On partially hyperbolic diffeomorphisms of 3-manifolds with commutative fundamental group. InModern dynamical systems and applications, 307–312, Cambridge Univ

Abstract. Let f be a dynamically coherent partially hyperbolic diffeomorphism of a compact three dimensional manifold whose fundamental group is abelian. We show that the action f ∗ induced by f on the 1-dimensional real homologies, is also partially hyper-bolic: it has an eigenvalue of modulus> 1 and an eigenvalue of modulus < 1. In particular, there are no such diffeomorphisms on S3. The property of dynamical coherence follows from the unique integrability of the central distribution. We also discuss a weaker integrability property of the central distribution. 1. Introduction an