Character varieties, A–polynomials and the AJ conjecture

Lê, Thang¹ ; Zhang, Xingru²

¹School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, United States
²Department of Mathematics, University at Buffalo, Buffalo, NY 14214-3093, United States

Algebraic and Geometric Topology, Tome 17 (2017) no. 1, pp. 157-188

Résumé

We establish some facts about the behavior of the rational-geometric subvariety of the SL2(ℂ) or PSL2(ℂ) character variety of a hyperbolic knot manifold under the restriction map to the SL2(ℂ) or PSL2(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 a certain class of knots in S3 including in particular any 2–bridge knot over which the double branched cover of S3 is a lens space of prime order.

Détail

DOI : 10.2140/agt.2017.17.157

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

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