Monday, September 23, 2019
09/23/2019 - 4:15pm
I will define bounded cohomology of discrete groups, illustrated by some examples coming from computing the volumes of locally geodesic simplices in hyperbolic manifolds. To each complete hyperbolic metric of infinite volume on a fixed 3-manifold, we associate its volume class in bonded cohomology. We will see that the volume class is a complete invariant of the bi-Lipschitz class of such a metric, modulo discrepancies in cusps. We will also study the behavior of linear combinations of volume classes and give a geometric interpretation of addition.