Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds

Sergio Fenley, Rafael Potrie

We study conservative partially hyperbolic dieomorphisms in hyperbolic 3-manifolds. We show that they are always accessible and deduce as a result that every conservative C^{1+} partially hyperbolic in a hyperbolic 3-manifold must be ergodic, giving an affirmative answer to a conjecture of Hertz-Hertz-Ures in the context of hyperboilc 3-manifolds. Some of the intermediary steps are also done for general partially diffeomorphic diffeomorphisms homotopic to the identity.