{
  "id": "1707.07028",
  "version": "v1",
  "published": "2017-07-21T19:30:10.000Z",
  "updated": "2017-07-21T19:30:10.000Z",
  "title": "A rank-one CAT(0) group is determined by its Morse boundary",
  "authors": [
    "Ruth Charney",
    "Devin Murray"
  ],
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "The Morse boundary of a proper geodesic metric space is designed to encode hypberbolic-like behavior in the space. A key property of this boundary is that a quasi-isometry between two such spaces induces a homeomorphism on their Morse boundaries. In this paper we investigate when the converse holds. We prove that for cocompact CAT(0) spaces, a homeomorphism of Morse boundaries is induced by a quasi-isometry if and only if the homeomorphism is quasi-mobius and 2-stable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-21T19:30:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "57M07"
    ],
    "keywords": [
      "morse boundary",
      "rank-one cat",
      "proper geodesic metric space",
      "homeomorphism",
      "encode hypberbolic-like behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}