A generalized skein relation for Khovanov homology and a categorification of the θ-invariant

The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov homology. Thanks to this...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2021-12, Vol.151 (6), p.1731-1757
Main Authors: Chlouveraki, M., Goundaroulis, D., Kontogeorgis, A., Lambropoulou, S.
Format: Article
Language:English
Subjects:
Algebra
Analysis of PDEs
Homology
Invariants
Mathematics
Polynomials
Skeins
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov homology. Thanks to this relation, we are able to generalize the Khovanov homology in order to obtain a categorification of the θ-invariant, which is itself a generalization of the Jones polynomial.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2020.78