Exact Lagrangian tori in symplectic Milnor fibers constructed with fillings

Capovilla-Searle, Orsola

doi:10.2140/agt.2025.25.3225

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Exact Lagrangian tori in symplectic Milnor fibers constructed with fillings

Orsola Capovilla-Searle

Algebraic & Geometric Topology 25 (2025) 3225–3249

DOI: 10.2140/agt.2025.25.3225

Abstract

We use exact Lagrangian fillings and Weinstein handlebody diagrams to construct infinitely many distinct exact Lagrangian tori in $4$ -dimensional Milnor fibers of isolated hypersurface singularities with positive modality. We also provide a generalization of a criterion for when the symplectic homology of a Weinstein $4$ -manifold is nonvanishing given an explicit Weinstein handlebody diagram.

Keywords

Weinstein, Milnor fiber, Lagrangian surface, Legendrian

Mathematical Subject Classification

Primary: 53Dxx

Secondary: 57Kxx

References

Publication

Received: 11 February 2022

Revised: 5 December 2023

Accepted: 19 May 2024

Published: 1 October 2025

Authors

Orsola Capovilla-Searle
Department of Mathematics University of California Davis Davis, CA United States

Open Access made possible by participating institutions via Subscribe to Open.

Volume 25, issue 6 (2025)