{
  "id": "1110.3746",
  "version": "v2",
  "published": "2011-10-17T18:03:05.000Z",
  "updated": "2011-10-21T14:29:19.000Z",
  "title": "Teichmüller polynomials, Alexander polynomials and finite covers of surfaces",
  "authors": [
    "Thomas Koberda"
  ],
  "comment": "8 pages, submitted version. Fixed some inaccurate statements in the previous version",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this note we explore a connection between finite covers of surfaces and the Teichm\\\"uller polynomial of a fibered face of a hyperbolic 3--manifold. We consider the action of a homological pseudo-Anosov homeomorphism $\\psi$ on the homology groups of a class of finite abelian covers of a surface $\\Sigma_{g,n}$. Eigenspaces of the deck group actions on these covers are naturally parametrized by rational points on a torus. We show that away from the trivial eigenspace, the spectrum of the action of $\\psi$ on these eigenspaces is bounded away from the dilatation of $\\psi$. We show that the action $\\psi$ on these eigenspaces is governed by the Teichm\\\"uller polynomial.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-21T14:29:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M10",
      "57M27"
    ],
    "keywords": [
      "finite covers",
      "alexander polynomials",
      "teichmüller polynomials",
      "deck group actions",
      "finite abelian covers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.3746K"
    }
  }
}