On the AJ conjecture for knots

By Thang T. Q. Lê, Anh T. Tran. 2011

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We confirm the AJ conjecture [Ga04] that relates the A-polynomial and the colored Jones polynomial for those 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 [Le06] where he established the AJ conjecture for a large class of two-bridge knots, including all twist knots. Along the way, we explicitly calculate the universal character ring of the knot group of the (-2,3,2n+1)-pretzel knot and show that it is reduced for all integers n.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/21b56df61767b492a2751610809d98775553e05d