We investigate the relationship between the boundary of a relatively hyperbolic group and the boundary of a quotient obtained via a long Dehn filling. As an application of our techniques, we prove that if the original boundary is S^2, then the boundary of the quotient is also S^2, and we deduce a relative version of the Cannon conjecture from the absolute version. I will try to explain what all of these things mean and explain some of the main results and ideas that go into the proofs.
This is joint work with Jason Manning and Alessandro Sisto. Speaker(s): Daniel Groves (University of Illinois at Chicago)