虚对称表示与标记高斯图
Virtually Symmetric representations and marked Gauss diagrams
摘要：
本文定义了虚辫群的表示的虚对称表示的概念，并证明了许多已知的表示与虚对称表示是等价的。使用这样的表示，我们定义的概念，虚拟链路组，这是一个扩展的虚拟链路组定义考夫曼。此外，我们引入了标记高斯图的概念作为高斯图的推广和他们的解释，在结状图。我们将虚链群的定义扩展到标记高斯图，并定义了它们的外围结构。定义了$C_m$ -群，证明了由$1$ -不可约$C_1$ -亏数表示$1$或$2$表示的群都可以实现为一个有标记高斯图的群.
英文摘要：
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.
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