Regular Lagrangians in Lefschetz fibrations

2025/10/14 by Breen, Joseph, Roy, Agniva, Wang, Luya
#53D05 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2510.12170

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, Muñoz, and Presas. As an application, given a Legendrian link in tight S³ 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.

Citations

• From Morse Functions to Lefschetz Fibrations on Cotangent Bundles
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• Topologically Distinct Lagrangian and Symplectic Fillings
• Closed exact Lagrangians in the symplectization of contact manifolds
• Legendrian knots and exact Lagrangian cobordisms
• Lefschetz fibrations and symplectic homology
• Algebraic functions and closed braids
• Lagrangian submanifolds and Lefschetz pencils
• Homological mirror symmetry for the quartic surface
• Contact Structures with Distinct Heegaard Floer Invariants
• Subcritical Stein manifolds are split

Related

• Characterizing Regular Lagrangians by Lefschetz Fibration
• Flexible Lagrangians
• Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations
• Inequivalent Lefschetz fibrations on rational and ruled surfaces
• Symplectic Lefschetz Fibrations from a Lie-theoretical Viewpoint