The Kanenobu knots and Khovanov-Rozansky homology

Lobb, Andrew

doi:10.1090/s0002-9939-2014-11863-6

The Kanenobu knots and Khovanov-Rozansky homology

Lobb, Andrew

Authors

Professor Andrew Lobb andrew.lobb@durham.ac.uk
Professor

Abstract

Kanenobu has given infinite families of knots with the same HOMFLYPT polynomials. We show that these knots also have the same and HOMFLYPT homologies, thus giving the first example of an infinite family of knots indistinguishable by these invariants. This is a consequence of a structure theorem about the homologies of knots obtained by twisting up the ribbon of a ribbon knot with one ribbon.

Citation

Lobb, A. (2014). The Kanenobu knots and Khovanov-Rozansky homology. Proceedings of the American Mathematical Society, 142(4), 1447-1455. https://doi.org/10.1090/s0002-9939-2014-11863-6

Journal Article Type	Article
Acceptance Date	May 17, 2012
Online Publication Date	Jan 28, 2014
Publication Date	Jan 1, 2014
Deposit Date	Feb 11, 2014
Publicly Available Date	Feb 21, 2014
Journal	Proceedings of the American Mathematical Society
Print ISSN	0002-9939
Electronic ISSN	1088-6826
Publisher	American Mathematical Society
Peer Reviewed	Peer Reviewed
Volume	142
Issue	4
Pages	1447-1455
DOI	https://doi.org/10.1090/s0002-9939-2014-11863-6

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Copyright Statement
First published in Proceedings of the American Mathematical Society in 2014, published by the American Mathematical Society. © 2014 American Mathematical Society
Reverts to public domain 28 years from publication.