{
  "id": "math/0509578",
  "version": "v1",
  "published": "2005-09-24T03:59:56.000Z",
  "updated": "2005-09-24T03:59:56.000Z",
  "title": "A Refinement of the Ray-Singer Torsion",
  "authors": [
    "Maxim Braverman",
    "Thomas Kappeler"
  ],
  "comment": "6 pages, to apper in Comptes rendus Acad. Sci. Paris",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "This is a short version of math.DG/0505537. For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation. This new invariant can be viewed as an analytic counterpart of the refined combinatorial torsion introduced by Turaev. The refined analytic torsion is a holomorphic function of the representation of the fundamental group. When the representation is unitary, the absolute value of the refined analytic torsion is equal to the Ray-Singer torsion, while its phase is determined by the eta-invariant. The fact that the Ray-Singer torsion and the eta-invariant can be combined into one holomorphic function allows to use methods of complex analysis to study both invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-24T03:59:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ray-singer torsion",
      "refinement",
      "refined analytic torsion",
      "fundamental group",
      "holomorphic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9578B"
    }
  }
}