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
Author(s):
Le, Thang T. Q.;
Tran, Anh T. (UT Dallas);
Huynh, Vu Q.
Keywords: Show Keywords
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.
ISSN: 0022-2518
Persistent Link: http://hdl.handle.net/10735.1/5382
http://dx.doi.org/10.1512/iumj.2015.64.5602
Bibliographic Citation: 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
Terms of Use: ©2015 Indiana University Mathematics Journal. All rights reserved.

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