On the 2-systole of stretched enough positive scalar curvature metrics on S 2 x S 2

Abstract

We use recent developments by Gromov and Zhu to derive an upper bound for the 2-systole of the homology class of S 2 x { * } in a S 2 x S 2 with a positive scalar curvature metric such that the set of spheres homologous to S 2 x { * } is wide enough in some sense.

A topological lemma a bout the connectedness of separating hyper surfaces has been added, as well as some further discussion on a possible rigidity statement