Volume 8, issue 1 (2004)

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Extended Bloch group and the Cheeger–Chern–Simons class

Walter D Neumann

Geometry & Topology 8 (2004) 413–474

arXiv: math.GT/0307092

Abstract

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.

Keywords
extended Bloch group, Cheeger–Chern–Simons class, hyperbolic, 3–manifold
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 19E99, 57T99
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Publication
Received: 23 July 2003
Revised: 17 January 2004
Accepted: 14 February 2004
Published: 14 February 2004
Proposed: Robion Kirby
Seconded: Shigeyuki Morita, Benson Farb
Authors
Walter D Neumann
Department of Mathematics
Barnard College
Columbia University
New York
New York 10027
USA