{
  "id": "1106.5634",
  "version": "v1",
  "published": "2011-06-28T12:02:43.000Z",
  "updated": "2011-06-28T12:02:43.000Z",
  "title": "On the Kawauchi conjecture about the Conway polynomial of achiral knots",
  "authors": [
    "Nicola Ermotti",
    "Cam Van Quach Hongler",
    "Claude Weber"
  ],
  "comment": "8 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give a counterexample to the Kawauchi conjecture on the Conway polynomial of achiral knots which asserts that the Conway polynomial $C(z)$ of an achiral knot satisfies the splitting property $C(z)=F(z)F(-z)$ for a polynomial $F(z)$ with integer coefficients. We show that the Bonahon-Siebenmann decomposition of an achiral and alternating knot is reflected in the Conway polynomial. More explicitly, the Kawauchi conjecture is true for quasi-arborescent knots and counterexamples in the class of alternating knots must be quasi-polyhedral.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-28T12:02:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "conway polynomial",
      "kawauchi conjecture",
      "achiral knot satisfies",
      "alternating knot",
      "integer coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.5634E"
    }
  }
}