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.

中文翻译：

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复合结和阿贝尔扩展的Quandle着色和cocycle不变量

研究了复合结的Quandle着色和cocycle不变量，并应用于手性和阿贝尔扩展。例如，方形结和奶奶结可以通过四边形着色来区分，因此三叶草及其镜子可以通过复合结的四边形着色来区分。我们调查这个和相关的现象。研究了与连通和的quandle着色相关的Quandle cocycle不变量，并给出了从复合结的着色数计算cocycle不变量的公式。研究了与 quandles 的相应阿贝尔扩展的关系，并检查了小型连通 quandles 表的扩展，称为 Rig quandles。介绍了计算机计算，并讨论了输出摘要。