Dynamical incoherence for a large class of partially hyperbolic diffeomorphisms

Thomas Barthelme, Sergio Fenley, Steven Frankel, Rafael Potrie

We show that if a partially hyperbolic diffeomorphism of a Seifert manifold induces a map in the base which has a pseudo-Anosov component then it cannot be dynamically coherent. This extends BGHP to the whole isotopy class. We relate the techniques with the study of certain partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds performed in BFFP. The appendix reviews some consequences of the Nielsen-Thurston classification of surface homeomorphisms to the dynamics of lifts of such maps to the universal cover.