增广是勒让图的束

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Symplectic Geometry 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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来源期刊

Journal of Symplectic Geometry 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.