Year: 2025
Type: article
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. 53Dxx; 57KxxWe obtain the following corollary by either applying properties of Milnor fibers of adjacent singularities to Theorem 1.1 or to Vianna's result [41, Section 6.2].Corollary 1.2 If M f is the Milnor fiber of a positive-modality isolated hypersurface singularity f , then M f contains infinitely many Hamiltonian nonisotopic exact Maslov-0 Lagrangian tori that are all smoothly isotopic.Milnor fibers of isolated hypersurface singularities have been extensively studied in homological mirror symmetry, singularity theory and low-dimensional topology.An isolated hypersurface singularity is the equivalence class of the germ of a holomorphic function, f W C nC1 !C whose differential has an isolated
Source: Algebraic & Geometric Topology
Author: Orsola Capovilla-Searle
Institution: University of California, Davis
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: National Science Foundation
OpenAlex ID: W4414963059