论文标题
关于周期性编织的分类和增厚表面中链路的通用覆盖
On the classification of periodic weaves and universal cover of links in thickened surfaces
论文作者
论文摘要
周期性编织是嵌入在加厚表面到通用盖的特定链接的提升。它的组件是无限无结的简单开放曲线，可以在至少两组不同的线程中分区。周期性编织的分类可以简化为它们的生成细胞之一，即它们的编织基序。但是，由于未编码通用覆盖物的周期性，因此无法通过增厚表面中的链接的经典理论来实现此分类。在本文中，我们首先介绍双曲线周期性编织的概念，该编织概念将嵌入欧几里得增厚平面中的双重周期性编织概述。然后，将第一和第二个猜想扩展到最小降低的交替编织基序，并使用定义的广泛的kauffman支架多项式定义为欧几里得平面的周期性编织图定义，并将其推广到双曲平面。第一个猜想指出，任何最小的交替交替的编织基序都有最小的交叉数量，而第二个则提出了两个类似的织造基序具有相同的writhe。
A periodic weave is the lift of a particular link embedded in a thickened surface to the universal cover. Its components are infinite unknotted simple open curves that can be partitioned in at least two distinct sets of threads. The classification of periodic weaves can be reduced to the one of their generating cells, namely their weaving motifs. However, this classification cannot be achieved through the classical theory of links in thickened surfaces since periodicity in the universal cover is not encoded. In this paper, we first introduce the notion of hyperbolic periodic weaves, which generalizes our doubly periodic weaves embedded in the Euclidean thickened plane. Then, Tait First and Second Conjectures are extended to minimal reduced alternating weaving motifs and proved using a generalized Kauffman bracket polynomial defined for periodic weaving diagrams of the Euclidean plane and generalized to the hyperbolic plane. The first conjecture states that any minimal alternating reduced weaving motif has the minimum possible number of crossings, while the second one formulates that two such oriented weaving motifs have the same writhe.
