{
  "id": "1803.10153",
  "version": "v2",
  "published": "2018-03-27T15:53:13.000Z",
  "updated": "2018-08-30T15:14:32.000Z",
  "title": "Rigidity Properties for Hyperbolic Generalizations",
  "authors": [
    "Brendan Burns Healy"
  ],
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We make a few observations on the absence of geometric and topological rigidity for acylindrically hyperbolic and relatively hyperbolic groups. In particular, we demonstrate the lack of a well defined limit set for acylindrical actions on hyperbolic spaces, even under the assumption of universality. We also prove a statement about relatively hyperbolic groups inspired by a remark asserted by Groves, Manning, and Sisto about the quasi-isometry type of combinatorial cusps. Finally, we summarize these results in a table in order to assert a meta-statement about the decay of metric rigidity as the conditions on hyperbolic actions are loosened.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-08-30T15:14:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic generalizations",
      "rigidity properties",
      "relatively hyperbolic groups",
      "hyperbolic spaces",
      "hyperbolic actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}