Regular Lagrangians in Lefschetz fibrations
Symplectic Geometry
2025-10-21 v2
Abstract
We characterize regularity of Lagrangian submanifolds in Weinstein Lefschetz fibrations, establishing a conjecture of Giroux and Pardon. Our main result is the Weinstein analogue of a closed symplectic Lefschetz pencil result of Auroux, Mu\~noz, and Presas. As an application, given a Legendrian link in tight and an exact filling which is part of an arboreal skeleton for the -ball, we build a Lefschetz fibration such that the image of the filling and all of its mutations are arcs in the base.
Cite
@article{arxiv.2510.12170,
title = {Regular Lagrangians in Lefschetz fibrations},
author = {Joseph Breen and Agniva Roy and Luya Wang},
journal= {arXiv preprint arXiv:2510.12170},
year = {2025}
}
Comments
v2: references updated; Corollary 1.1 replaced with Question 1.2 and surrounding discussion updated