Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups

Abstract

We present the first known nontrivial topological obstructions to the existence ofpartially hyperbolic diffeomorphisms. In particular, we show thatthere are no partially hyperbolic diffeomorphisms on the 3-sphere.More generally, we show that for a partially hyperbolic diffeomorphismof a 3-mani-fold with an Abelian fundamental group,the induced action in the first homology group is partially hyperbolic.This improves the results of [4] by dropping the assumptionof dynamical coherence.