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