Relative Calabi-Yau structure on microlocalization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916350425825280 |
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| author | Kuo, Christopher Li, Wenyuan |
| author_facet | Kuo, Christopher Li, Wenyuan |
| contents | For an oriented manifold $M$ and a compact subanalytic Legendrian $Λ\subseteq S^*M$, we construct a canonical strong smooth relative Calabi--Yau structure on the microlocalization at infinity and its left adjoint $m_Λ^l: \operatorname{μsh}_Λ(Λ) \rightleftharpoons \operatorname{Sh}_Λ(M)_0 : m_Λ$ between compactly supported sheaves on $M$ with singular support on $Λ$ and microsheaves on $Λ$. We also construct a canonical strong Calabi-Yau structure on microsheaves $\operatorname{μsh}_Λ(Λ)$. Our approach does not require local properness and hence does not depend on arborealization. We thus obtain a canonical smooth relative Calabi-Yau structure on the Orlov functor for wrapped Fukaya categories of cotangent bundles with Weinstein stops, such that the wrap-once functor is the inverse dualizing bimodule. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative Calabi-Yau structure on microlocalization Kuo, Christopher Li, Wenyuan Symplectic Geometry Algebraic Topology K-Theory and Homology For an oriented manifold $M$ and a compact subanalytic Legendrian $Λ\subseteq S^*M$, we construct a canonical strong smooth relative Calabi--Yau structure on the microlocalization at infinity and its left adjoint $m_Λ^l: \operatorname{μsh}_Λ(Λ) \rightleftharpoons \operatorname{Sh}_Λ(M)_0 : m_Λ$ between compactly supported sheaves on $M$ with singular support on $Λ$ and microsheaves on $Λ$. We also construct a canonical strong Calabi-Yau structure on microsheaves $\operatorname{μsh}_Λ(Λ)$. Our approach does not require local properness and hence does not depend on arborealization. We thus obtain a canonical smooth relative Calabi-Yau structure on the Orlov functor for wrapped Fukaya categories of cotangent bundles with Weinstein stops, such that the wrap-once functor is the inverse dualizing bimodule. |
| title | Relative Calabi-Yau structure on microlocalization |
| topic | Symplectic Geometry Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2408.04085 |