Relative Calabi-Yau structure on microlocalization

Christopher Kuo; Wenyuan Li

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arXiv · 2408.04085

Relative Calabi-Yau structure on microlocalization

Christopher Kuo·Wenyuan Li

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Abstract

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.

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BibTeX RIS

Christopher Kuo, Wenyuan Li. 2024-08-07. Relative Calabi-Yau structure on microlocalization. https://arxiv.org/abs/2408.04085

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