Geodesic flow for CAT(0)–groups

Bartels, Arthur; Lück, Wolfgang

doi:10.2140/gt.2012.16.1345

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

Arthur Bartels and Wolfgang Lück

Geometry & Topology 16 (2012) 1345–1391

DOI: 10.2140/gt.2012.16.1345

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/

Volume 16, issue 3 (2012)