Partially hyperbolic diffeormorphisms, ergodicity, and transverse foliations in dimension 3

Abstract

We give a complete topological classification of transitive partially hyperbolic diffeomorphisms in 3-manifolds in terms of Anosov flows, completing a program proposed by Pujals. In particular, this also allows to give a full answer to the ergodicity conjecture of Hertz-Hertz-Ures for partially hyperbolic diffeomorphisms in dimension 3. This is achieved by showing a general result about pairs of transverse $2$-dimensional foliations in 3-manifolds with Gromov hyperbolic leaves which may be of independent interest.