{
  "id": "1709.08843",
  "version": "v1",
  "published": "2017-09-26T05:50:32.000Z",
  "updated": "2017-09-26T05:50:32.000Z",
  "title": "Hyperbolicities in CAT(0) cube complexes",
  "authors": [
    "Anthony Genevois"
  ],
  "comment": "47 pages",
  "categories": [
    "math.GR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-26T05:50:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67"
    ],
    "keywords": [
      "cube complex",
      "hyperbolicities",
      "applications",
      "universal acylindrical actions",
      "cubulable groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}