Year: 2025
Type: article
Abstract: We construct a Lagrangiansubmanifold in the cotangent bundle of a 3‐torus whose projection to the fiber is a neighborhood of a tropical curve with a single 4‐valent vertex. This Lagrangian submanifold has an isolated conical singular point, and its smooth locus is diffeomorphic to the minimally twisted five‐component chain link complement, a cusped hyperbolic 3‐manifold. From this singular Lagrangian, we construct a Lagrangian immersion, and identify a moduli space of objects in the wrapped Fukaya category that it supports. We show that for a generic line in projective 3‐space, there is a local system on this Lagrangian immersion such that the resulting object of the wrapped Fukaya category is homologically mirror to an object of the derived category supported on the line. In the course of the proof, we construct a version of the wrapped Fukaya category with objects supported on Lagrangian immersions, which may be of independent interest.
Source: Journal of Topology
DOI: 10.1112/topo.70057
Author: Sebastian Haney
Institution: Harvard University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W7117710264