Quandle coloring and cocycle invariants of composite knots and abelian extensions.
Quandle coloring and cocycle invariants of composite knots and abelian extensions.
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复合结和阿贝尔扩张的 Quandle 着色和余循环不变量。
DOI：
10.1142/s0218216516500243
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发表时间：
2016
影响因子：
0.5
通讯作者：
Vendramin,Leandro
中科院分区：
文献类型：
--
作者：
Clark,WEdwin;Saito,Masahico;Vendramin,Leandro
研究了复合纽结的Quandle染色和上循环不变量，并将其应用于手征性和阿贝尔扩张。例如，方形结和奶奶结可以通过quandle着色来区分，所以三叶草和它的镜像可以通过复合结的quandle着色来区分。我们研究这个和相关的现象。研究了连通和的Quandle染色与Quandle上循环不变量的关系，给出了由复合纽结的染色个数计算上循环不变量的公式。关系到相应的交换扩展的quandles进行了研究，并检查扩展表的小连接quandles，称为钻机quandles。计算机计算，并讨论了输出的摘要。
Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror can be distinguished by quandle coloring of composite knots. We investigate this and related phenomena. Quandle cocycle invariants are studied in relation to quandle coloring of the connected sum, and formulas are given for computing the cocycle invariant from the number of colorings of composite knots. Relations to corresponding abelian extensions of quandles are studied, and extensions are examined for the table of small connected quandles, called Rig quandles. Computer calculations are presented, and summaries of outputs are discussed.