{
  "id": "0903.1488",
  "version": "v2",
  "published": "2009-03-09T07:13:57.000Z",
  "updated": "2009-04-09T11:34:50.000Z",
  "title": "The diffeotopy group of S^1 \\times S^2 via contact topology",
  "authors": [
    "Fan Ding",
    "Hansjörg Geiges"
  ],
  "comment": "17 pages, 10 figures; v2: simplified proof of Lemma 6 (and extension to higher dimensions)",
  "journal": "Compos. Math. 146 (2010), 1096-1112",
  "doi": "10.1112/S0010437X09004606",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "As shown by H. Gluck in 1962, the diffeotopy group of S^1 \\times S^2 is isomorphic to Z_2 + Z_2 + Z_2. Here an alternative proof of this result is given, relying on contact topology. We then discuss two applications to contact topology: (i) it is shown that the fundamental group of the space of contact structures on S^1 \\times S^2, based at the standard tight contact structure, is isomorphic to the integers; (ii) inspired by previous work of M. Fraser, an example is given of an integer family of Legendrian knots in S^1 \\times S^2 # S^1 \\times S^2 (with its standard tight contact structure) that can be distinguished with the help of contact surgery, but not by the classical invariants (topological knot type, Thurston-Bennequin invariant, and rotation number).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-09T11:34:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R50",
      "57R52",
      "53D10",
      "57M25"
    ],
    "keywords": [
      "contact topology",
      "diffeotopy group",
      "standard tight contact structure",
      "legendrian knots",
      "isomorphic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1488D"
    }
  }
}