Groups acting on CAT(0) cube complexes
classification
🧮 math.GR
math.DG
keywords
cubecomplexesdimensionalfinitegroupslocallyactingactions
read the original 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.
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