Spherical adjunction and Serre functor from microlocalization
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914808365842432 |
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| author | Kuo, Christopher Li, Wenyuan |
| author_facet | Kuo, Christopher Li, Wenyuan |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_06643 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Spherical adjunction and Serre functor from microlocalization Kuo, Christopher Li, Wenyuan Symplectic Geometry 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. |
| title | Spherical adjunction and Serre functor from microlocalization |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2210.06643 |