Tits Alternative for groups acting properly on $2$-dimensional recurrent complexes (with an appendix written jointly with Jon McCammond)

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.

Final version accepted for publication

References in corpus (3)

• Large-type Artin groups are systolic
• Cubical-like geometry of quasi-median graphs and applications to geometric group theory
• Torsion groups do not act on $2$-dimensional $\mathrm{CAT}(0)$ complexes