  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 work of Bonatti, Gogolev, Hammerlindl and
Potrie to the whole isotopy class. We relate the techniques with the study of
certain partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds
performed in the previous paper by the authors. 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.

Dynamical Systems;Geometric Topology