Categorification of Legendrian knots

Abstract

Perverse schober defined by Kapranov--Schechtman is a categorification of the notion of perverse sheaf. In their definition, a key ingredient is certain purity property of perverse sheaves. In this short note, we attempt to describe a real analogue of the above story, as categorification of Legendrian points/knots. The notion turns out to include various notions such as semi-orthogonal decomposition, mutation braiding, spherical functor, N-spherical functor, and irregular perverse schober.

arXiv comment13 pages. v2: corrected statements and definitions. The author thanks F. Sanda

References in corpus (7)

• Introduction to Stokes structures
• Cluster varieties from Legendrian knots
• An analogue of Dubrovin's conjecture
• A microlocal approach to the enhanced Fourier-Sato transform in dimension one
• Perverse sheaves of categories and some applications
• Perverse schobers and wall crossing
• Perverse schobers on Riemann surfaces: constructions and examples