Volume 8, issue 1 (2004)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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
References
Forward citations
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