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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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13 Sep 2002 | Journal: | New York J. Math.}, 8:1--7 (electronic), 2002 | Subject: | Metric Geometry; Geometric Topology MSC-class: 20F67 (hyperbolic groups), 55R35 (classifying spaces), 57M07 | math.MG math.GT | Affiliation: | Universitaet der Bundeswehr Muenchen) Thomas Schick (Universitaet Goettingen | 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. | Source: | arXiv, math.MG/0209163 | Services: | Forum | Review | PDF | Favorites |
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