Tits Alternative for groups acting properly on 2-dimensional recurrent complexes

Abstract

We prove the Tits Alternative for groups acting on 2-dimensional “recurrent” complexes with uniformly bounded cell stabilisers. This class of complexes includes, among others: 2-dimensional Euclidean buildings, 2-dimensional systolic complexes, B(6)-small cancellation complexes, and standard Cayley complexes for Artin groups of extra-large type.In the appendix written jointly with Jon McCammond we extend the result to a class of 2-dimensional Artin groups containing all large-type Artin groups.