基于Dijkgraaf-Witten不变量和Inoue-Kabaya映射的群与quandles的第三同调
On third homologies of groups and of quandles via the Dijkgraaf-Witten invariant and Inoue-Kabaya map
摘要：
本文提出了一种从群上圈生成quandle上圈的简单方法，作为对Inoue-Kabaya链映射的改进。我们进一步表明，对于“普遍中心扩展的quandles”，链映射诱导它们的第三同调之间的同构。例如，所有的Mochizuki quandle 3-上圈都是由某些非阿贝尔群的群上圈导出的。作为应用，我们利用环的上循环不变量计算了某些循环分支覆盖空间的Dijkgraaf-Witten不变量的$\Z$ -等变部分.
英文摘要：
We propose a simple method to produce quandle cocycles from group cocycles, as a modification of Inoue-Kabaya chain map. We further show that, in respect to "universal central extended quandles", the chain map induces an isomorphism between their third homologies. For example, all Mochizuki's quandle 3-cocycles are shown to be derived from group cocycles of some non-abelian group. As an application, we calculate some $\Z$-equivariant parts of the Dijkgraaf-Witten invariants of some cyclic branched covering spaces, via some cocycle invariant of links.
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