{
  "id": "math/0102009",
  "version": "v1",
  "published": "2001-02-01T17:19:26.000Z",
  "updated": "2001-02-01T17:19:26.000Z",
  "title": "Sur les transformations de contact au-dessus des surfaces",
  "authors": [
    "Emmanuel Giroux"
  ],
  "comment": "15 pages, LaTeX",
  "categories": [
    "math.GT",
    "math.DG",
    "math.SG"
  ],
  "abstract": "Let S be a compact surface - or the interior of a compact surface - and let V be the manifold of cooriented contact elements of S equiped with its canonical contact structure. A diffeomorphism of V that preserves the contact structure and its coorientation is called a contact transformation over S. We prove the following results. 1) If S is neither a sphere nor a torus then the inclusion of the diffeomorphism group of S into the contact transformation group is 0-connected. 2) If S is a sphere then the contact transformation group is connected. 3) if S is a torus then the homomorphism from the contact transformation group of S to the automorphism group of $H_1(V) \\simeq Z^3$ has connected fibers and the image is (known to be) the stabilizer of $Z^2 \\times \\{0\\}$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-02-01T17:19:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57R17",
      "53D35",
      "53D10"
    ],
    "keywords": [
      "contact transformation group",
      "contact au-dessus",
      "compact surface",
      "cooriented contact elements",
      "canonical contact structure"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......2009G"
    }
  }
}