{
  "id": "1101.2695",
  "version": "v1",
  "published": "2011-01-13T23:51:46.000Z",
  "updated": "2011-01-13T23:51:46.000Z",
  "title": "Dubois' Torsion, A-polynomial and Quantum Invariants",
  "authors": [
    "Charles Frohman",
    "Joanna Kania-Bartoszynska"
  ],
  "comment": "34 pages, 3 figures",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "It is shown that for knots with a sufficiently regular character variety the Dubois' torsion detects the A-polynomial of the knot. A global formula for the integral of the Dubois torsion is given. The formula looks like the heat kernel regularization of the formula for the Witten-Reshetikhin-Turaev invariant of the double of the knot complement. The Dubois' torsion is recognized as the pushforward of a measure on the character variety of the double of the knot complement coming from the square root of Reidemeister torsion. This is used to motivate a conjecture about quantum invariants detecting the A-polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-13T23:51:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "quantum invariants",
      "a-polynomial",
      "knot complement",
      "sufficiently regular character variety",
      "heat kernel regularization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 884658,
      "adsabs": "2011arXiv1101.2695F"
    }
  }
}