Non-characteristic expansions of Legendrian singularities
David Nadler
TL;DR
This paper introduces an algorithm to deform Legendrian singularities into simpler forms and establishes an equivalence of microlocal sheaves, providing a combinatorial model and calculation method.
Contribution
It presents a novel algorithm for deforming Legendrian singularities and links microlocal sheaves on original and deformed singularities, enabling combinatorial modeling.
Findings
Deformation algorithm for Legendrian singularities
Equivalence of microlocal sheaves categories
Concrete combinatorial model for microlocal sheaves
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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Equations and Dynamical Systems · Homotopy and Cohomology in Algebraic Topology