The Tits alternative for CAT(0) cubical complexes

2004/05/02 by Michah Sageev, Sageev, Michah, Daniel T. Wise +1 · 1 citation
Mathematics · #20E08 #20F67 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20E08 #msc:20F67

paper · pdf · doi:10.48550/arxiv.math/0405022

5 pages

arxiv created 2004/05/02 · arxiv updated 2009/12/01

Abstract

We prove a Tits alternative theorem for groups acting on CAT(0) cubical complexes. Namely, suppose that G is a group for which there is a bound on the orders of its finite subgroups. We prove that if G acts properly on a finite-dimensional CAT(0) cubical complex, then either G contains a free subgroup of rank 2 or G is finitely generated and virtually abelian. In particular the above conclusion holds for any group G with a free action on a finite-dimensional CAT(0) cubical complex.

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