5-MOVE EQUIVALENCE CLASSES OF LINKS AND THEIR ALGEBRAIC INVARIANTS
5-MOVE EQUIVALENCE CLASSES OF LINKS AND THEIR ALGEBRAIC INVARIANTS
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链接的 5 步等价类及其代数不变量
DOI：
10.1142/s0218216507005877
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发表时间：
2007
影响因子：
0.5
通讯作者：
Jozef H.Przytycki
中科院分区：
文献类型：
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作者：
Mieczyslaw K.Dabkowski;M. Ishiwata;Jozef H.Przytycki
我们开始对多达5个移动等效的链接进行系统分析。我们的动机是开发工具，以后可以用来研究绞链模块的基础上的绞链关系是变形的5-移动（以类似的方式作为考夫曼绞链模块是变形的2-移动，即交叉变化）。我们的主要工具是Jones和Kauffman多项式以及S3的沿沿着环的2重分支覆盖的基本群。我们还使用了这样一个事实，即一个5-移动是两个有理±（2，2）-移动（即$\pm \frac{5}{2}$-移动）的组合，并且有理移动可以使用Fox着色群及其非阿贝尔版本（链接的伯恩赛德群）进行分析。一个奇怪的观察是，由一个（2，2）-移动相关的链接不等于5-移动。特别是，我们部分分类（最多5个动作）3-辫子，椒盐卷饼和蒙特西诺斯链接，并链接到9个十字路口。
We start a systematic analysis of links up to 5-move equivalence. Our motivation is to develop tools which later can be used to study skein modules based on the skein relation being deformation of a 5-move (in an analogous way as the Kauffman skein module is a deformation of a 2-move, i.e. a crossing change). Our main tools are Jones and Kauffman polynomials and the fundamental group of the 2-fold branch cover of S3 along a link. We use also the fact that a 5-move is a composition of two rational ±(2, 2)-moves (i.e. $\pm \frac{5}{2}$-moves) and rational moves can be analyzed using the group of Fox colorings and its non-abelian version, the Burnside group of a link. One curious observation is that links related by one (2, 2)-move are not 5-move equivalent. In particular, we partially classify (up to 5-moves) 3-braids, pretzel and Montesinos links, and links up to 9 crossings.