Geometry & Topology

Extended Bloch group and the Cheeger–Chern–Simons class

Walter D Neumann

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

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

Received: 23 July 2003
Revised: 17 January 2004
Accepted: 14 February 2004
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 19E99: None of the above, but in this section 57T99: None of the above, but in this section

extended Bloch group Cheeger–Chern–Simons class hyperbolic 3–manifold


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.

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