The Cannon Conjecture states that a hyperbolic group with 2-sphere
boundary is virtually the fundamental group of a hyperbolic
3-manifold. We'll state a relative version of this conjecture, and
sketch a proof that it is equivalent to the usual Cannon conjecture.
The proof uses new theorems relating the boundary of a relatively
hyperbolic group to the boundaries of its Dehn fillings.

This is joint work with Daniel Groves and Alessandro Sisto.