Geodesic flow for CAT(0)–groups

Bartels, Arthur¹ ; Lück, Wolfgang²

¹ Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany
² Mathematisches Institut, Rheinische Wilhelms-Universität Bonn, Endenicher Allee 62, 53115 Bonn, Germany

Geometry & topology, Tome 16 (2012) no. 3, pp. 1345-1391.

Résumé

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.

Détail

DOI : 10.2140/gt.2012.16.1345

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

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