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The Kanenobu knots and Khovanov-Rozansky homology


Author: Andrew Lobb
Journal: Proc. Amer. Math. Soc. 142 (2014), 1447-1455
MSC (2010): Primary 57M25
DOI: https://doi.org/10.1090/S0002-9939-2014-11863-6
Published electronically: January 28, 2014
MathSciNet review: 3162264
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Abstract: Kanenobu has given infinite families of knots with the same
HOMFLYPT polynomials. We show that these knots also have the same $ sl(n)$ 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.


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Additional Information

Andrew Lobb
Affiliation: Department of Mathematical Sciences, Durham University, Durham DH1 3LE, United Kingdom
Email: andrew.lobb@durham.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2014-11863-6
Received by editor(s): October 5, 2011
Received by editor(s) in revised form: May 15, 2012
Published electronically: January 28, 2014
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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