Character varieties, A–polynomials and the AJ conjecture

Lê, Thang; Zhang, Xingru

doi:10.2140/agt.2017.17.157

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

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

Thang T Q Lê and Xingru Zhang

Algebraic & Geometric Topology 17 (2017) 157–188

DOI: 10.2140/agt.2017.17.157

Abstract

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 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

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

Volume 17, issue 1 (2017)