On Khovanov complexes

In this paper, we discuss a proof of the invariance under isotopy of a parametrized Khovanov link homology including categorifications of the Jones polynomial and the Kauffman bracket polynomial. In order to present an easy-to-follow proof, we give an explicit description of retractions and chain ho...

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Bibliographic Details
Published in:Topology and its applications 2021-09, Vol.301, p.107514, Article 107514
Main Author: Ito, Noboru
Format: Article
Language:English
Subjects:
Chain homotopy
Khovanov homology
Reidemeister moves
Retraction
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Summary:In this paper, we discuss a proof of the invariance under isotopy of a parametrized Khovanov link homology including categorifications of the Jones polynomial and the Kauffman bracket polynomial. In order to present an easy-to-follow proof, we give an explicit description of retractions and chain homotopies between complexes to induce the invariance under isotopy of links.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2020.107514