Partially wrapped Fukaya categories of simplicial skeleta

TL;DR

This paper establishes the well-definedness of certain partially wrapped Fukaya categories in cotangent bundles and demonstrates their role as homological mirrors to categories of coherent sheaves on toric varieties, offering a new Floer theoretic perspective on mirror symmetry.

Contribution

It introduces a new class of partially wrapped Fukaya categories and proves their equivalence to coherent sheaf categories on toric varieties in specific cases, advancing the understanding of mirror symmetry.

Findings

Partially wrapped Fukaya categories are well-defined in cotangent bundles.

These categories serve as homological mirrors to coherent sheaves on toric varieties.

Provides a Floer theoretic formulation of mirror symmetry in non-complete cases.

Abstract

A class of partially wrapped Fukaya categories in $T^* N$ are proven to be well defined and then studied. In the case of $N$ diffeomorphic to $\mathbb{R}^m \times \mathbb{T}^n$, it is shown that these categories provide homological mirrors to equivariant and non-equivariant categories of coherent sheaves on toric varieties. This gives a new Floer theoretic formulation of mirror symmetry in the non-complete case.