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.

中文翻译：

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增广是勒让德图的层

在这篇文章中，与（边界的）Legendrian 图相关联，我们研究并展示了两个分类 Legendrian 同位素不变量之间的等价性：增广类别，单位 $A_\infty$ 类别，它提升了相关 Chekanov 的增广集–Eliashberg DGA，以及前平面上可构造滑轮的 DG 类别，在接触无穷远处具有由（边界）Legendrian 图控制的微支撑。换句话说，概括[21]，我们在单数情况下证明“增广是层”。