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

2019/04/16 by Damian Osajda, Osajda, Damian, Piotr Przytycki +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR

paper · pdf · doi:10.48550/arxiv.1904.07796

Final version accepted for publication

openalex publication_date 2019/04/16 · openalex created_date 2019/06/27 · arxiv created 2021/07/22 · arxiv updated 2021/07/26 · openalex updated_date 2026/07/28

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.

Citations

• Cubical-like geometry of quasi-median graphs and applications to geometric group theory

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