Hyperbolicities in CAT(0) cube complexes

By Anthony Genevois. L'Enseignement mathématique, 2017

67 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b6002836875c6a43a00deca606e36a27f48f1adb

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On strongly quasiconvex subgroups (2017, methodology): “ly super linear. Genevois provides an alternative proof for the equivalence among strongly quasiconvex, stable, and purely loxodromic subgroups of one-ended rightangled Artin groups in Theorem B.1 of [Gen]. However, Corollary 1.17 also provides a classiﬁcation of the possible lower relative divergen”
GROUPS ACTING ACYLINDRICALLY ON HYPERBOLIC SPACES (2017, background): “graph products of groups and, even more generally, subgroups of graph products [47]. For a survey of examples of acylindrically hyperbolic groups arising from actions on CAT(0) cubical complexes, see [30]. 6 (d) Fundamental groups of graphs of groups. In [47], Minasyan and the author prove the follo”