We establish some facts about the behavior of the rational-geometric subvariety of the or character variety of a hyperbolic knot manifold under the restriction map to the or character variety of the boundary torus, and use the results to get some properties about the –polynomials and to prove the AJ conjecture for a certain class of knots in including in particular any –bridge knot over which the double branched cover of is a lens space of prime order.
"Character varieties, $A$–polynomials and the AJ conjecture." Algebr. Geom. Topol. 17 (1) 157 - 188, 2017. https://doi.org/10.2140/agt.2017.17.157