Exact Lagrangian tori in symplectic Milnor fibers constructed with fillings

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 non-vanishing given an explicit Weinstein handlebody diagrams.

Major revisions. Theorem 1.1 from version 1 was incorrect and has been removed. New examples added in section 5

References in corpus (3)

• Homological mirror symmetry for log Calabi-Yau surfaces
• Families of monotone Lagrangians in Brieskorn--Pham hypersurfaces
• On Newton polytopes of Lagrangian augmentations