A note on the acylindrical hyperbolicity of groups acting on CAT(0) cube complexes

Indira Chatterji, Alexandre Martin

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

5 Citations (Scopus)

Abstract

We study the acylindrical hyperbolicity of groups acting by isometries on CAT(0) cube complexes, and obtain simple criteria formulated in terms of stabilisers for the action. Namely, we show that a group acting essentially and non-elementarily on a finite dimensional irreducible CAT(0) cube complex is acylindrically hyperbolic if there exist two hyperplanes whose stabilisers intersect along a finite subgroup. We also give further conditions on the geometry of the complex so that the result holds if we only require the existence of a single pair of points whose stabilisers intersect along a finite subgroup.
Original languageEnglish
Title of host publicationBeyond Hyperbolicity
PublisherCambridge University Press
Pages160-178
Number of pages19
ISBN (Electronic)9781108559065
ISBN (Print)9781108447294
Publication statusPublished - Aug 2019

Publication series

NameLondon Mathematical Society Lecture Notes Series
Volume454

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