Duke Mathematical Journal

The volume and Chern-Simons invariant of a representation

Christian K. Zickert

Abstract

We give an efficient simplicial formula for the volume and Chern-Simons invariant of a boundary-parabolic ${\rm PSL}(2,{\mathds C})$-representation of a tame $3$-manifold. If the representation is the geometric representation of a hyperbolic $3$-manifold, our formula computes the volume and Chern-Simons invariant directly from an ideal triangulation with no use of additional combinatorial topology. In particular, the Chern-Simons invariant is computed just as easily as the volume

Article information

Source
Duke Math. J., Volume 150, Number 3 (2009), 489-532.

Dates
First available in Project Euclid: 27 November 2009

https://projecteuclid.org/euclid.dmj/1259332507

Digital Object Identifier
doi:10.1215/00127094-2009-058

Mathematical Reviews number (MathSciNet)
MR2582103

Zentralblatt MATH identifier
1246.58019

Subjects
Primary: 58J28: Eta-invariants, Chern-Simons invariants
Secondary: 57M27: Invariants of knots and 3-manifolds

Citation

Zickert, Christian K. The volume and Chern-Simons invariant of a representation. Duke Math. J. 150 (2009), no. 3, 489--532. doi:10.1215/00127094-2009-058. https://projecteuclid.org/euclid.dmj/1259332507

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