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The Tits alternative for CAT(0) cubical complexes

Michah Sageev·Daniel T. Wise
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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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Michah Sageev, Daniel T. Wise. 2004-05-02. The Tits alternative for CAT(0) cubical complexes. https://arxiv.org/abs/math/0405022

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