Classification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group

Abstract

A classification of partially hyperbolic diffeomorphisms on three-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus, then it is dynamically coherent and leaf conjugate to a known algebraic example. This classification includes manifolds which support Anosov flows, and it confirms conjectures regarding dynamical coherence and leaf conjugacy in the specific case of solvable fundamental group.