The Fukaya category of symplectic neighborhood of a non-Hausdorff manifold

TL;DR

This paper introduces a method to compute the Fukaya category of specific symplectic manifolds by relating it to the Morse category of a non-Hausdorff manifold, extending Fukaya-Oh's approach.

Contribution

It develops a novel technique to analyze the Fukaya category via Morse theory on non-Hausdorff manifolds, providing new computational tools.

Findings

Reduction of Fukaya category to Morse category

Application to exact symplectic manifolds

Extension of Fukaya-Oh's method

Abstract

In this paper, using similar idea as in Fukaya-Oh's work ([9]), we devise a method to compute the Fukaya category of certain exact symplectic manifolds by reducing it to the corresponding Morse category of non-Hausdorff manifold as perturbation of the Lagrangian skeleton of the exact symplectic manifold.