Hyperbolicities in CAT(0) cube complexes

  • Anthony Genevois

    Université Paris-Sud, Orsay, France
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Abstract

This paper is a survey dedicated to the following question: given a group acting on a 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.

Cite this article

Anthony Genevois, Hyperbolicities in CAT(0) cube complexes. Enseign. Math. 65 (2019), no. 1/2, pp. 33–100

DOI 10.4171/LEM/65-1/2-2