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

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

2002-12-10

arxiv.org/abs/math/0212147v1

Geom. Topol. 8(2004), 413-474

Mathematics

Geometric Topology

This incomplete preprint is identical to the version that has been on my web site since 1998. Since it has been quoted in the

Scientific paper

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.

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