Character varieties, A-polynomials, and the AJ Conjecture

Abstract

We establish some facts about the behavior of the rational-geometric subvariety of the $S{L}_2(\stackrel{¸}{)}$ or $PS{L}_2(\stackrel{¸}{)}$ character variety of a hyperbolic knot manifold under the restriction map to the $S{L}_2(\stackrel{¸}{)}$ or $PS{L}_2(\stackrel{¸}{)}$ 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.

24 pages

References in corpus (1)

• Difference equation of the colored Jones polynomial for torus knot

Cited by in corpus (5)

• Quantum Teichmüller spaces and quantum trace map
• Infinite families of hyperbolic $3$-manifolds with finite dimensional skein modules
• Volume function and Mahler measure of exact polynomials
• An embedding of skein algebras of surfaces into quantum tori from Dehn-Thurston coordinates
• Quantizing Derived Mapping Stacks