Recognizing products of surfaces and simply connected 4-manifolds

TL;DR

This paper characterizes when a closed smooth 6-manifold is diffeomorphic to a product of a surface and a simply connected 4-manifold using invariants like fundamental groups and cohomology, and shows isometries of the intersection form are realizable.

Contribution

It provides necessary and sufficient conditions for such product structures and demonstrates that all isometries of the intersection form are realized by self-diffeomorphisms.

Findings

Characterization of 6-manifolds as products of surfaces and 4-manifolds

Realization of intersection form isometries by self-diffeomorphisms

Conditions based on fundamental group and cohomological data

Abstract

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 x F.