The Tits Alternative for Cat(0) Cubical Complexes

Abstract

a tits alternative theorem is proved in this paper for groups acting on cat(0) cubical complexes. that is, a proof is given to show that if $g$ is assumed to be a group for which there is a bound on the orders of its finite subgroups, and 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.