Shadow biquandles and local biquandles
Shadow biquandles and local biquandles
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影子 biquandles 和局部 biquandles
DOI：
10.1016/j.topol.2019.107041
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发表时间：
2020
影响因子：
0.6
通讯作者：
Oshiro Kanako
中科院分区：
文献类型：
--
作者：
Nakamura Takuji;Nakanishi Yasutaka;Satoh Shin;Oshiro Kanako
给定一个由双束束B和强连通B集X组成的阴影双束束（B， X），我们在X上得到一个局部双束束结构，这种阴影双束束的（co）同调群与相应的局部双束束同构。此外，有向连杆和有向曲面连杆的环不变量与使用相应的局部双轴的环不变量重合。这些结果表明，在某些情况下，结点论三元拟群的[12]，[13]，[14]中的Niebrzydowski理论与阴影双量子理论是相同的。我们还证明了Niebrzydowski （co）同调理论的一些局部双双环2-或3-环和一些1-或2-环可以由Mochizuki的（bi）双双环导出。
Given a shadow biquandle (B, X) composed of a biquandle B and a strongly connected B-set X, we have a local biquandle structure on X. The (co) homology groups of such shadow biquandles are isomorphic to those of the corresponding local biquandles. Moreover, cocycle invariants, of oriented links and oriented surface-links, using such shadow biquandles coincide with those using the corresponding local biquandles. These results imply that for some cases, the Niebrzydowski's theory in [12],[13],[14] for knot-theoretic ternary quasigroups is the same as shadow biquandle theory. We also show that some local biquandle 2-or 3-cocycles and some 1-or 2-cocycles of the Niebrzydowski's (co) homology theory can be induced from Mochizuki's (bi) quandle cocycles.