Khovanov-Rozansky homology and the braid index of a knot

Kawamuro, Keiko

doi:10.1090/S0002-9939-09-09743-3

Khovanov-Rozansky homology and the braid index of a knot
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Proc. Amer. Math. Soc. 137 (2009), 2459-2469 Request permission

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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