Infinite Volume and Bounded Cohomology

Geometry & Topology
Event time: 
Tuesday, November 6, 2018 - 4:15pm
James Farre
Speaker affiliation: 
Utah and Yale
Event description: 
To a hyperbolic 3-manifold M, we associate the class in cohomology that computes the volume of geodesic tetrahedra in M. We will be interested in the setting that M has infinite volume, so this cohomology class is necessarily zero. To circumvent this shortcoming, we introduce bounded cohomology. To each hyperbolic structure on the underlying manifold, we get potentially different bounded volume classes. The goal of this talk will be to explain how these bounded classes change as the isometry type of the hyperbolic structure changes.  We will also explore the normed and linear structure of degree 3 bounded cohomology of surface groups in terms of the asymptotic geometry of the ends of hyperbolic 3-manifolds. 
Research Area(s):