Hyperbolic 3-manifolds and the Cheeger-Chern-Simons class.

摘要

We give a simple formula for the volume and Chern-Simons invariant of a PSL(2, C )-representation of a tame 3-manifold. If the representation is the geometric representation of a hyperbolic 3-manifold, our formula gives the volume and Chern-Simons invariant directly from an ideal triangulation without the use of additional combinatorial topology. In particular, our formula computes the Chern-Simons invariant just as fast as the volume.