{
  "id": "2312.00350",
  "version": "v1",
  "published": "2023-12-01T04:55:40.000Z",
  "updated": "2023-12-01T04:55:40.000Z",
  "title": "The colored Jones polynomial of the figure-eight knot and an $\\operatorname{SL}(2;\\mathbb{R})$-representation",
  "authors": [
    "Hitoshi Murakami"
  ],
  "comment": "45 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the asymptotic behavior of the $N$-dimensional colored Jones polynomial of the figure-eight knot, evaluated at $\\exp\\bigl((u+2p\\pi\\sqrt{-1})/N\\bigr)$ as $N$ tends to infinity, where $u>\\operatorname{arccosh}(3/2)$ is a real number and $p\\ge1$ is an integer. It turns out that it corresponds to an $\\operatorname{SL}(2;\\mathbb{R})$ representation of the fundamental group of the knot complement. Moreover, it defines the adjoint Reidemeister torsion and the Chern--Simons invariant associated with the representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-01T04:55:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K14",
      "57K16"
    ],
    "keywords": [
      "figure-eight knot",
      "representation",
      "adjoint reidemeister torsion",
      "dimensional colored jones polynomial",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}