{
  "id": "1404.7732",
  "version": "v2",
  "published": "2014-04-30T14:23:05.000Z",
  "updated": "2014-12-18T15:06:43.000Z",
  "title": "Classical invariants of Legendrian knots in the 3-dimensional torus",
  "authors": [
    "Paul A. Schweitzer SJ",
    "Fábio S. Souza"
  ],
  "comment": "22 pages, 11 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "All knots in $R^3$ possess Seifert surfaces, and so the classical Thurston-Bennequin and rotation (or Maslov) invariants for Legendrian knots in a contact structure on $R^3$ can be defined. The definitions extend easily to null-homologous knots in any $3$-manifold $M$ endowed with a contact structure $\\xi$. We generalize the definition of Seifert surfaces and use them to define these invariants for all Legendrian knots, including those that are not null-homologous, in a contact structure on the $3$-torus $T^3$. We show how to compute the Thurston-Bennequin and rotation invariants in a tight oriented contact structure on $T^3$ using projections.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-30T14:23:05.000Z",
      "abstract": "All knots in R^3 possess Seifert surfaces, and so the classical Thurston-Bennequin invariant for Legendrian knots in a contact structure on R^3 can be defined. The definitions extend easily to null-homologous knots in a 3-manifold M endowed with a contact structure \\xi. We generalize the definition of Seifert surfaces and use them to define the Thurston-Bennequin invariant for all Legendrian knots, including those that are not null-homologous, in a contact structure on the 3-torus T^3. Finally, we show how to compute the Thurston-Bennequin and Maslov (or rotation) invariants in a tight oriented contact structure on T^3 using projections.",
      "comment": "20 pages, 11 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-18T15:06:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R17",
      "57M27"
    ],
    "keywords": [
      "legendrian knots",
      "classical invariants",
      "possess seifert surfaces",
      "tight oriented contact structure",
      "classical thurston-bennequin invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.7732S"
    }
  }
}