Khovanov-Rozansky homology and the braid index of a knot
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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.References
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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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2459-2469
- MSC (2000): Primary 57M25, 57M27; Secondary 57M50
- DOI: https://doi.org/10.1090/S0002-9939-09-09743-3
- MathSciNet review: 2495283