Groups acting on CAT(0) cube complexes

Details Groups acting on CAT(0) cube complexes Groups acting on CAT(0) cube complexes

1997-02-07

arxiv.org/abs/math/9702231v1

Geom. Topol. 1 (1997), 1-7

Mathematics

Group Theory

7 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper1.abs.html

Scientific paper

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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