We present the first known nontrivial topological obstructions to the existence of
partially hyperbolic diffeomorphisms. In particular, we show that
there are no partially hyperbolic diffeomorphisms on the 3-sphere.
More generally, we show that for a partially hyperbolic diffeomorphism
of 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  by dropping the assumption
of dynamical coherence.