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Hyperbolicities in CAT(0) cube complexes

Hyperbolicities in CAT(0) cube complexes

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 …