Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 3

Special Issue: In Honor of Prof. Kyoji Saito’s 75th Birthday

Guest Editors: Stanislaw Janeczko, Si Li, Jie Xiao, Stephen S.T. Yau, and Huaiqing Zuo

Categorification of Legendrian knots

Pages: 421 – 437

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n3.a4


Tatsuki Kuwagaki (Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, Japan)


The concept of a perverse schober defined by Kapranov–Schechtman is a categorification of the notion of a perverse sheaf. In their definition, a key ingredient is a 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.

2010 Mathematics Subject Classification


This work was supported by World Premier International Research Center Initiative (WPI), MEXT, Japan and JSPS KAKENHI Grant Number JP18K13405.

Received 17 February 2019

Accepted 23 August 2019

Published 11 November 2020