Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices
复制标题
按交叉数和矩阵对双周期无捻 (p,q) 组织进行分类
DOI：
10.1142/s0218216523500323
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发表时间：
2023
影响因子：
0.5
通讯作者：
and Sonia Mahmoudi
中科院分区：
文献类型：
--
作者：
Mizuki Fukuda;Motoko Kotani;and Sonia Mahmoudi
织纹是一种特殊类型的四价平面连通图的加厚欧几里德平面的提升，其中每个顶点具有上交叉或下交叉信息，并且使得提升的分量是不相交的简单开曲线。本文给出了三维缠结结构编织的形式拓扑定义，并通过引入一个新的不变量交叉矩阵刻画了双周期无捻编织的等价类。最后，我们提出了一个组合的方法来分类这一类特定的编织交叉数。
A weave is the lift to the thickened Euclidean plane of a particular type of quadrivalent planar connected graph with an over or under crossing information to each vertex and such that the lifted components are non-intersecting simple open curves. In this paper, we introduce a formal topological definition of weaves as three-dimensional entangled structures and characterize the equivalence classes of doubly periodic untwisted-weaves by introducing a new invariant, called crossing matrix. Finally, we suggest a combinatorial approach to classify this specific class of weaves by their crossing number.