{
  "id": "math/0212147",
  "version": "v1",
  "published": "2002-12-10T20:52:29.000Z",
  "updated": "2002-12-10T20:52:29.000Z",
  "title": "Extended Bloch group and the Chern-Simons class (Incomplete working version)",
  "authors": [
    "Walter D Neumann"
  ],
  "comment": "This incomplete preprint is identical to the version that has been on my web site since 1998. Since it has been quoted in the permanent literature, as well as in arXiv preprints by Baseilhac and Benedetti, it is being placed here for archival purposes",
  "journal": "Geom. Topol. 8(2004), 413-474",
  "categories": [
    "math.GT"
  ],
  "abstract": "We define an extended Bloch group and show it is isomorphic to $H_3(PSL(2,C)^\\delta;Z)$. Using the Rogers dilogarithm function this leads to an exact simplicial formula for the universal Cheeger-Simons class on this homology group. It also leads to an independent proof of the analytic relationship between volume and Chern-Simons invariant of hyperbolic manifolds conjectured in \\cite{neumann-zagier} and proved in \\cite{yoshida}, as well as an effective formula for the Chern-Simons invariant of a hyperbolic manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-12-10T20:52:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extended bloch group",
      "incomplete working version",
      "chern-simons class",
      "hyperbolic manifold",
      "chern-simons invariant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....12147N"
    }
  }
}