{
  "id": "math/0307092",
  "version": "v2",
  "published": "2003-07-08T16:26:37.000Z",
  "updated": "2004-02-15T21:10:04.000Z",
  "title": "Extended Bloch group and the Cheeger-Chern-Simons class",
  "authors": [
    "Walter D Neumann"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper10.abs.html",
  "journal": "Geom. Topol. 8(2004) 413-474",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We define an extended Bloch group and show it is naturally 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-Chern-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 3-manifolds conjectured by Neumann and Zagier [Topology 1985] and proved by Yoshida [Invent. Math. 1985] as well as effective formulae for the Chern-Simons invariant of a hyperbolic 3-manifold.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-02-15T21:10:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "19E99",
      "57T99"
    ],
    "keywords": [
      "extended bloch group",
      "chern-simons invariant",
      "exact simplicial formula",
      "universal cheeger-chern-simons class",
      "rogers dilogarithm function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7092N"
    }
  }
}