Hofer's distance on diameters and the Maslov index

TL;DR

This paper establishes an upper bound on Hofer's distance between two diameters of the open 2-disk, expressed in terms of the Maslov index of their intersection points, linking geometric and topological invariants.

Contribution

It introduces a novel bound connecting Hofer's distance and the Maslov index for diameters in the open 2-disk, advancing understanding of symplectic geometry.

Findings

Hofer's distance is bounded above by the Maslov index of intersection points.

The result provides a new link between symplectic invariants and intersection theory.

The bound enhances the understanding of geometric structures in symplectic topology.

Abstract

We prove that Hofer's distance between two diameters of the open 2-disk admits an upper bound in terms of the Maslov index of their intersection points.