A pair of Jones polynomial positivity obstructions

2023/03/23 by Buchanan, Lizzie · 2 citations
#57K14 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2303.13481

Abstract

We provide a new bound on the maximum degree of the Jones polynomial of a positive link with second Jones coefficient equal to ± 1 or ± 2. This builds upon the result of our previous work, in which we found such a bound for positive fibered links. We also show that each of these three bounds obstruct positivity for infinitely many almost-positive diagrams, allowing us to classify infinitely many knots as almost-positive.

Cited by

• A condition on the Khovanov homology of three families of positive links
• A condition on the Jones polynomial for a family of positive links

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