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arXiv · 2210.06643

Spherical adjunction and Serre functor from microlocalization

Christopher Kuo·Wenyuan Li
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Abstract

For a subanalytic Legendrian $\Lambda \subseteq S^{*}M$, we prove that when $\Lambda$ is either swappable or a full Legendrian stop, the microlocalization at infinity $m_\Lambda: \operatorname{Sh}_\Lambda(M) \rightarrow \operatorname{\mu sh}_\Lambda(\Lambda)$ is a spherical functor, and the spherical cotwist is the Serre functor on the subcategory $\operatorname{Sh}_\Lambda^b(M)_0$ 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.

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Christopher Kuo, Wenyuan Li. 2022-10-13. Spherical adjunction and Serre functor from microlocalization. https://arxiv.org/abs/2210.06643

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