Recognizing products of surfaces and simply connected 4 4 -manifolds

We give necessary and sufficient conditions for a closed smooth $6$ -manifold $N$ to be diffeomorphic to a product of a surface $F$ and a simply connected $4$ -manifold $M$ in terms of basic invariants like the fundamental group and cohomological data. Any isometry of the intersection form of $M$ is realized by a self-diffeomorphism of $M\times F$ .