A condition on the Jones polynomial for a family of positive links

Abstract

We provide a bound on the maximum degree of the Jones polynomial of any positive link with second Jones coefficient equal to $\pm 1$. This builds on the result of our previous work, in which we found such a bound for positive fibered links.

16 pages, 12 figures. This is Part 1 of a version of arXiv:2303.13481, split up for publication, with updated proofs and definitions