Third Bounded Cohomology of Kleinian Groups

We study the function on the singular chain complex of a hyperbolic 3-manifold that assigns, to each 3-simplex, the volume of its straightening. One checks that this function defines a class in bounded cohomology, which is known as the bounded fundamental class. We explore the behavior of bounded fundamental classes as we vary the complete hyperbolic structures of infinite volume on a fixed manifold.