Geometry & Topology

Groups acting on CAT(0) cube complexes

Graham A Niblo and Lawrence Reeves

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Abstract

We show that groups satisfying Kazhdan’s property (T) have no unbounded actions on finite dimensional CAT(0) cube complexes, and deduce that there is a locally CAT(−1) Riemannian manifold which is not homotopy equivalent to any finite dimensional, locally CAT(0) cube complex.

Article information

Source
Geom. Topol., Volume 1, Number 1 (1997), 1-7.

Dates
Received: 28 October 1996
Accepted: 6 February 1997
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513882841

Digital Object Identifier
doi:10.2140/gt.1997.1.1

Mathematical Reviews number (MathSciNet)
MR1432323

Zentralblatt MATH identifier
0887.20016

Subjects
Primary: 20F32
Secondary: 20E42: Groups with a $BN$-pair; buildings [See also 51E24] 20G20: Linear algebraic groups over the reals, the complexes, the quaternions

Keywords
Kazhdan's property (T) Tits' buildings hyperbolic geometry CAT(0) cube complexes locally CAT(-1) spaces $Sp(n,1)$–manifolds

Citation

Niblo, Graham A; Reeves, Lawrence. Groups acting on CAT(0) cube complexes. Geom. Topol. 1 (1997), no. 1, 1--7. doi:10.2140/gt.1997.1.1. https://projecteuclid.org/euclid.gt/1513882841


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References

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    Zentralblatt MATH: 0861.20041

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Geometry & Topology

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