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A Model for the Universal Space for Proper Actions of a Hyperbolic Group

David Meintrup·Thomas Schick
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Abstract

Let $G$ be a word hyperbolic group in the sense of Gromov and $P$ its associated Rips complex. We prove that the fixed point set $P^H$ is contractible for every finite subgroups $H$ of $G$. This is the main ingredient for proving that $P$ is a finite model for the universal space $e.g.$ of proper actions. As a corollary we get that a hyperbolic group has only finitely many conjugacy classes of finite subgroups.

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David Meintrup, Thomas Schick. 2007-02-21. A Model for the Universal Space for Proper Actions of a Hyperbolic Group. https://arxiv.org/abs/math/0209163

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