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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

M. Chlouveraki ,
D. Goundaroulis ,
A. Kontogeorgis  and
S. Lambropoulou
M. Chlouveraki
Affiliation:
Université Paris-Saclay, UVSQ, CNRS, Laboratoire de Mathématiques de Versailles, 45 avenue des Etats-Unis, 78000Versailles, France (maria.chlouveraki@uvsq.fr) http://chlouveraki.perso.math.cnrs.fr/
D. Goundaroulis
Affiliation:
Department of Molecular and Human Genetics, Baylor College of MedicineHoustonTX77030United States (dimos.gkountaroulis@bcm.edu)
A. Kontogeorgis
Affiliation:
Department of Mathematics, University of Athens, Panepistimioupolis, 15784Athens, Greece (kontogar@math.uoa.gr)
S. Lambropoulou
Affiliation:
School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografou campus, 15780Athens, Greece (sofia@math.ntua.gr) http://www.math.ntua.gr/~sofia
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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 θ-invariant, which is itself a generalization of the Jones polynomial.

Keywords

framizationcategorificationlink invariantsKhovanov homologyskein relationspectral sequences
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 1731 - 1757
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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