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

Original · EN

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 Efin(G) for the classifying space for proper G-actions with dim(Efin(G)) less or equal to d. Provided that the action is also cocompact, we prove the existence of a G-CW-model Eᵥcyc(G) for the classifying space of the family of virtually cyclic subgroups such that dim(Eᵥcyc(G)) is less or equal to d+1.