Positive Braid Links with Infinitely Many Fillings

TL;DR

This paper proves that positive braid Legendrian links, which are not equivalent to standard finite type links, have infinitely many exact Lagrangian fillings, expanding understanding of their geometric properties.

Contribution

It establishes that such links admit infinitely many exact Lagrangian fillings, a new result in the study of Legendrian links and their fillings.

Findings

Positive braid Legendrian links not isotopic to finite type links have infinitely many fillings.

The result applies to a broad class of Legendrian links.

It advances the understanding of the relationship between braid positivity and Lagrangian fillings.

Abstract

We prove that any positive braid Legendrian link not isotopic to a standard finite type link admits infinitely many exact Lagrangian fillings.