Shifting chain maps in quandle homology and cocycle invariants
Shifting chain maps in quandle homology and cocycle invariants
复制标题
Quandle 同调和余循环不变量中的平移链图
DOI：
10.1090/tran/8707
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发表时间：
2022
影响因子：
1.3
通讯作者：
Tanaka Kokoro
中科院分区：
文献类型：
--
作者：
Hashimoto Yu;Tanaka Kokoro
Quandle同调理论已经发展起来，上循环已经被用来定义定向经典或表面链接的不变量。我们引入一个移动链映射对每个quandle链复杂，降低了一个维度。通过使用它的拉回，每个上循环给我们上循环。对于-空间中的定向经典链环，我们探讨了它们的quandle上循环不变量与shadow上循环不变量之间的关系。对于面向表面链接的空间，我们探讨如何强大的quandle上循环不变量与。讨论了低维（余）同调群的移位映射的代数性质。引用
Quandle homology theory has been developed and cocycles have been used to define invariants of oriented classical or surface links. We introduce a shifting chain mapon each quandle chain complex that lowers the dimensions by one. By using its pull-back, each-cocyclegives us the-cocycle. For oriented classical links in the-space, we explore relation between their quandle-cocycle invariants associated withand their shadow-cocycle invariants associated with. For oriented surface links in the-space, we explore how powerful their quandle-cocycle invariants associated withare. Algebraic behavior of the shifting maps for low-dimensional (co) homology groups is also discussed. References