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arXiv · 2510.12170

Regular Lagrangians in Lefschetz fibrations

Joseph Breen·Agniva Roy·Luya Wang
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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 $S^3$ and an exact filling which is part of an arboreal skeleton for the $4$-ball, we build a Lefschetz fibration such that the image of the filling and all of its mutations are arcs in the base.

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Joseph Breen, Agniva Roy, Luya Wang. 2025-10-14. Regular Lagrangians in Lefschetz fibrations. https://arxiv.org/abs/2510.12170

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