On the AJ conjecture for cable knots

TL;DR

This paper investigates the AJ conjecture for (r,2)-cables of knots, demonstrating its validity for many such cables of specific two-bridge and pretzel knots using skein theory.

Contribution

It proves the AJ conjecture for a broad class of (r,2)-cables of certain knots, expanding the understanding of the conjecture's applicability.

Findings

AJ conjecture holds for most (r,2)-cables of some two-bridge knots

AJ conjecture holds for most (r,2)-cables of some pretzel knots

Skein theory is used to establish these results

Abstract

We study the AJ conjecture for $(r,2)$-cables of a knot, where $r$ is an odd integer. Using skein theory, we show that the AJ conjecture holds true for most $(r,2)$-cables of some classes of two-bridge knots and pretzel knots.