On the AJ Conjecture for Knots

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On the AJ Conjecture for Knots

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title On the AJ Conjecture for Knots
contributor.author Le, Thang T. Q.
contributor.author Tran, Anh T. (UT Dallas)
contributor.author Huynh, Vu Q.
description.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.
identifier.issn 0022-2518
identifier.uri http://hdl.handle.net/10735.1/5382
identifier.uri http://dx.doi.org/10.1512/iumj.2015.64.5602
identifier.bibliographicCitation Le, Thang T. Q., Anh T. Tran, and Vu Q. Huynh. 2015. "On the AJ Conjecture for Knots." Indiana University Mathematics Journal 64(4), doi: 10.1512/iumj.2015.64.5602
identifier.volume 64
identifier.issue 4
subject Knot polynomials
subject AJ conjecture
subject Colored Jones polynomials
subject Two-bridge knots
subject Double twist knots
subject Pretzel knots
subject Universal character ring
date.issued 1905-07-07
rights ©2015 Indiana University Mathematics Journal. All rights reserved.
source.journal Indiana University Mathematics Journal

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