On the classifying space of the family of finite and of virtually cyclic subgroups for CAT(0)-groups

Details On the classifying space of the family of finite and of virtually cyclic subgroups for CAT(0)-groups On the classifying space of the family of finite and of virtually cyclic subgroups for CAT(0)-groups

2009-02-04

arxiv.org/abs/0902.0718v1

Mathematics

Algebraic Topology

14 pages

Scientific paper

Let G be a discrete group which acts properly and isometrically on a complete CAT(0)-space X. Consider an integer d with d=1 or d greater or equal to 3 such that the topological dimension of X is bounded by d. We show the existence of a G-CW-model E_fin(G) for the classifying space for proper G-actions with dim(E_fin(G)) less or equal to d. Provided that the action is also cocompact, we prove the existence of a G-CW-model E_vcyc(G) for the classifying space of the family of virtually cyclic subgroups such that dim(E_vcyc(G)) is less or equal to d+1.

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