Extended Bloch group and the Cheeger-Chern-Simons class
几何拓扑
2014-11-11 v2 代数拓扑
摘要
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.
引用
@article{arxiv.math/0307092,
title = {Extended Bloch group and the Cheeger-Chern-Simons class},
author = {Walter D Neumann},
journal= {arXiv preprint arXiv:math/0307092},
year = {2014}
}
备注
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper10.abs.html