{
  "id": "1001.5094",
  "version": "v7",
  "published": "2010-01-28T03:36:07.000Z",
  "updated": "2012-04-18T20:30:09.000Z",
  "title": "Polynomial invariants of pseudo-Anosov maps",
  "authors": [
    "Joan Birman",
    "Peter Brinkmann",
    "Keiko Kawamuro"
  ],
  "comment": "Published in Journal of Topology and Analysis, Vol. 4, No 1 (2012) 13-47",
  "journal": "Journal of Topology and Analysis, Vol. 4, No 1 (2012) 13-47",
  "doi": "10.1142/S1793525312500033",
  "categories": [
    "math.GT"
  ],
  "abstract": "We investigate the structure of the characteristic polynomial det(xI-T) of a transition matrix T that is associated to a train track representative of a pseudo-Anosov map [F] acting on a surface. As a result we obtain three new polynomial invariants of [F], one of them being the product of the other two, and all three being divisors of det(xI-T). The degrees of the new polynomials are invariants of [F ] and we give simple formulas for computing them by a counting argument from an invariant train track. We give examples of genus 2 pseudo-Anosov maps having the same dilatation, and use our invariants to distinguish them.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2012-04-18T20:30:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57M50"
    ],
    "keywords": [
      "pseudo-anosov map",
      "polynomial invariants",
      "invariant train track",
      "characteristic polynomial det",
      "transition matrix"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.5094B"
    }
  }
}