Volume 1, issue 1 (1997)

Download this article
For printing
Recent Issues

Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
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
Forward citations
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