2019/12/23 by An, Byung Hee, Bae, Youngjin, Su, Tao
#14F05 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Primary: 57R17 #Secondary: 57M15 #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1912.10782
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∞-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.