Categorification of Legendrian knots
Algebraic Geometry
2019-02-19 v2 Symplectic Geometry
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.
Cite
@article{arxiv.1902.04269,
title = {Categorification of Legendrian knots},
author = {Tatsuki Kuwagaki},
journal= {arXiv preprint arXiv:1902.04269},
year = {2019}
}
Comments
13 pages. v2: corrected statements and definitions. The author thanks F. Sanda