{
  "id": "0903.1689",
  "version": "v1",
  "published": "2009-03-10T14:29:18.000Z",
  "updated": "2009-03-10T14:29:18.000Z",
  "title": "Twisted Alexander polynomials of 2-bridge knots associated to metabelian representations",
  "authors": [
    "Mikami Hirasawa",
    "Kunio Murasugi"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "Suppose the knot group G(K) of a knot K has a non-abelian representation \\rho on A_4 \\subset GL(4,Z). We conjecture that the twisted Alexander polynomial of K associated to \\rho is of the form: \\Delta_K(t)/(1-t) \\phi(t^3), where \\Delta_K (t) is the Alexander polynomial of K and \\phi(t^3) is an integer polynomial in t^3. We prove the conjecture for 2-bridge knots K whose group G(K) can be mapped onto a free product Z/2*Z/3. Later, we discuss more general metabelian representations of the knot groups and propose a similar conjecture on the form of the twisted Alexander polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-10T14:29:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "twisted alexander polynomial",
      "knot group",
      "general metabelian representations",
      "free product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1689H"
    }
  }
}