Partially wrapped Fukaya categories of simplicial skeleta

Abstract

A class of partially wrapped Fukaya categories in $T^{\ast }N$ 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.

References in corpus (2)

• On triangulated orbit categories
• Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions