Algebraic & Geometric Topology 10 (2010) 2229–2250

DOI: 10.2140/agt.2010.10.2229

Abstract

If Γ is a group acting properly by semisimple isometries on a proper CAT(0) space X, then we build models for the classifying spaces E_VCΓ and E_FBCΓ under the additional assumption that the action of Γ has a well-behaved collection of axes in X. We verify that the latter assumption is satisfied in two cases: (i) when X has isolated flats, and (ii) when X is a simply connected real analytic manifold of nonpositive sectional curvature. We conjecture that Γ has a well-behaved collection of axes in the great majority of cases.

Our classifying spaces are natural variations of the constructions due to Connolly, Fehrman and Hartglass [arXiv:math.AT/0610387] of E_VCΓ for crystallographic groups Γ.

Keywords

CAT(0) space, classifying space, virtually cyclic group

Mathematical Subject Classification

Primary: 18F25, 55N15

Secondary: 20F65

References

Publication

Received: 14 February 2009
Revised: 31 August 2010
Accepted: 2 September 2010
Published: 30 October 2010

Authors