Wrapped sheaves

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 $\Lambda \subset S^{\ast }M$ 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.

65 pages, 6 figures. Published version. A new example, Example 2.52

References in corpus (3)

• Covariantly functorial wrapped Floer theory on Liouville sectors
• Persistence-like distance on Tamarkin's category and symplectic displacement energy
• Compact exact Lagrangian intersections in cotangent bundles via sheaf quantization (with an appendix by Tomohiro Asano)

Cited by in corpus (3)

• Duality and kernels in microlocal geometry
• Lagrangian cobordism and shadow distance in Tamarkin category
• Variation of GIT and Variation of Lagrangian Skeletons I: Flip and Flop