## Geometry & Topology

### Extended Bloch group and the Cheeger–Chern–Simons class

Walter D Neumann

#### Abstract

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 by Neumann and Zagier and proved by Yoshida, as well as effective formulae for the Chern–Simons invariant of a hyperbolic $3$–manifold.

#### Article information

Source
Geom. Topol., Volume 8, Number 1 (2004), 413-474.

Dates
Revised: 17 January 2004
Accepted: 14 February 2004
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513883371

Digital Object Identifier
doi:10.2140/gt.2004.8.413

Mathematical Reviews number (MathSciNet)
MR2033484

Zentralblatt MATH identifier
1053.57010

#### Citation

Neumann, Walter D. Extended Bloch group and the Cheeger–Chern–Simons class. Geom. Topol. 8 (2004), no. 1, 413--474. doi:10.2140/gt.2004.8.413. https://projecteuclid.org/euclid.gt/1513883371

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