Extended Bloch group and the Cheeger–Chern–Simons class

Abstract

We define an extended Bloch group and show it is naturally isomorphic to H 3 (PSL(2, C) ; 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 in