{
  "id": "math/0502428",
  "version": "v1",
  "published": "2005-02-20T14:53:57.000Z",
  "updated": "2005-02-20T14:53:57.000Z",
  "title": "The colored Jones polynomials and the Alexander polynomial of the figure-eight knot",
  "authors": [
    "Hitoshi Murakami"
  ],
  "comment": "13 pages",
  "journal": "JP J. Geom. Topol. 2 (2007), 249--269",
  "categories": [
    "math.GT"
  ],
  "abstract": "The volume conjecture and its generalization state that the series of certain evaluations of the colored Jones polynomials of a knot would grow exponentially and its growth rate would be related to the volume of a three-manifold obtained by Dehn surgery along the knot. In this paper, we show that for the figure-eight knot the series converges in some cases and the limit equals the inverse of its Alexander polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-20T14:53:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25"
    ],
    "keywords": [
      "colored jones polynomials",
      "alexander polynomial",
      "figure-eight knot",
      "volume conjecture",
      "limit equals"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2428M"
    }
  }
}