On the 2-Systole of Stretched Enough Positive Scalar Curvature Metrics on 𝕊² × 𝕊²

Abstract

We use recent developments by Gromov and Zhu to derive an upper bound for the 2-systole of the homology class of 𝕊² × {∗} in a 𝕊² × 𝕊² with a positive scalar curvature metric such that the set of surfaces homologous to 𝕊² × {∗} is wide enough in some sense.