The volume and Chern-Simons invariant of a hyperbolic manifold

Christian Zickert, Columbia

Let M be a hyperbolic manifold. If M is complete and of finite volume,
it follows from Mostow rigidity that the volume is a topological
invariant of M. The Chern-Simons invariant is defined by integrating a
certain 3-form over a section of the orthonormal frame bundle. It can
be regarded as the imaginary part of a complex volume with the real
part being the usual volume. In this talk we shall discuss methods of
computing the complex volume from purely topological descriptions of
M.  As a result, we obtain a very efficient algorithm for computing
the Chern-Simons invariant.