Sheaves via augmentations of Legendrian surfaces

2019/12/12 by Rutherford, Dan, Sullivan, Michael G.
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1912.06186

Abstract

Given an augmentation for a Legendrian surface in a 1-jet space, Λ⊂ J¹(M), we explicitly construct an object, F ∈ Sh_Λ, of the (derived) category from arXiv:1402.0490 of constructible sheaves on M× R with singular support determined by Λ. In the construction, we introduce a simplicial Legendrian DGA (differential graded algebra) for Legendrian submanifolds in 1-jet spaces that, based on arXiv:1608.02984 and arXiv:1608.03011, is equivalent to the Legendrian contact homology DGA in the case of Legendrian surfaces. In addition, we extend the approach of arXiv:1402.0490 for 1-dimensional Legendrian knots to obtain a combinatorial model for sheaves in Sh_Λ in the 2-dimensional case.

Related

• Generating families and constructible sheaves
• Augmentations are sheaves for Legendrian graphs
• Cellular Legendrian contact homology for surfaces, part I
• Cellular Legendrian contact homology for surfaces, part II
• Families of Legendrian Submanifolds via Generating Families