Volume 1, issue 1 (1997)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Groups acting on CAT(0) cube complexes

Graham A Niblo and Lawrence Reeves

Geometry & Topology 1 (1997) 1–7

arXiv: math.GR/9702231

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.

Keywords
Kazhdan's property (T), Tits' buildings, hyperbolic geometry, CAT(0) cube complexes, locally CAT(-1) spaces, $Sp(n,1)$–manifolds
Mathematical Subject Classification
Primary: 20F32
Secondary: 20E42, 20G20
References
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Publication
Received: 28 October 1996
Accepted: 6 February 1997
Published: 7 February 1997
Proposed: Walter Neumann
Seconded: David Gabai, Robion Kirby
Authors
Graham A Niblo
Faculty of Mathematical Studies
University of Southampton
Highfield
Southampton
SO17 1BJ
United Kingdom
Lawrence Reeves
Institute of Mathematics
Hebrew University of Jerusalem
Givat Ram
Jerusalem 91904
Israel