Pure and Applied Mathematics Quarterly
Volume 16 (2020)
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
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