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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Geodesic flow for $\mathrm{CAT}(0)$–groups

Arthur Bartels and Wolfgang Lück

Geometry & Topology 16 (2012) 1345–1391
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.

Keywords
geodesic flow space, $\mathrm{CAT}(0)$–groups, Farrell–Jones Conjecture
Mathematical Subject Classification 2000
Primary: 20F67
References
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/