The volume and Chern-Simons invariant of a representation

Understand

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.