论文标题
归一化套装理论的Yang-baxter同源性的几何实现
The geometric realization of a normalized set-theoretic Yang-Baxter homology of biquandles
论文作者
论文摘要
Biracks和Biquandles对于研究结理论很有用，是固定理论Yang-baxter方程的特殊系列。 Carter，Elhamdadi和Saito开发了一种针对Bettoic Yang-Baxter方程的同源理论，以构建结的不变性。在本文中，我们构建了Yang-Baxter方程的固定理论解的归一化（CO）同源理论。我们获得了亚历山大·比克德尔斯（Alexander Biquandles）的非平凡$ n $ cocycles的一些具体例子。对于Biquandle $ X，讨论了其几何实现$ BX $，这有可能建立链接和打结的表面的不变性。特别是，我们证明，如果Biquandle $ x $有限，则将第二个同型组$ BX $有限生成。
Biracks and biquandles, which are useful for studying the knot theory, are special families of solutions of the set-theoretic Yang-Baxter equation. A homology theory for the set-theoretic Yang-Baxter equation was developed by Carter, Elhamdadi, and Saito in order to construct knot invariants. In this paper, we construct a normalized (co)homology theory of a set-theoretic solution of the Yang-Baxter equation. We obtain some concrete examples of non-trivial $n$-cocycles for Alexander biquandles. For a biquandle $X,$ its geometric realization $BX$ is discussed, which has the potential to build invariants of links and knotted surfaces. In particular, we demonstrate that the second homotopy group of $BX$ is finitely generated if the biquandle $X$ is finite.
