On the AJ conjecture for knots
On the AJ conjecture for knots
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关于结的 AJ 猜想
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Anh T. Tran
中科院分区：
文献类型：
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作者：
Thang T. Q. Lê;Anh T. Tran
我们证实了AJ猜想[Ga 04]，该猜想将满足一定条件的双曲节的A-多项式和有色琼斯多项式联系起来。特别是，我们证明了猜想成立的一些类的两桥结和椒盐卷饼结。这扩展了第一作者在[Le 06]中的结果，在那里他建立了一个大类的二桥结，包括所有的扭曲结的AJ猜想。沿着这条路，我们明确地计算了（-2，3，2n +1）-pretzel纽结群的泛特征标环，并证明了它对所有整数n都是约化的.
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.