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.