A FORMULA FOR THE A-POLYNOMIAL OF TWIST KNOTS
A FORMULA FOR THE A-POLYNOMIAL OF TWIST KNOTS
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捻结的A多项式的计算公式
DOI：
10.1142/s0218216504003081
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发表时间：
2004
影响因子：
0.5
通讯作者：
Patrick D. Shanahan
中科院分区：
文献类型：
--
作者：
J. Hoste;Patrick D. Shanahan
2桥结的基本群有一个特别好的表示，只有两个生成元和一个关系。对于某些族的2-桥结，如环面结，或扭曲结，关系采取一个特别简单的形式。利用这一形式，我们推导出一个公式的A-多项式的捻结。我们的方法扩展到至少一个其他无限家庭（非环面）2桥结。使用这些公式，我们确定相关的牛顿多边形。进一步证明了扭纽结的A-多项式是不可约的。
The fundamental group of a 2-bridge knot has a particularly nice presentation, having only two generators and a single relation. For certain families of 2-bridge knots, such as the torus knots, or the twist knots, the relation takes on an especially simple form. Exploiting this form, we derive a formula for the A-polynomial of twist knots. Our methods extend to at least one other infinite family of (non-torus) 2-bridge knots. Using these formulae we determine the associated Newton polygons. We further prove that the A-polynomials of twist knots are irreducible.