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skein relation

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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A generalized skein relation for Khovanov homology and a categorification of the θ-invariant
M. Chlouveraki, D. Goundaroulis, A. Kontogeorgis, S. Lambropoulou
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 6 / December 2021

Published online by Cambridge University Press:

05 November 2020, pp. 1731-1757

Print publication:

December 2021
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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.