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

Regular Lagrangians in Lefschetz fibrations
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, Muñoz, 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 …