#### 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
##### Publication
Received: 16 September 2010
Revised: 12 March 2012
Accepted: 2 June 2012
Published: 20 July 2012
Proposed: Martin R Bridson
Seconded: Walter Neumann, Steve Ferry
##### Authors
 Arthur Bartels Mathematisches Institut Westfälische Wilhelms-Universität Münster Einsteinstr. 62 D-48149 Münster Germany http://www.math.uni-muenster.de/u/bartelsa/ Wolfgang Lück Mathematisches Institut Rheinische Wilhelms-Universität Bonn Endenicher Allee 62 53115 Bonn Germany http://www.him.uni-bonn.de/lueck/