Wrapped sheaves

TL;DR

This paper develops a sheaf-theoretic analogue of the wrapped Fukaya category, establishing an equivalence with categories of sheaves microsupported in certain isotropic subsets, thus connecting sheaf theory with symplectic topology.

Contribution

It constructs a sheaf-theoretic version of the wrapped Fukaya category and proves an equivalence with sheaves microsupported in subanalytic isotropics, extending the sheaf-Fukaya comparison theorem.

Findings

Constructed a sheaf-theoretic wrapped Fukaya category.

Proved an equivalence with categories of microsupported sheaves.

Extended the sheaf-Fukaya comparison theorem.

Abstract

We construct a sheaf-theoretic analogue of the wrapped Fukaya category in Lagrangian Floer theory, by localizing a category of sheaves microsupported away from some given $\Lambda \subset S^*M$ along continuation maps constructed using the Guillermou-Kashiwara-Schapira sheaf quantization. When $\Lambda$ is a subanalytic singular isotropic, we also construct a comparison map to the category of compact objects in the category of unbounded sheaves microsupported in $\Lambda$, and show that it is an equivalence. The last statement can be seen as a sheaf theoretical incarnation of the sheaf-Fukaya comparison theorem of Ganatra-Pardon-Shende.