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math.SG2026
Nearly Lefschetz fibrations, Stein structures, and regular Lagrangians
Joseph Breen, Agniva Roy, Luya Wang
We study Stein structures on nearly Lefschetz fibrations, with applications to symplectic and Lagrangian submanifolds in Weinstein domains. We prove that, up to Weinstein deformati…
math.SG2025
Regular Lagrangians in Lefschetz fibrations
Joseph Breen, Agniva Roy, Luya Wang
We characterize regularity of Lagrangian submanifolds in Weinstein Lefschetz fibrations, establishing a conjecture of Giroux and Pardon. Our main result is the Weinstein analogue o…
math.SG2024
Regularly slice implies once-stably decomposably slice
Joseph Breen
We investigate the relationship between regular and decomposable Lagrangian cobordisms in -dimensional symplectizations. First, we show that regular sliceness implies once-stabl…