Character varieties, A–polynomials and the AJ conjecture

Thang T.Q. Lê; Xingru Zhang

doi:10.2140/agt.2017.17.157

Character varieties, A–polynomials and the AJ conjecture

Thang T.Q. Lê
, Xingru Zhang

Mathematics

Georgia Institute of Technology

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	157-188
Number of pages	32
Journal	Algebraic and Geometric Topology
Volume	17
Issue number	1
DOIs	https://doi.org/10.2140/agt.2017.17.157
State	Published - Jan 26 2017

Keywords

A-polynomial
AJ conjecture
Character variety

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abstract = "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.",

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AU - Zhang, Xingru

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AB - 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.

KW - A-polynomial

KW - AJ conjecture

KW - Character variety

UR - https://www.scopus.com/pages/publications/85011827255

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JO - Algebraic and Geometric Topology

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IS - 1

ER -

Character varieties, A–polynomials and the AJ conjecture

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Keywords

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