Sharpness of the Morton-Franks-Williams inequality for positive knots and links

2022/11/29 by Alekseev, Ilya
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2211.16434

Abstract

We provide a combinatorial characterisation of positive diagrams satisfying the equality in the Morton-Franks-Williams bound for the degrees of the HOMFLY-PT polynomial. This characterisation allows generating with relative ease examples of diagrams realizing the crossing number, the braid index, and the maximal self-linking number. Besides, we suggest a conjecture concerning the sharpness of the Morton-Franks-Williams inequality for strongly quasipositive links.

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• A new condition on the Jones polynomial of a fibered positive link
• The HOMFLY Polynomial of Links in Closed Braid Form