Knots of (canonical) genus two
Knots of (canonical) genus two
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DOI：
10.4064/fm200-1-1
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发表时间：
2008-01-01
影响因子：
0.6
通讯作者：
Stoimenow, A.
中科院分区：
文献类型：
--
作者：
Stoimenow, A.
给出了正则亏格2和正则亏格3的所有纽结图的描述，并给出了正纽结、交错纽结和齐次纽结的应用，包括非手性亏格2交错纽结、切片纽结或非手性2几乎正纽结的分类，3-和4-移动纽结的证明，以及正则（弱）亏格2纽结的最大双曲体积的计算.我们还研究了单位根上的链环多项式的值，推广了Jones的稠密性结果。利用这些值，找到了非尖锐Morton不等式的纽结例子，并将几个结果推广到任意典型亏格。
We give a description of all knot diagrams of canonical genus 2 and 3, and give applications to positive, alternating and homogeneous knots, including a classification of achiral genus 2 alternating knots, slice or achiral 2-almost positive knots, a proof of the 3- and 4-move conjectures, and the calculation of the maximal hyperbolic volume for canonical (weak) genus 2 knots. We also study the values of the link polynomials at roots of unity, extending denseness results of Jones. Using these values, examples of knots with non-sharp Morton (canonical genus) inequality are found. Several results axe generalized to arbitrary canonical genus.