Character varieties, A-polynomials, and the AJ Conjecture

Thang T. Q. Le; Xingru Zhang

doi:10.2140/agt.2017.17.157

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arXiv · 1509.03277

Character varieties, A-polynomials, and the AJ Conjecture

Thang T. Q. Le·Xingru Zhang

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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 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.

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BibTeX RIS

Thang T. Q. Le, Xingru Zhang. 2015-09-10. Character varieties, A-polynomials, and the AJ Conjecture. https://doi.org/10.2140/agt.2017.17.157

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