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.

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

Volume 1, issue 1 (1997)

Graham A Niblo and Lawrence Reeves