Volume 1, issue 1 (1997)

Download this article
For printing
Recent Issues

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

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
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
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