{
  "id": "1205.1977",
  "version": "v2",
  "published": "2012-05-09T13:29:06.000Z",
  "updated": "2012-07-30T10:07:10.000Z",
  "title": "Twisted Alexander polynomials, character varieties and Reidemeister torsion of double branched covers",
  "authors": [
    "Yoshikazu Yamaguchi"
  ],
  "comment": "30 pages, 3 figures; v2: expositions improved, typos corrected, one reference added",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give an extension of Fox's formula of the Alexander polynomial for double branched covers over the three-sphere. Our formula provides the Reidemeister torsion of a double branched cover along a knot for a non-trivial one dimensional representation by the product of two factors derived from the knot group. One of the factors is determined by the twisted Alexander polynomial and the other is determined by a rational function on the character variety. As an application, we show that these products distinguish isotopy classes of two-bridge knots up to mirror images.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-30T10:07:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M05",
      "57M12",
      "57M25"
    ],
    "keywords": [
      "double branched cover",
      "twisted alexander polynomial",
      "character variety",
      "reidemeister torsion",
      "products distinguish isotopy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.1977Y"
    }
  }
}