{
  "id": "0712.0866",
  "version": "v1",
  "published": "2007-12-06T02:40:01.000Z",
  "updated": "2007-12-06T02:40:01.000Z",
  "title": "Alexander polynomials and hyperbolic volume of arborescent links",
  "authors": [
    "A. Stoimenow"
  ],
  "comment": "31 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We realize a given (monic) Alexander polynomial by a (fibered) hyperbolic arborescent knot and link of any number of components, and by infinitely many such links of at least 4 components. As a consequence, a Mahler measure minimizing polynomial, if it exists, is realized as the Alexander polynomial of a fibered hyperbolic link of at least 2 components. For given polynomial, we give also an upper bound on the minimal hyperbolic volume of knots/links, and contrarily, construct knots of arbitrarily large volume, which are arborescent, or have given free genus at least 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-06T02:40:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M12",
      "57M50"
    ],
    "keywords": [
      "alexander polynomial",
      "arborescent links",
      "minimal hyperbolic volume",
      "mahler measure minimizing polynomial",
      "components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.0866S"
    }
  }
}