On the AJ Conjecture for Knots

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2015-07-07

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Abstract

We confirm the AJ conjecture [Ga2] that relates the A-polynomial and the colored Jones polynomial for hyperbolic knots satisfying certain conditions. In particular, we show that the conjecture holds true for some classes of two-bridge knots and pretzel knots. This extends the result of the first author in [Le2], who established the AJ conjecture for a large class of two-bridge knots, including all twist knots. Along the way, we explicitly calculate the universal SL₂(C)-character ring of the knot group of the (−2, 3, 2n + 1)-pretzel knot, and show it is reduced for all integers n.

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Knot polynomials, AJ conjecture, Colored Jones polynomials, Two-bridge knots, Double twist knots, Pretzel knots, Universal character ring

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©2015 Indiana University Mathematics Journal. All rights reserved.

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