On the existence of disk-like global sections for Reeb flows on the tight 3-sphere

TL;DR

This paper establishes precise conditions under which a periodic Reeb orbit on the tight 3-sphere bounds a disk-like global section, advancing understanding of Reeb dynamics in contact topology.

Contribution

It provides necessary and sufficient criteria for the existence of disk-like global sections bounded by periodic Reeb orbits on the tight 3-sphere with non-degenerate contact forms.

Findings

Characterization of when a periodic Reeb orbit bounds a disk-like global section.

Conditions are both necessary and sufficient.

Focus on non-degenerate contact forms on the tight 3-sphere.

Abstract

We consider Reeb dynamics on the 3-sphere associated to a tight contact form. Our main result gives necessary and sufficient conditions for a periodic Reeb orbit to bound a disk-like global section for the Reeb flow, when the contact form is assumed to be non-degenerate.