Relative Calabi-Yau structure on microlocalization

2024/08/07 by Christopher Kuo, Wenyuan Li, Kuo, Christopher +1
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometry and complex manifolds #K-Theory and Homology (math.KT) #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2408.04085

openalex publication_date 2024/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an oriented manifold M and a compact subanalytic Legendrian Λ⊆ S^*M, we construct a canonical strong smooth relative Calabi--Yau structure on the microlocalization at infinity and its left adjoint m_Λ^l: μsh_Λ(Λ) \rightleftharpoons 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 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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