增广是勒让图的束

Pub Date : 2019-12-23 DOI:10.4310/jsg.2022.v20.n2.a1

B. An, Youngjin Bae, Tao Su

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引用次数: 5

摘要

本文结合(有边)Legendrian图，研究并证明了两个范畴Legendrian不变量之间的等价性:增强范畴，一个提升相关Chekanov-Eliashberg DGA的增广集合的一元$A_{\infty}$ -范畴，和一个在前平面上具有微支撑的DG范畴，在接触无穷远处由(有边)Legendrian图控制。换句话说，推广[21]，我们证明了在奇异情况下“增广是束”。

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Augmentations are sheaves for Legendrian graphs

In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical Legendrian isotopy invariants: the augmentation category, a unital $A_{\infty}$-category, which lifts the set of augmentations of the associated Chekanov-Eliashberg DGA, and a DG category of constructible sheaves on the front plane, with micro-support at contact infinity controlled by the (bordered) Legendrian graph. In other words, generalizing [21], we prove "augmentations are sheaves" in the singular case.

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