#### Volume 17, issue 1 (2017)

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Character varieties, $A$–polynomials and the AJ conjecture

### Thang T Q Lê and Xingru Zhang

Algebraic & Geometric Topology 17 (2017) 157–188
##### Abstract

We establish some facts about the behavior of the rational-geometric subvariety of the ${SL}_{2}\left(ℂ\right)$ or ${PSL}_{2}\left(ℂ\right)$ character variety of a hyperbolic knot manifold under the restriction map to the ${SL}_{2}\left(ℂ\right)$ or ${PSL}_{2}\left(ℂ\right)$ character variety of the boundary torus, and use the results to get some properties about the $A$–polynomials and to prove the AJ conjecture for a certain class of knots in ${S}^{3}$ including in particular any $2$–bridge knot over which the double branched cover of ${S}^{3}$ is a lens space of prime order.

##### Keywords
character variety, $A$–polynomial, AJ conjecture
Primary: 57M25