{
  "id": "1103.5060",
  "version": "v2",
  "published": "2011-03-25T18:46:35.000Z",
  "updated": "2012-06-06T12:26:03.000Z",
  "title": "Bounded orbits and global fixed points for groups acting on the plane",
  "authors": [
    "Kathryn Mann"
  ],
  "comment": "v2 reflects published version. Added argument in section 2, results unchanged",
  "journal": "Algebraic & Geometric Topology 12 (2012) 421-433",
  "doi": "10.2140/agt.2012.12.421",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "Let G be a group acting on the plane by orientation-preserving homeomorphisms. We show that if for some k>0 there is a ball of radius r > k/\\sqrt{3} such that each point x in the ball satisfies |gx -hx| < k for all g, h in G, and the action of G satisfies a nonwandering hypothesis, then the action has a global fixed point. In particular, any group of measure-preserving orientation preserving homeomorphisms of the plane with uniformly bounded orbits has a global fixed point. The constant k/\\sqrt{3} is sharp. We also show that a group acting on the plane with orbits bounded as above is left orderable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-06T12:26:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global fixed point",
      "bounded orbits",
      "groups acting",
      "measure-preserving orientation preserving homeomorphisms",
      "ball satisfies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.5060M"
    }
  }
}