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arxiv: math/0307092 · v2 · pith:A5GB3R4Gnew · submitted 2003-07-08 · 🧮 math.GT · math.AT

Extended Bloch group and the Cheeger-Chern-Simons class

Walter D Neumann This is my paper
classification 🧮 math.GT math.AT
keywords groupblochcheeger-chern-simonschern-simonsclassextendedhyperbolicinvariant
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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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