Knots and distributive homology: from arc colorings to Yang-Baxter homology
Knots and distributive homology: from arc colorings to Yang-Baxter homology
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DOI：
10.1142/9789814630627_0011
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发表时间：
2014-09
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通讯作者：
J. Przytycki
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作者：
J. Przytycki
本文是我的论文《代数结构同调理论中的分配性与结合性》（Demonstratio Math., 44(4), 2011, 821 - 867 (arXiv:1109.4850 [math.GT])）的续篇。我们从弧着色的朴素不变量出发，综述结合与分配广群以及它们与纽结理论相关的同调。我们通过杨 - 巴克斯特算子概述了与霍万诺夫同调及范畴化的潜在关系。我们在此利用了杨 - 巴克斯特方程可被视为自分配性的一种推广这一事实。我们展示了如何定义和可视化杨 - 巴克斯特同调，特别是给出了双辫子同调的一种简单描述。
This paper is a sequel to my essay "Distributivity versus associativity in the homology theory of algebraic structures" Demonstratio Math., 44(4), 2011, 821-867 (arXiv:1109.4850 [math.GT]). We start from naive invariants of arc colorings and survey associative and distributive magmas and their homology with relation to knot theory. We outline potential relations to Khovanov homology and categorification, via Yang-Baxter operators. We use here the fact that Yang-Baxter equation can be thought of as a generalization of self-distributivity. We show how to define and visualize Yang-Baxter homology, in particular giving a simple description of homology of biquandles.