Partial Hyperbolicity and Pseudo-Anosov Dynamics

Abstract

We show that if a hyperbolic 3-manifold admits a partially hyperbolic diffeomorphism then it also admits an Anosov flow. Moreover, we give a complete classification of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds as well as partially hyperbolic diffeomorphisms in Seifert manifolds inducing pseudo-Anosov dynamics in the base. This classification is given in terms of the structure of their center (branching) foliations and the notion of collapsed Anosov flows.