{
  "id": "0903.0147",
  "version": "v1",
  "published": "2009-03-01T14:56:17.000Z",
  "updated": "2009-03-01T14:56:17.000Z",
  "title": "Twisted Alexander polynomials of 2-bridge knots associated to metacyclic representations",
  "authors": [
    "Mikami Hirasawa",
    "Kunio Murasugi"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "Let p be an odd prime and D_p a dihedral group of order 2p. Let \\rho: G(K) --> D_p --> GL(p,Z) be a non-abelian representation of the knot group G(K) of a knot K in 3-sphere. Let \\Delta_{\\rho,K} (t) be the twisted Alexander polynomial of K associated to \\rho. Let H(p) is the set of 2-bridge knots K, such that G(K) is mapped onto a non-trivial free product Z/2 * Z/p. Then we prove that for any 2-bridge knot K in H(p), \\Delta_{\\rho,K}(t) is of the form \\Delta_{K}(t)/(1-t) f(t) f(-t) for some integer polynomial f(t), where \\Delta_K (t) is the Alexander polynomial of K. Further, it is proved that f(t) \\equiv {\\Delta_K (t)/(1+t)}^n (mod p). Later we discuss the twisted Alexander polynomial associated to the general metacyclic representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-01T14:56:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "twisted alexander polynomial",
      "general metacyclic representation",
      "non-trivial free product",
      "integer polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.0147H"
    }
  }
}