On the AJ conjecture for cables of twist knots
Volume 230 / 2015
Fundamenta Mathematicae 230 (2015), 291-307
MSC: Primary 57N10; Secondary 57M25.
DOI: 10.4064/fm230-3-5
Abstract
We study the AJ conjecture that relates the A-polynomial and the colored Jones polynomial of a knot in $S^3$. We confirm the AJ conjecture for $(r,2)$-cables of the $m$-twist knot, for all odd integers $r$ satisfying $$\begin{cases} (r+8)(r-8m)>0 &\mbox{if } m> 0, \\ r(r+8m-4)>0 &\mbox{if } m<0. \end{cases} $$
