{
  "id": "0705.3386",
  "version": "v1",
  "published": "2007-05-23T14:21:22.000Z",
  "updated": "2007-05-23T14:21:22.000Z",
  "title": "Isometries of CAT(0) cube complexes are semi-simple",
  "authors": [
    "Frédéric Haglund"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We show that an automorphism of an arbitrary CAT(0) cube complex either has a fixed point or preserves some combinatorial axis. It follows that when a group contains a distorted cyclic subgroup, it admits no proper action on a discrete space with walls.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-23T14:21:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "53C21",
      "20F18"
    ],
    "keywords": [
      "cube complexes",
      "isometries",
      "semi-simple",
      "discrete space",
      "arbitrary cat"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.3386H"
    }
  }
}