Khovanov-Rozansky homology and the braid index of a knot

Details Khovanov-Rozansky homology and the braid index of a knot Khovanov-Rozansky homology and the braid index of a knot

2007-07-08

arxiv.org/abs/0707.1130v2

Mathematics

Geometric Topology

Scientific paper

We prove the existence of a knot whose braid index the Morton-Franks-Williams
inequality fails to detect but a related inequality (KR-MFW inequality), which
uses new information of Khovanov-Rozansky homology, detects. We also prove, by
examples, that there exists infinitely many knots for which the KR-MFW
inequality fails to detect the braid indices.

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