On the AJ conjecture for cables of twist knots

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 $\{\begin{array}{ll}(r+8)(r-8m)>0& ifm>0,\\ r(r+8m-4)>0& ifm<0.\end{array}$

arXiv commentResults in Section 3 are corrected. arXiv admin note: text overlap with arXiv:1111.5258, arXiv:1405.4055; and with arXiv:math/0407521 by other authors