论文标题
实际上对称表示和标记的高斯图
Virtually Symmetric representations and marked Gauss diagrams
论文作者
论文摘要
在本文中，我们定义了虚拟编织组表示的几乎对称表示的概念，并证明许多已知的表示等同于虚拟对称。使用一个这样的表示形式，我们定义了虚拟链接组的概念，这是Kauffman定义的虚拟链接组的扩展。此外，我们介绍了标记高斯图的概念，作为高斯图的概括及其在打结图方面的解释。我们将虚拟链接组的定义扩展到标记的高斯图并定义其外围结构。我们定义$ c_m $ - 群体，并证明每个组以$ 1 $ - 摩尔德$ C_1 $ - 缺陷$ 1 $或$ 2 $的呈现为标记的高斯图组。
In this paper, we define the notion of a virtually symmetric representation of representations of virtual braid groups and prove that many known representations are equivalent to virtually symmetric. Using one such representation, we define the notion of virtual link groups which is an extension of virtual link groups defined by Kauffman. Moreover, we introduce the concept of marked Gauss diagrams as a generalisation of Gauss diagrams and their interpretation in terms of knot-like diagrams. We extend the definition of virtual link groups to marked Gauss diagrams and define their peripheral structure. We define $C_m$-groups and prove that every group presented by a $1$-irreducible $C_1$-presentation of deficiency $1$ or $2$ can be realized as the group of a marked Gauss diagram.
