{
  "id": "math/0106097",
  "version": "v1",
  "published": "2001-06-12T19:30:20.000Z",
  "updated": "2001-06-12T19:30:20.000Z",
  "title": "A rationality conjecture about Kontsevich integral of knots and its implications to the structure of the colored Jones polynomial",
  "authors": [
    "L. Rozansky"
  ],
  "comment": "LaTeX, 35 pages, 3 pictures",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "We formulate a conjecture (already proven by A. Kricker) about the structure of Kontsevich integral of a knot. We describe its value in terms of the generating functions for the numbers of external edges attached to closed 3-valent diagrams. We conjecture that these functions are rational functions of the exponentials of their arguments, their denominators being the powers of the Alexander-Conway polynomial. This conjecture implies the existence of an expansion of a colored Jones (HOMFLY) polynomial in powers of q-1 whose coefficients are rational functions of q^color. We show how to derive the first Kontsevich integral polynomial associated to the theta-graph from the rational expansion of the colored SU(3) Jones polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-06-12T19:30:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "colored jones polynomial",
      "rationality conjecture",
      "implications",
      "rational functions",
      "first kontsevich integral polynomial"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......6097R"
    }
  }
}