Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part II: Branching foliations
Thomas Barthelme, Sergio Fenley, Steven Frankel, Rafael Potrie
Using branching foliations, and extending tools from foliation theory to this more general context, we remove the assumption of dynamical coherence from the first part of our work, BFFP-part1. In particular, in Seifert manifolds, we finish the classification of partially hyperbolic diffeomorphisms homotopic to the identity. In hyperbolic manifolds, we obtain that a partially hyperbolic diffeomorphism is either dynamically coherent and, up to a power, a discretized Anosov flow; or it is of a special type that we call double translation, for which we can describe its branching foliations and understand its coarse dynamics. More general, albeit less complete results, are also obtained on general 3-manifolds.