Extended Bloch group and the Cheeger–Chern–Simons class

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

We present a formula for the full Cheeger-Chern-Simons class of the tautological flat complex vector bundle of rank 2 over BSL(2, C). Our formula improves the formula in [DZ], where the class is only computed modulo 2-torsion.

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

Bundle Gerbes for Chern-simons and Wess-zumino-witten Theories

We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal G-bundle with connection and a class in H(BG, Z) for a compact semi-simple Lie group G. The ChernSimons bundle 2-gerbe realises differential geometrically the Cheeger-Simons invariant. We apply these notions to refine the Dijkgraaf-Witten correspondence between three dimensional Ch...