{
  "id": "1406.5575",
  "version": "v2",
  "published": "2014-06-21T03:55:09.000Z",
  "updated": "2014-10-15T03:33:49.000Z",
  "title": "Left-orderable groups that don't act on the line",
  "authors": [
    "Kathryn Mann"
  ],
  "comment": "13 pages. V2 contains corrections and improvements to section 4",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "We show that the group of germs at infinity of orientation-preserving homeomorphisms of R admits no action on the line. This gives an example of a left-orderable group of the same cardinality as Homeo+(R) that does not embed in Homeo+(R). As an application of our techniques, we construct a finitely generated group of germs that does not extend to Homeo+(R) and, separately, extend a theorem of E. Militon on homomorphisms between groups of homeomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-21T03:55:09.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-15T03:33:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "left-orderable group",
      "dont act",
      "orientation-preserving homeomorphisms",
      "cardinality",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.5575M"
    }
  }
}