A generalized skein relation for Khovanov homology and a categorification of the $\theta$-invariant

Maria Chlouveraki; Dimos Goundaroulis; Aristides Kontogeorgis; Sofia Lambropoulou

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arXiv · 1904.07794

A generalized skein relation for Khovanov homology and a categorification of the $\theta$-invariant

Maria Chlouveraki·Dimos Goundaroulis·Aristides Kontogeorgis·Sofia Lambropoulou

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Abstract

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 $\theta$-invariant, which is itself a generalization of the Jones polynomial.

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Maria Chlouveraki, Dimos Goundaroulis, Aristides Kontogeorgis, Sofia Lambropoulou. 2019-04-16. A generalized skein relation for Khovanov homology and a categorification of the $\theta$-invariant. https://arxiv.org/abs/1904.07794

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