English

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

R2 v1 2026-06-23T07:38:27.327Z