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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 SL2() or PSL2() character variety of a hyperbolic knot manifold under the restriction map to the SL2() or PSL2() 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.

Keywords
character variety, $A$–polynomial, AJ conjecture
Mathematical Subject Classification 2010
Primary: 57M25
References
Publication
Received: 25 September 2015
Revised: 13 March 2016
Accepted: 15 June 2016
Published: 26 January 2017
Authors
Thang T Q Lê
School of Mathematics
Georgia Institute of Technology
686 Cherry Street
Atlanta, GA 30332-0160
United States
Xingru Zhang
Department of Mathematics
University at Buffalo
Buffalo, NY 14214-3093
United States