Knot Cabling and the Degree of the Colored Jones Polynomial II

TL;DR

This paper investigates how knot cabling affects the degree of the colored Jones polynomial, verifies related conjectures, and extends previous work on Jones slopes and linear terms.

Contribution

It determines the behavior of Jones slopes and linear terms under cabling under certain hypotheses, and verifies key conjectures for specific classes of knots.

Findings

Jones slopes and linear terms behave predictably under cabling

Garoufalidis' Slope Conjecture is verified for cable knots

Conjectures hold for 2-fusion knots

Abstract

We continue our study of the degree of the colored Jones polynomial under knot cabling started in "Knot Cabling and the Degree of the Colored Jones Polynomial" (arXiv:1501.01574). Under certain hypothesis on this degree, we determine how the Jones slopes and the linear term behave under cabling. As an application we verify Garoufalidis' Slope Conjecture and a conjecture of the authors for cables of a two-parameter family of closed 3-braids called 2-fusion knots.