微定位的相对 Calabi-Yau 结构

Christopher Kuo, Wenyuan Li
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引用次数: 0

摘要

对于一个定向流形 $M$ 和一个紧凑的亚解析 Legendrian $\Lambda\subseteq S^*M$,我们在无穷远处的微定位及其左邻接$m_\Lambda^l上构造了一个典型的强光滑相对 Calabi--Yaustructure :\operatorname\{mu sh}_\Lambda(\Lambda) \rightleftharpoons\operatorname{Sh}_\Lambda(M)_0 : m_\Lambda$ 在$M$上具有奇异支持的紧凑支持的剪切与$Lambda$上的微剪切之间。我们还在微波$operatorname/{mu sh}_\Lambda(\Lambda)$上构造了一个典型的强卡拉比-尤结构。我们的方法不要求局部正确性,因此也不依赖于arborealization。因此,我们在具有韦恩斯坦止境的共切束的包裹富卡雅范畴的奥洛夫函子上得到了一个非对立的光滑相对卡拉比-尤结构,从而使包裹-一次函子成为逆对偶双模子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Relative Calabi-Yau structure on microlocalization
For an oriented manifold $M$ and a compact subanalytic Legendrian $\Lambda \subseteq S^*M$, we construct a canonical strong smooth relative Calabi--Yau structure on the microlocalization at infinity and its left adjoint $m_\Lambda^l: \operatorname{\mu sh}_\Lambda(\Lambda) \rightleftharpoons \operatorname{Sh}_\Lambda(M)_0 : m_\Lambda$ between compactly supported sheaves on $M$ with singular support on $\Lambda$ and microsheaves on $\Lambda$. We also construct a canonical strong Calabi-Yau structure on microsheaves $\operatorname{\mu sh}_\Lambda(\Lambda)$. 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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