{
  "id": "1801.00614",
  "version": "v1",
  "published": "2018-01-02T11:35:27.000Z",
  "updated": "2018-01-02T11:35:27.000Z",
  "title": "On Bennequin type inequalities for links in tight contact 3-manifolds",
  "authors": [
    "Alberto Cavallo"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that a version of the Thurston-Bennequin inequality holds for Legendrian and transverse links in a rational homology contact 3-sphere $(M,\\xi)$, whenever $\\xi$ is tight. More specifically, we show that the self-linking number of a transverse link $T$ in $(M,\\xi)$, such that the boundary of its tubular neighbourhood consists of incompressible tori, is bounded by the Thurston norm $||T||_T$ of $T$. A similar inequality is given for Legendrian links by using the notions of positive and negative transverse push-off. We apply this bound to compute the tau-invariant for every strongly quasi-positive link in $S^3$. This is done by proving that our inequality is sharp for this family of smooth links.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-02T11:35:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57R17"
    ],
    "keywords": [
      "bennequin type inequalities",
      "tight contact",
      "transverse link",
      "tubular neighbourhood consists",
      "rational homology contact"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}