{
  "id": "1712.01416",
  "version": "v1",
  "published": "2017-12-04T23:43:15.000Z",
  "updated": "2017-12-04T23:43:15.000Z",
  "title": "Homological eigenvalues of lifts of pseudo-Anosov mapping classes to finite covers",
  "authors": [
    "Asaf Hadari"
  ],
  "comment": "30 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $\\Sigma$ be a compact orientable surface of finite type with at least one boundary component. Let $f \\in \\textup{Mod}(\\Sigma)$ be a pseudo Anosov mapping class. We prove a conjecture of McMullen by showing that there exists a finite cover $\\widetilde{\\Sigma} \\to \\Sigma$ and a lift $\\widetilde{f}$ of $f$ such that $\\wt{f}_*: H_1(\\wt{\\Sigma}; \\mathbb{Z}) \\to H_1(\\wt{\\Sigma}; \\mathbb{Z})$ has an eigenvalue off the unit circle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-04T23:43:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pseudo-anosov mapping classes",
      "finite cover",
      "homological eigenvalues",
      "pseudo anosov mapping class",
      "compact orientable surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}