Extended Bloch group and the Cheeger-Chern-Simons class

Details Extended Bloch group and the Cheeger-Chern-Simons class Extended Bloch group and the Cheeger-Chern-Simons class

2003-07-08

arxiv.org/abs/math/0307092v2

Geom. Topol. 8(2004) 413-474

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper10.abs.html

Scientific paper

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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