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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Khovanov-Rozansky homology and the braid index of a knot


Author: Keiko Kawamuro
Journal: Proc. Amer. Math. Soc. 137 (2009), 2459-2469
MSC (2000): Primary 57M25, 57M27; Secondary 57M50
Published electronically: February 23, 2009
MathSciNet review: 2495283
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Abstract: We construct a knot whose braid index is not detected by the Morton-Franks-Williams (MFW) inequality but is detected by a related KR-MFW inequality that comes from the Khovanov-Rozansky homology. We also construct infinitely many knots whose braid indices are not detected by the KR-MFW inequality.


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Additional Information

Keiko Kawamuro
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005
Address at time of publication: School of Mathematics, The Institute for Advanced Study, Princeton, New Jersey 08540
Email: kk6@ias.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09743-3
PII: S 0002-9939(09)09743-3
Received by editor(s): November 9, 2007
Received by editor(s) in revised form: July 2, 2008
Published electronically: February 23, 2009
Additional Notes: The author was partially supported by NSF grants DMS-0806492 and DMS-0635607.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.