{
  "id": "math/0606232",
  "version": "v3",
  "published": "2006-06-09T21:36:37.000Z",
  "updated": "2009-07-29T14:24:25.000Z",
  "title": "Amenable groups that act on the line",
  "authors": [
    "Dave Witte Morris"
  ],
  "comment": "This is the version published by Algebraic & Geometric Topology on 15 December 2006",
  "journal": "Algebr. Geom. Topol. 6 (2006) 2509-2518",
  "doi": "10.2140/agt.2006.6.2509",
  "categories": [
    "math.GR",
    "math.DS",
    "math.GT",
    "math.RT"
  ],
  "abstract": "Let Gamma be a finitely generated, amenable group. Using an idea of E Ghys, we prove that if Gamma has a nontrivial, orientation-preserving action on the real line, then Gamma has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Gamma has a faithful action on the circle, then some finite-index subgroup of Gamma has the property that all of its nontrivial, finitely generated subgroups have infinite, cyclic quotients. It also means that every left-orderable, amenable group is locally indicable. This answers a question of P Linnell.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-07-29T14:24:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F60",
      "06F15",
      "37C85",
      "37E05",
      "37E10",
      "43A07",
      "57S25"
    ],
    "keywords": [
      "amenable group",
      "cyclic quotient",
      "nontrivial",
      "real line",
      "finite-index subgroup"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}