Legendrian ribbons and strongly quasipositive links in an open book

TL;DR

This paper establishes a characterization of strongly quasipositive links in open books via Legendrian ribbons, extending previous results from the three-sphere to more general contact structures, with applications to fibered links and satellites.

Contribution

It generalizes the characterization of strongly quasipositive links using Legendrian ribbons from the three-sphere to arbitrary open books with contact structures.

Findings

A link in an open book is strongly quasipositive if and only if it bounds a Legendrian ribbon.

Techniques for determining strong quasipositivity are discussed, with applications to fibered links and satellites.

Extension of Baader and Ishikawa's result to broader contact geometric settings.

Abstract

We show that a link in an open book can be realized as a strongly quasipositive braid if and only if it bounds a Legendrian ribbon with respect to the associated contact structure. This generalizes a result due to Baader and Ishikawa for links in the three-sphere. We highlight some related techniques for determining whether or not a link is strongly quasipositive, emphasizing applications to fibered links and satellites.