The volume and Chern-Simons invariant of a representation

Abstract

We give an efficient simplicial formula for the volume and Chern-Simons invariant of a boundary-parabolic PSL(2,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.

32 pages, 10 figures

References in corpus (2)

• A dilogarithmic formula for the Cheeger-Chern-Simons class
• The Extended Bloch Group and the Cheeger-Chern-Simons Class

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