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Hyperbolicities in CAT(0) cube complexes

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arxiv 1709.08843 v2 pith:5BB4KTKR submitted 2017-09-26 math.GR

Anthony Genevois This is my paper · ORCID
classification math.GR
keywords applicationscubegroupactingactionactionsacylindricalacylindrically
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This paper is a survey dedicated to the following question: given a group acting on some CAT(0) cube complex, how to exploit this action to determine whether or not the group is Gromov / relatively / acylindrically hyperbolic? As much as possible, the different criteria we mention are illustrated by applications. We also propose a model for universal acylindrical actions of cubulable groups and give a few applications to Morse, stable and hyperbolically embedded subgroups.

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Cited by 1 Pith paper

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  1. Algorithms detecting stability and Morseness for finitely generated groups

    math.GR 2019-08 conditional novelty 6.0 of 10

    A set of algorithms detects stability and Morseness of finitely generated subgroups in mapping class groups, right-angled Artin groups, toral relatively hyperbolic groups, and limit groups.

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