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2010 Constructions of $E_{\mathcal{VC}}$ and $E_{\mathcal{FBC}}$ for groups acting on $\mathrm{CAT}(0)$ spaces
Daniel Farley
Algebr. Geom. Topol. 10(4): 2229-2250 (2010). DOI: 10.2140/agt.2010.10.2229


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 EVCΓ and ECΓ 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 EVCΓ for crystallographic groups Γ.


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Daniel Farley. "Constructions of $E_{\mathcal{VC}}$ and $E_{\mathcal{FBC}}$ for groups acting on $\mathrm{CAT}(0)$ spaces." Algebr. Geom. Topol. 10 (4) 2229 - 2250, 2010.


Received: 14 February 2009; Revised: 31 August 2010; Accepted: 2 September 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1251.20038
MathSciNet: MR2745670
Digital Object Identifier: 10.2140/agt.2010.10.2229

Primary: 18F25 , 55N15
Secondary: 20F65

Keywords: $\mathrm{CAT}(0)$ space , classifying space , virtually cyclic group

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.10 • No. 4 • 2010
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