2022/04/08 by Lizzie Buchanan, Buchanan, Lizzie · 2 citations
Engineering · Mathematics · #57K14 #Adhesion, Friction, and Surface Interactions #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2204.03846
openalex publication_date 2022/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a new upper bound on the maximum degree of the Jones polynomial of a fibered positive link. In particular, we prove that the maximum degree of the Jones polynomial of a fibered positive knot is at most four times the minimum degree. Using this result, we can complete the classification of all knots of crossing number ≤ 12 as positive or not positive, by showing that the seven remaining knots for which positivity was unknown are not positive. That classification was also done independently at around the same time by Stoimenow.