TY - JOUR
T1 - Augmentations are sheaves for Legendrian graphs
AU - An, Byung Hee
AU - Bae, Youngjin
AU - Su, Tao
N1 - Publisher Copyright:
© 2022, International Press, Inc.. All rights reserved.
PY - 2022
Y1 - 2022
N2 - In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical Legen-drian 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 infin-ity controlled by the (bordered) Legendrian graph. In other words, generalizing [21], we prove “augmentations are sheaves” in the singular case.
AB - In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical Legen-drian 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 infin-ity controlled by the (bordered) Legendrian graph. In other words, generalizing [21], we prove “augmentations are sheaves” in the singular case.
UR - http://www.scopus.com/inward/record.url?scp=85144688344&partnerID=8YFLogxK
U2 - 10.4310/JSG.2022.v20.n2.a1
DO - 10.4310/JSG.2022.v20.n2.a1
M3 - Article
AN - SCOPUS:85144688344
SN - 1527-5256
VL - 20
SP - 259
EP - 416
JO - Journal of Symplectic Geometry
JF - Journal of Symplectic Geometry
IS - 2
ER -