Augmentations are sheaves for Legendrian graphs

Abstract

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.

arXiv comment87 pages

References in corpus (8)

• Covariantly functorial wrapped Floer theory on Liouville sectors
• Legendrian knots and constructible sheaves
• Microlocal Morse theory of wrapped Fukaya categories
• Generating families and augmentations for Legendrian surfaces
• Noncommutative augmentation categories
• Sheaves via augmentations of Legendrian surfaces
• Ruling polynomials and augmentations for Legendrian tangles
• Augmentations and ruling polynomials for Legendrian graphs

Cited by in corpus (4)

• Microlocal Morse theory of wrapped Fukaya categories
• Sheaf quantization in Weinstein symplectic manifolds
• Augmentations and ruling polynomials for Legendrian graphs
• Augmentations and sheaves for links