{
  "id": "1711.08781",
  "version": "v1",
  "published": "2017-11-23T17:25:38.000Z",
  "updated": "2017-11-23T17:25:38.000Z",
  "title": "Torsion function on character varieties",
  "authors": [
    "Léo Bénard"
  ],
  "comment": "21 pages, 4 figures, comments welcome",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we define the Reidemeister torsion as a rational function on a geometric component of the character variety of a one-cusped hyperbolic manifold $M$. We study its poles and zeros and deduce that under some mild hypothesis on the manifold $M$ this function is non-constant, answering partially to a question addressed in the article \"Twisted Alexander Polynomials of Hyperbolic Knots\" of N. Dunfield, S. Friedl and N. Jackson.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-23T17:25:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "character variety",
      "torsion function",
      "hyperbolic knots",
      "reidemeister torsion",
      "rational function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}