Groups acting on CAT(0) cube complexes

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.

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

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