{
  "id": "0804.1355",
  "version": "v1",
  "published": "2008-04-08T20:06:13.000Z",
  "updated": "2008-04-08T20:06:13.000Z",
  "title": "Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation",
  "authors": [
    "Chris Herald",
    "Paul Kirk",
    "Charles Livingston"
  ],
  "comment": "24 pages, 1 figure",
  "journal": "Mathematische Zeitschrift 265 (2010) 925-949",
  "categories": [
    "math.GT"
  ],
  "abstract": "Given a knot complement X and its p-fold cyclic cover X_p, we identify twisted polynomials associated to 1-dimensional linear representations of the fundamental group of X_p with twisted polynomials associated to related p-dimensional linear representations of the fundamental group of X. This provides a simpler and faster algorithm to compute these twisted polynomials, allowing us to prove that 16 (of 18 previously unknown) algebraically slice knots of 12 or fewer crossings are not slice. We also use this improved algorithm to prove that the 24 mutants of the pretzel knot P(3,7,9,11,15), corresponding to permutations of (7,9,11,15), represent distinct concordance classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-08T20:06:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "twisted alexander polynomials",
      "metabelian representations",
      "knot slicing",
      "represent distinct concordance classes",
      "fundamental group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.1355H"
    }
  }
}