What question did this study set out to answer?

The aim is to establish a bound on the maximum degree of the Jones polynomial for positive links with a second Jones coefficient of ±1.

January 18, 2026

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

Key Points

The aim is to establish a bound on the maximum degree of the Jones polynomial for positive links with a second Jones coefficient of ±1.
Analyzed properties of the Jones polynomial for positive links
Compared results with previous findings on positive fibered links
Identified specific bounds for the maximum degree of the Jones polynomial
Confirmed the second Jones coefficient condition of ±1 influences polynomial degree

Abstract

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

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