{
  "id": "2009.10470",
  "version": "v1",
  "published": "2020-09-22T11:46:42.000Z",
  "updated": "2020-09-22T11:46:42.000Z",
  "title": "Abstract group actions of locally compact groups on CAT(0) spaces",
  "authors": [
    "Philip Möller",
    "Olga Varghese"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.GR"
  ],
  "abstract": "We study abstract group actions of locally compact Hausdorff groups on CAT(0) spaces. Under mild assumptions on the action we show that it is continuous or has a global fixed point. This mirrors results by Dudley and Morris-Nickolas for actions on trees. As a consequence we obtain a geometric proof for the fact that any abstract group homomorphism from a locally compact Hausdorff group into a torsion free CAT(0) group is continuous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-22T11:46:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "22D05"
    ],
    "keywords": [
      "locally compact groups",
      "locally compact hausdorff group",
      "study abstract group actions",
      "abstract group homomorphism",
      "torsion free cat"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}