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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.06643 |
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Table of Contents:
- For a subanalytic Legendrian $Λ\subseteq S^{*}M$, we prove that when $Λ$ is either swappable or a full Legendrian stop, the microlocalization at infinity $m_Λ: \operatorname{Sh}_Λ(M) \rightarrow \operatorname{μsh}_Λ(Λ)$ is a spherical functor, and the spherical cotwist is the Serre functor on the subcategory $\operatorname{Sh}_Λ^b(M)_0$ of compactly supported sheaves with perfect stalks. This is a sheaf theory counterpart (with weaker assumptions) of the results on the cap functor and cup functors between Fukaya categories. When proving spherical adjunction, we deduce the Sato-Sabloff fiber sequence and construct the Guillermou doubling functor for any Reeb flow.