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

TL;DR

This paper establishes an upper bound on the 2-systole of certain positive scalar curvature metrics on S 2 x S 2, utilizing recent geometric developments to relate curvature conditions to topological invariants.

Contribution

It introduces a new upper bound for the 2-systole in positive scalar curvature metrics on S 2 x S 2, based on recent advances by Gromov and Zhu.

Findings

Derived an explicit upper bound for the 2-systole

Connected curvature conditions to topological invariants

Extended previous results to a broader class of metrics

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.