On sufficiency of the definition of MCQ Alexander pairs in terms of invariants for handlebody-knots
On sufficiency of the definition of MCQ Alexander pairs in terms of invariants for handlebody-knots
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关于 MCQ 亚历山大对在手柄体结不变量方面的定义的充分性
DOI：
10.1007/s13366-022-00652-0
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Murao Tomo
中科院分区：
文献类型：
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作者：
Alexandra Wolf;Shunsuke Tamura;Kazuo Ueda;Yoji Hirano;Murao Tomo
多重共轭难题是一种代数结构，其公理源自手柄体结理论。通过使用 MCQ Alexander 对（一对对应于多重共轭问题的线性扩展的映射），我们可以构造 f 扭曲 Alexander 矩阵，该矩阵为手柄体结产生不变量。本文的目的是从多重共轭分形的线性扩展角度证明MCQ亚历山大对的定义在构造f扭曲亚历山大矩阵时的充分性。此外，我们引入了 MCQ 亚历山大对的上同源概念，这为手柄体结引入了相同的不变量。
A multiple conjugation quandle is an algebraic structure whose axioms are motivated from handlebody-knot theory. By using an MCQ Alexander pairf, which is a pair of maps corresponding to a linear extension of a multiple conjugation quandle, we can construct thef-twisted Alexander matrices, which produce invariants for handlebody-knots. The purpose of this paper is to show the sufficiency of the definition of MCQ Alexander pairs in constructing thef-twisted Alexander matrices from the aspect of linear extensions of multiple conjugation quandles. Furthermore, we introduce the notion of cohomologous for MCQ Alexander pairs, which induces the same invariant for handlebody-knots.