The geometric realization of a normalized set-theoretic Yang–Baxter homology of biquandles
The geometric realization of a normalized set-theoretic Yang–Baxter homology of biquandles
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双分位数归一化集合论 Yang–Baxter 同调的几何实现
DOI：
10.1142/s0218216522500511
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Seung Yeop Yang
中科院分区：
文献类型：
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作者：
Xiao Wang;Seung Yeop Yang
Birack和Biquandles是集合论Yang-Baxter方程的特殊解族，对研究纽结理论很有用。集合论的Yang-Baxter方程的同调理论是由Carter等人提出的。以构造纽结不变量。本文构造了杨-巴克斯特方程集合论解的归一化(上)同调理论。我们得到了一些非平凡的具体例子[公式：参见Alexander biquandles的文本上循环。对于二元数[公式：参见文本其几何实现[公式：参见文本进行了讨论，这有可能建立链接和结点曲面的不变量。特别地，我们证明了如果双对偶[公式：见文本是有限的，则[公式：见文本]的第二同伦群是有限生成的。
Biracks and biquandles, which are useful for studying the knot theory, are special families of solutions of the set-theoretic Yang–Baxter equation. A homology theory for the set-theoretic Yang–Baxter equation was developed by Carter et al. in order to construct knot invariants. In this paper, we construct a normalized (co)homology theory of a set-theoretic solution of the Yang–Baxter equation. We obtain some concrete examples of nontrivial [Formula: see text-cocycles for Alexander biquandles. For a biquandle [Formula: see text its geometric realization [Formula: see text is discussed, which has the potential to build invariants of links and knotted surfaces. In particular, we demonstrate that the second homotopy group of [Formula: see text is finitely generated if the biquandle [Formula: see text is finite.