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      The Extended Bloch Group and the Cheeger-Chern-Simons Class

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          Abstract

          We present a formula for the full Cheeger-Chern-Simons class of the tautological flat complex vector bundle of rank two over BSL(2,\C^\delta). Our formula improves the formula by Dupont and Zickert, where the class is only computed modulo 2-torsion.

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          Extended Bloch group and the Cheeger-Chern-Simons class

          (2004)
          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.
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            Scissors congruences, II

            Johan L. Dupont, Chih-Han Sah (1982)
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              The dilogarithm as a characteristics class for flat bundles

              Johan L. Dupont (1987)
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                Publication date Created: 03 May 2007
                Article
                DOI: 10.2140/gt.2007.11.1623
                ArXiV ID: 0705.0500
                SO-VID: 6dcaf5ba-9b5c-4846-a217-c52c6986b8a2
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                ACM classes 57R20 (Primary) 11G55 (Secondary)
                Journal reference Geom. Topol. 11 (2007) 1623-1635
                Comments LaTeX2e, 9 pages
                Categories math.GT

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