Constructions of E_{vc} and E_{fbc} for groups acting on CAT(0) spaces

Abstract

If G is a group acting properly by semisimple isometries on a proper CAT(0) space X, then we build models for the classifying spaces E_{vc} and E_{fbc} under the additional assumption that the action of G has a well-behaved collection of axes in X. (This hypothesis is described in the paper.) We conjecture that the latter hypothesis is satisfied in a large range of cases. Our classifying spaces resemble those created by Connolly, Fehrman, and Hartglass for crystallographic groups G.

16 pages, no figures

References in corpus (1)

• Hadamard spaces with isolated flats

Cited by in corpus (2)

• On classifying spaces for the family of virtually cyclic subgroups in mapping class groups
• Models for classifying spaces for $\mathbb{Z}⋊\mathbb{Z}$