Extended Bloch Group and the Chern - Simons
نویسنده
چکیده
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 well as an effective formula for the Chern-Simons invariant of a hyperbolic manifold.
منابع مشابه
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...
متن کاملExtended 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], ...
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