{
  "id": "1206.5437",
  "version": "v1",
  "published": "2012-06-23T20:44:45.000Z",
  "updated": "2012-06-23T20:44:45.000Z",
  "title": "On the S^1 x S^2 HOMFLY-PT invariant and Legendrian links",
  "authors": [
    "Mikhail Lavrov",
    "Dan Rutherford"
  ],
  "comment": "20 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In \\cite{GZ}, Gilmer and Zhong established the existence of an invariant for links in $S^1\\times S^2$ which is a rational function in variables $a$ and $s$ and satisfies the HOMFLY-PT skein relations. We give formulas for evaluating this invariant in terms of a standard, geometrically simple basis for the HOMFLY-PT skein module of the solid torus. This allows computation of the invariant for arbitrary links in $S^1\\times S^2$ and shows that the invariant is in fact a Laurent polynomial in $a$ and $z= s -s^{-1}$. Our proof uses connections between HOMFLY-PT skein modules and invariants of Legendrian links. As a corollary, we extend HOMFLY-PT polynomial estimates for the Thurston-Bennequin number to Legendrian links in $S^1\\times S^2$ with its tight contact structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-23T20:44:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "legendrian links",
      "homfly-pt invariant",
      "homfly-pt skein module",
      "extend homfly-pt polynomial estimates",
      "homfly-pt skein relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.5437L"
    }
  }
}