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Groups acting on CAT(0) cube complexes

Groups acting on CAT(0) cube complexes
Groups acting on CAT(0) cube complexes
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.
kazhdan's property (t), tits' buildings, hyperbolic geometry, cat(0) cube complexes, locally cat(-1) spaces, Sp(n, 1)–manifolds
1464-8997
1-7
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
Reeves, Lawrence
864c4df0-4a83-429d-8411-7deffe430c61
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
Reeves, Lawrence
864c4df0-4a83-429d-8411-7deffe430c61

Niblo, Graham and Reeves, Lawrence (1997) Groups acting on CAT(0) cube complexes. Geometry and Topology Monographs: The Epstein Birthday Schrift, 1, 1-7. (doi:10.2140/gt.1997.1.1).

Record type: Article

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.

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Published date: 1997
Keywords: kazhdan's property (t), tits' buildings, hyperbolic geometry, cat(0) cube complexes, locally cat(-1) spaces, Sp(n, 1)–manifolds

Identifiers

Local EPrints ID: 29814
URI: http://eprints.soton.ac.uk/id/eprint/29814
ISSN: 1464-8997
PURE UUID: 375f5458-3ab0-4e89-8e71-385df5abae94
ORCID for Graham Niblo: ORCID iD orcid.org/0000-0003-0648-7027

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Date deposited: 06 Feb 2007
Last modified: 16 Mar 2024 02:44

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Contributors

Author: Graham Niblo ORCID iD
Author: Lawrence Reeves

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