来自Yang-Baxter算子的曲面辫子不变量及其上同调
Surface Braid Invariants from Yang-Baxter Operators and Their Cohomology
- University of South Florida（南佛罗里达大学）
- Idaho State University（爱达荷州立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出利用Yang-Baxter算子通过辫子系统构造曲面辫子不变量，并借助图表使用其3-上循环，推广了quandle上循环不变量，讨论了闭包定义纽结曲面不变量的方法。
AI中文摘要：
曲面辫子是辫子向4-圆盘中曲面的推广。它们由称为图表的平面图和称为辫子系统的辫子词序列描述，这些辫子系统表示投影中分支点的单值性。Yang-Baxter算子（YBOs）已被广泛用于纽结理论中，通过辫子群表示构造Jones多项式及其他多项式。我们提出使用YBOs通过辫子系统构造曲面辫子不变量。特征空间的交集用于此构造。我们进一步通过图表使用Yang-Baxter上同调理论的3-上循环，类似于quandle上循环不变量，但更一般地利用模的张量积。讨论了通过曲面辫子的闭包定义纽结曲面不变量的方法。
英文摘要：
Surface braids are a generalization of braids to surfaces in the 4-disk. They are described by planar graphs called charts, and sequences of braid words called braid systems, that represent monodromies of branch points in projections. Yang-Baxter operators (YBOs) have been used extensively in knot theory for constructions of Jones and other polynomials, defined by braid group representations. We propose to use YBOs for constructing surface braid invariants through braid systems. The intersections of eigenspaces are used for this construction. We further use 3-cocycles of the Yang-Baxter cohomology theories via charts, in an analogue of quandle cocycle invariants but more generally utilizing tensor products of modules. An approach towards defining knotted surface invariants through closures of surface braids is discussed.
