The AJ-Conjecture for Cables of Two Bridge Knots

Abstract

The AJ-conjecture for a knot K ⊂ S 3 relates the A-polynomial and the colored Jones polynomial of K. If a two-bridge knot K satisfies the AJ-conjecture, we give sufficient conditions on K for the (r, 2)-cable knot C to also satisfy the AJconjecture. If a reduced alternating diagram of K has η + positive crossings and η − negative crossings, then C will satisfy the AJ-conjecture when (r+4η − )(r−4η + ) > 0 and the conditions of the main theorem are satisfied.