1345–1391
##### Abstract

We associate to a $CAT\left(0\right)$–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 $CAT\left(0\right)$–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.

##### Keywords
geodesic flow space, $\mathrm{CAT}(0)$–groups, Farrell–Jones Conjecture
Primary: 20F67