Sheaf quantization and intersection of rational Lagrangian immersions

Pub Date : 2020-05-11 DOI:10.5802/aif.3554
Tomohiro Asano, Yuichi Ike
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引用次数: 11

Abstract

We study rational Lagrangian immersions in a cotangent bundle, based on the microlocal theory of sheaves. We construct a sheaf quantization of a rational Lagrangian immersion and investigate its properties in Tamarkin category. Using the sheaf quantization, we give an explicit bound for the displacement energy and a Betti/cup-length estimate for the number of the intersection points of the immersion and its Hamiltonian image by a purely sheaf-theoretic method.
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有理拉格朗日浸入的束量化与交
基于微局部槽轮理论,我们研究了余切丛中的有理拉格朗日浸入。我们构造了有理拉格朗日浸入的sheaf量子化,并研究了它在Tamarkin范畴中的性质。利用sheaf量子化,我们用纯sheaf理论的方法给出了位移能量的显式界,并给出了浸入及其Hamiltonian像的交点数量的Betti/cup长度估计。
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