{
  "id": "1510.00264",
  "version": "v1",
  "published": "2015-10-01T14:51:47.000Z",
  "updated": "2015-10-01T14:51:47.000Z",
  "title": "The L^2-torsion function and the Thurston norm of 3-manifolds",
  "authors": [
    "Stefan Friedl",
    "Wolfgang Lück"
  ],
  "comment": "22 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let M be an oriented irreducible 3-manifold with infinite fundamental group and empty or toroidal boundary. Consider any element \\phi in the first cohomology of M with integral coefficients. Then one can define the \\phi-twisted L^2-torsion function of the universal covering which is a function from the set of positive real numbers to the set of real numbers. By earlier work of the second author and Schick the evaluation at t=1 determines the volume. In this paper we show that its degree, which is a number extracted from its asymptotic behavior at 0 and at infinity, agrees with the Thurston norm of \\phi.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-01T14:51:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thurston norm",
      "infinite fundamental group",
      "first cohomology",
      "integral coefficients",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151000264F"
    }
  }
}