On the AJ conjecture for knots

Details On the AJ conjecture for knots On the AJ conjecture for knots

2011-11-22

arxiv.org/abs/1111.5258v1

Mathematics

Geometric Topology

Scientific paper

We confirm the AJ conjecture \cite{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 \cite{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 integer $n$.

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