{
  "id": "math/0604077",
  "version": "v1",
  "published": "2006-04-04T16:35:44.000Z",
  "updated": "2006-04-04T16:35:44.000Z",
  "title": "The Action of Thompson's Group on a CAT(0) Boundary",
  "authors": [
    "Daniel Farley"
  ],
  "comment": "33 pages, 28 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "One way to show that Thompson's group F is non-amenable is to exhibit an action of F on a locally compact CAT(0) space X containing no F-invariant flats and having no global fixed points in its boundary-at-infinity. We study the actions of Thompson's groups F, T, and V on the boundaries-at-infinity of proper CAT(0) cubical complexes. In particular, we show that Thompson's groups T and V act without fixing any points in the boundaries of their CAT(0) cubical complexes. This in particular gives another proof of the well-known fact that these groups are non-amenable. We obtain a partial description of the fixed set for F: Thompson's group F fixes an arc in the boundary of its cubical complex. We leave open the possibility that there are more fixed points, but describe a region of the boundary which must contain all of the others.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-04T16:35:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F69"
    ],
    "keywords": [
      "thompsons group",
      "cubical complexes",
      "well-known fact",
      "f-invariant flats",
      "leave open"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4077F"
    }
  }
}