The Extended Bloch Group and the Cheeger-chern-simons Class Sebastian Goette and Christian Zickert

Extended Bloch group and the Cheeger–Chern–Simons class

We define an extended Bloch group and show it is naturally isomorphic to H3(PSL(2,C) δ ;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 [16] a...

Extended Bloch Group and the Chern - Simons

We define an extended Bloch group and show it is isomorphic to H3(PSL(2,C);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 [14] and proved in [17], as...

Extended Bloch Group and the Chern - Simons Class ( Incomplete Working

We deene an extended Bloch group and show it is isomorphic to H 3 (PSL(2; C) ; 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 14] and proved in 17], ...

Lectures on Algebro-geometric Chern-weil and Cheeger-chern-simons Theory for Vector Bundles

Geometric interpretation of simplicial formulas for the Chern-Simons invariant

Chern-Simons theory was first introduced by S. S. Chern and J. Simons in [CS] as secondary characteristic classes: given a Lie group G and a flat Gbundle P over a manifoldM , all Chern-Weil characteristic classes of P has to vanish as P have a flat connection whereas the bundle might be non trivial. The Chern-Simons functional is a non trivial invariant of G-bundles with connections. This theor...