Title: Infinite volume and bounded cohomology
Speaker: James Farre (Yale University)
Abstract: To a hyperbolic 3-manifold M, we associate the class in cohomology that computes the volume of geodesic tetrahedra in M. When M has infinite volume, this cohomology class is zero. To circumvent this shortcoming, we introduce bounded cohomology, and we get potentially different bounded volume classes when we vary the hyperbolic structure on a fixed manifold. The goal of this talk will be to explain how these bounded classes change as the (quasi-) isometry type of the hyperbolic structure changes. Along the way, we will contemplate the classification of Kleinian groups by their end invariants and explore some interesting properties of bounded cohomology.
Seminar URL: https://research.math.osu.edu/topology/