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A generalized skein relation for Khovanov homology and a categorification of the θ-invariant
Published online by Cambridge University Press: 05 November 2020
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 θ-invariant, which is itself a generalization of the Jones polynomial.
Keywords
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 1731 - 1757
- Copyright
- Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh