Character varieties, A-polynomials, and the AJ Conjecture

Thang T. Q. Le, Xingru Zhang

Published 2015-09-10Version 1

We establish some facts about the behavior of the rational-geometric subvariety of the $SL_2(\c)$ or $PSL_2(\c)$ character variety of a hyperbolic knot manifold under the restriction map to the $SL_2(\c)$ or $PSL_2(\c)$ 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 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.