The colored Jones polynomial and the A-polynomial of Knots☆
The colored Jones polynomial and the A-polynomial of Knots☆
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DOI：
10.1016/j.aim.2006.01.006
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发表时间：
2004-07
影响因子：
1.7
通讯作者：
Thang T. Q. Lê
中科院分区：
文献类型：
--
作者：
Thang T. Q. Lê
研究了纽结的色琼斯多项式与A-多项式之间的关系。AJ猜想（Garoufaldet），涉及有色琼斯多项式和A-多项式建立了一个大类的二桥结，包括所有的扭曲结。我们制定了一个较弱的猜想，并证明它适用于所有的二桥结。沿着这条路，我们还计算了两桥纽结的补图的Kauffman括号绞链模。建立了色琼斯多项式的一些性质。
We study relationships between the colored Jones polynomial and the A-polynomial of a knot. The AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial is established for a large class of two-bridge knots, including all twist knots. We formulate a weaker conjecture and prove that it holds for all two-bridge knots. Along the way we also calculate the Kauffman bracket skein module of the complements of two-bridge knots. Some properties of the colored Jones polynomial are established.