The volume and Chern-Simons invariant of a representation

Details The volume and Chern-Simons invariant of a representation The volume and Chern-Simons invariant of a representation

2007-10-10

arxiv.org/abs/0710.2049v2

Duke Math. J., 150 (3):489-532, 2009

Mathematics

Geometric Topology

32 pages, 10 figures

Scientific paper

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.

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