Geodesic
Constructions of E𝒱𝒞 and Eℱℬ𝒞 for groups acting on CAT(0) spaces
Farley, Daniel1
1Department of Mathematics, Miami University, Room 123 Bachelor Hall, Oxford OH 45056, USA
Algebraic and Geometric Topology, Tome 10 (2010) no. 4, pp. 2229-2250
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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 EℱℬCΓ 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.

DOI : 10.2140/agt.2010.10.2229
Keywords: $\mathrm{CAT}(0)$ space, classifying space, virtually cyclic group

Farley, Daniel  1

1 Department of Mathematics, Miami University, Room 123 Bachelor Hall, Oxford OH 45056, USA 
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Farley, Daniel. Constructions of E𝒱𝒞 and Eℱℬ𝒞 for groups acting on CAT(0) spaces. Algebraic and Geometric Topology, Tome 10 (2010) no. 4, pp. 2229-2250. doi: 10.2140/agt.2010.10.2229

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