Homotopical interpretation of link invariants from finite quandles
Homotopical interpretation of link invariants from finite quandles
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有限四元组链接不变量的同伦解释
DOI：
10.1016/j.topol.2015.05.087
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Takefumi Nosaka
中科院分区：
文献类型：
--
作者：
Takefumi Nosaka
本文从同伦理论的角度证明了有限连通quandle X上链的quandle上循环不变量的拓扑意义：具体地说，对于任何不整除X型的素数，这个不变量的n-挠率等于循环分支覆盖空间的Dijkgraaf-Witten不变量的Z-等变部分与着色多项式之和.此外，我们的同伦方法包括应用计算的一些第三个同调群和第二同伦群的分类空间的quandles，从群上同调的结果。
This paper demonstrates a topological meaning of quandle cocycle invariants of links with respect to finite connected quandles X, from a perspective of homotopy theory: Specifically, for any prime ℓ which does not divide the type of X, the ℓ-torsion of this invariants is equal to a sum of the coloring polynomial and a Z-equivariant part of the Dijkgraaf–Witten invariant of a cyclic branched covering space. Moreover, our homotopical approach involves applications of computing some third homology groups and second homotopy groups of the classifying spaces of quandles, from results of group cohomology.