Extended Bloch group and the Chern-Simons class (Incomplete working version)

2002/12/10 by Walter D Neumann
Mathematics · #math.GT

paper · pdf

published as Geom. Topol. 8(2004), 413-474 · 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

arxiv created 2002/12/10 · arxiv updated 2009/11/30

Abstract

We define an extended Bloch group and show it is isomorphic to H₃(PSL(2,C)^δ;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 \citeneumann-zagier and proved in \citeyoshida, as well as an effective formula for the Chern-Simons invariant of a hyperbolic manifold.

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