The Extended Bloch Group and the Cheeger–Chern–Simons Class

Goette, Sebastian; Zickert, Christian

doi:10.2140/gt.2007.11.1623

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The Extended Bloch Group and the Cheeger–Chern–Simons Class

Sebastian Goette and Christian K Zickert

Geometry & Topology 11 (2007) 1623–1635

DOI: 10.2140/gt.2007.11.1623

arXiv: 0705.0500

Abstract

We present a formula for the full Cheeger–Chern–Simons class of the tautological flat complex vector bundle of rank $2$ over $B S L (2, ℂ^{δ})$ . This improves the formula by Dupont and Zickert [Geom. Topol. 10 (2006) 1347–1372], where the class is only computed modulo 2–torsion.

Keywords

Extended Bloch group, Cheeger-Chern-Simons class, Rogers dilogarithm

Mathematical Subject Classification 2000

Primary: 57R20, 11G55

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Publication

Received: 5 June 2007

Revised: 11 July 2007

Accepted: 4 July 2007

Published: 2 August 2007

Proposed: Robion Kirby

Seconded: Shigeyuki Morita, Joan Birman

Authors

Sebastian Goette
Mathematisches Institut Universität Freiburg Eckerstr. 1 79104 Freiburg Germany

Christian K Zickert
Department of Mathematics Columbia University New York NY 10027 USA

Volume 11, issue 3 (2007)