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...

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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
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Goundaroulis, D.
Kontogeorgis, A.
Lambropoulou, S.
description 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.
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subjects Algebra
Analysis of PDEs
Homology
Invariants
Mathematics
Polynomials
Skeins
title A generalized skein relation for Khovanov homology and a categorification of the θ-invariant
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