{
  "id": "2109.04664",
  "version": "v1",
  "published": "2021-09-10T04:49:42.000Z",
  "updated": "2021-09-10T04:49:42.000Z",
  "title": "On the asymptotic behavior of the colored Jones polynomial of the figure-eight knot associated with a real nubmer",
  "authors": [
    "Hitoshi Murakami",
    "Anh T. Tran"
  ],
  "comment": "26 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the asymptotic behavior of the $N$-dimensional colored Jones polynomial evaluated at $\\exp(\\xi/N)$ for a real number $\\xi$ greater than a certain constant. We prove that, from the asymptotic behavior, we can extract the $\\rm{SL}(2;\\mathbb{C})$ Chern--Simons invariant and the Reidemeister torsion twisted by the adjoint action both associated with a representation determined by $\\xi$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-10T04:49:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K16",
      "57K14",
      "57K10"
    ],
    "keywords": [
      "asymptotic behavior",
      "figure-eight knot",
      "real nubmer",
      "dimensional colored jones polynomial",
      "reidemeister torsion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}