Professor Andrew Lobb andrew.lobb@durham.ac.uk
Professor
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.
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 |
Accepted Journal Article
(185 Kb)
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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.
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