{
  "id": "1909.12360",
  "version": "v1",
  "published": "2019-09-26T19:50:46.000Z",
  "updated": "2019-09-26T19:50:46.000Z",
  "title": "Boundaries of groups with isolated flats are path connected",
  "authors": [
    "Michael Ben-Zvi"
  ],
  "comment": "36 pages, 6 figures",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "A seminal result in geometric group theory is that a 1-ended hyperbolic group has a locally connected visual boundary. As a consequence, a 1-ended hyperbolic group also has a path connected visual boundary. In this paper, we study when this phenomenon occurs for CAT(0) groups. We show if a 1-ended CAT(0) group with isolated flats acts geometrically on a CAT(0) space, then the visual boundary of the space is path connected. As a corollary, we prove all CAT(0) groups with isolated flats are semistable at infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-26T19:50:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67"
    ],
    "keywords": [
      "hyperbolic group",
      "path connected visual boundary",
      "geometric group theory",
      "locally connected visual boundary",
      "seminal result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}