Non-characteristic expansions of Legendrian singularities

Abstract

This paper presents an algorithm to deform any Legendrian singularity to a nearby Legendrian subvariety with singularities of a simple combinatorial nature. Furthermore, the category of microlocal sheaves on the original Legendrian singularity is equivalent to that on the nearby Legendrian subvariety. This yields a concrete combinatorial model for microlocal sheaves, as well as an elementary method for calculating them.

47 pages, 6 figures; revised introduction, updated references

References in corpus (5)

• Triangulated surfaces in triangulated categories
• Wrapped microlocal sheaves on pairs of pants
• Arboreal Singularities
• Family Floer cohomology and mirror symmetry
• A combinatorial calculation of the Landau-Ginzburg model $M={\mathbb{C}}^3,W=z_1{z}_2{z}_3$

Cited by in corpus (17)

• Cluster varieties from Legendrian knots
• Wrapped microlocal sheaves on pairs of pants
• The nonequivariant coherent-constructible correspondence for toric stacks
• Mirror symmetry for very affine hypersurfaces
• Arboreal Singularities in Weinstein Skeleta
• On the combinatorics of exact Lagrangian surfaces
• Calabi-Yau structures on topological Fukaya categories
• Sheaf quantization in Weinstein symplectic manifolds
• Relative Calabi-Yau completions
• Lagrangian Skeleta of Hypersurfaces in $({\mathbb{C}}^{\ast }{)}^n$
• A combinatorial calculation of the Landau-Ginzburg model $M={\mathbb{C}}^3,W=z_1{z}_2{z}_3$
• Arboreal singularities from Lefschetz fibrations
• Sheaf Quantization of Legendrian Isotopy
• Positive arborealization of polarized Weinstein manifolds
• Versality in mirror symmetry
• Lagrangian cobordism functor in microlocal sheaf theory I
• Arboreal singularities and loose Legendrians I