Geometry & Topology

A dilogarithmic formula for the Cheeger–Chern–Simons class

Johan Dupont and Christian Zickert

Full-text: Open access

Abstract

We present a simplification of Neumann’s formula for the universal Cheeger–Chern–Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final formula can be applied directly on a homology class in the bar complex.

Article information

Source
Geom. Topol., Volume 10, Number 3 (2006), 1347-1372.

Dates
Received: 2 August 2005
Accepted: 14 June 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799769

Digital Object Identifier
doi:10.2140/gt.2006.10.1347

Mathematical Reviews number (MathSciNet)
MR2255500

Zentralblatt MATH identifier
1130.57013

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57T30: Bar and cobar constructions [See also 18G55, 55Uxx]

Keywords
Extended Bloch group Cheeger–Chern–Simons class

Citation

Dupont, Johan; Zickert, Christian. A dilogarithmic formula for the Cheeger–Chern–Simons class. Geom. Topol. 10 (2006), no. 3, 1347--1372. doi:10.2140/gt.2006.10.1347. https://projecteuclid.org/euclid.gt/1513799769


Export citation

References

  • J Cheeger, J Simons, Differential characters and geometric invariants, from: “Geometry and topology (College Park, Md., 1983/84)”, Lecture Notes in Math. 1167, Springer, Berlin (1985) 50–80
  • S S Chern, J Simons, 0353327
  • J L Dupont, The dilogarithm as a characteristic class for flat bundles, J. Pure Appl. Algebra 44 (1987) 137–164
  • J L Dupont, Scissors congruences, group homology and characteristic classes, Nankai Tracts in Mathematics 1, World Scientific Publishing Co., River Edge, NJ (2001)
  • J L Dupont, W Parry, C-H Sah, Homology of classical Lie groups made discrete. II. $H\sb 2,H\sb 3,$ and relations with scissors congruences, J. Algebra 113 (1988) 215–260
  • J L Dupont, C H Sah, Scissors congruences. II, J. Pure Appl. Algebra 25 (1982) 159–195
  • W D Neumann, Extended Bloch group and the Cheeger-Chern-Simons class, Geom. Topol. 8 (2004) 413–474
  • W D Neumann, J Yang, Bloch invariants of hyperbolic $3$-manifolds, Duke Math. J. 96 (1999) 29–59
  • W Parry, C-H Sah, Third homology of ${\rm SL}(2,\,\mathbf{R})$ made discrete, J. Pure Appl. Algebra 30 (1983) 181–209
  • C-H Sah, Homology of classical Lie groups made discrete. III, J. Pure Appl. Algebra 56 (1989) 269–312