A Polyfold proof of Gromov's Non-squeezing Theorem

TL;DR

This paper provides a rigorous and accessible proof of Gromov's non-squeezing theorem using Polyfold Theory, showcasing the utility of this approach for moduli spaces of pseudoholomorphic curves.

Contribution

It offers the first polyfold-based proof of Gromov's non-squeezing theorem, demonstrating the method's effectiveness and clarity in symplectic geometry.

Findings

Successful application of Polyfold Theory to Gromov-Witten moduli spaces

A detailed, rigorous proof of Gromov's non-squeezing theorem

Clarification of polyfold description for spheres with minimal energy

Abstract

We re-prove Gromov's non-squeezing theorem by applying Polyfold Theory to a simple Gromov-Witten moduli space. Thus we demonstrate how to utilize the work of Hofer-Wysocki-Zehnder to give proofs involving moduli spaces of pseudoholomorphic curves that are relatively short and broadly accessible, while also fully detailed and rigorous. We moreover review the polyfold description of Gromov-Witten moduli spaces in the relevant case of spheres with minimal energy and one marked point.