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arXiv · 1709.08843

Hyperbolicities in CAT(0) cube complexes

Anthony Genevois
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Abstract

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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Anthony Genevois. 2019-04-26. Hyperbolicities in CAT(0) cube complexes. https://arxiv.org/abs/1709.08843

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