Arboreal singularities and loose Legendrians I

2019/02/13 by Emmy Murphy, Murphy, Emmy
Mathematics · #53D35 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1902.05056

openalex publication_date 2019/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Arboreal singularities are an important class of Lagrangian singularities. They are conical, meaning that they can be understood by studying their links, which are singular Legendrian spaces in S^2n-1_std. Loose Legendrians are a class of Legendrian spaces which satisfy an h--principle, meaning that their geometric classification is in bijective correspondence with their topological types. For the particular case of the linear arboreal singularities, we show that constructable sheaves suffice to detect whether any closed set of an arboreal link is loose.

Related

• Lagrangian Skeleta and Plane Curve Singularities
• Arboreal models and their stability
• h-principle for loose Legendrian embeddings
• Non-characteristic expansions of Legendrian singularities
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