{
  "id": "0908.0685",
  "version": "v1",
  "published": "2009-08-05T15:47:00.000Z",
  "updated": "2009-08-05T15:47:00.000Z",
  "title": "Semisimple actions of mapping class groups on CAT(0) spaces",
  "authors": [
    "Martin R Bridson"
  ],
  "comment": "To appear in \"The Geometry of Riemann Surfaces\", LMS Lecture Notes 368. Dedicated to Bill Harvey on his 65th birthday. 12 pages no figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Let S be an orientable surface of finite type and let Mod(S) be its mapping class group. We consider actions of Mod(S) by semisimple isometries on complete CAT(0) spaces. If the genus of S is at least 3, then in any such action all Dehn twists act as elliptic isometries. The action of Mod(S) on the completion of Teichm\\\"uller space with the Weil-Petersson metric shows that there are interesting actions of this type. Whenever the mapping class group of a closed orientable surface of genus g acts by semisimple isometries on a complete CAT(0) space of dimension less than g it must fix a point. The mapping class group of a closed surface of genus 2 acts properly by semisimple isometries on a complete CAT(0) space of dimension 18.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-05T15:47:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "57M50"
    ],
    "keywords": [
      "mapping class group",
      "semisimple actions",
      "semisimple isometries",
      "complete cat",
      "orientable surface"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.0685B"
    }
  }
}