Walter D Neumann
Published 2002-12-10Version 1
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.
Comments: 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
Extended Bloch group and the Cheeger-Chern-Simons class
Geometric interpretation of simplicial formulas for the Chern-Simons invariant
The G-index of a closed, spin, hyperbolic manifold of dimension 2 or 4
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