循环双结的集合论Yang-Baxter上同调
Set-theoretic Yang-Baxter cohomology of cyclic biquandles
AI总结：
本文完全确定了有限循环双结的集合论Yang-Baxter（上）同调群的自由部分，计算了低维同调群的挠子群，给出了高维挠阶的上界，部分解决了规范化同调猜想，并引入了非平凡的挠同调类。
摘要：
我们完全确定了有限循环双结的集合论Yang-Baxter（上）同调群的自由部分，并充分计算了其第1和第2同调群的挠子群。此外，我们为第3维及更高维同调群中挠的阶提供了上界。这项工作部分解决了以下猜想：循环双结的规范化集合论Yang-Baxter同调在$n$为奇数时满足$H_{n}^{NYB}(C_{m}) = \mathbb{Z}^{(m-1)^{n-1}} \oplus \mathbb{Z}_{m}$，在$n$为偶数时满足$H_{n}^{NYB}(C_{m}) = \mathbb{Z}^{(m-1)^{n-1}}$。此外，我们获得了循环双结有理上同调群基的上闭链代表元，并引入了若干非平凡的挠同调类。
英文摘要：
We completely determine the free parts of the set-theoretic Yang-Baxter (co)homology groups of finite cyclic biquandles, along with fully computing the torsion subgroups of their 1st and 2nd homology groups. Furthermore, we provide upper bounds for the orders of torsions in the 3rd and higher dimensional homology groups. This work partially solves the conjecture that the normalized set-theoretic Yang-Baxter homology of cyclic biquandles satisfy $H_{n}^{NYB}(C_{m}) = \mathbb{Z}^{(m-1)^{n-1}} \oplus \mathbb{Z}_{m}$ when $n$ is odd and $H_{n}^{NYB}(C_{m}) = \mathbb{Z}^{(m-1)^{n-1}}$ when $n$ is even. In addition, we obtain cocycle representatives of a basis for the rational cohomology group of a cyclic biquandle and introduce several non-trivial torsion homology classes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
