Virtually symmetric representations and marked Gauss diagrams

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

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 Cm-groups and prove that every group presented by a 1-irreducible C1-presentation of deficiency 1 or 2 can be realised as the group of a marked Gauss diagram.

Язык оригиналаанглийский
Номер статьи107936
ЖурналTopology and its Applications
Том306
DOI
СостояниеОпубликовано - 1 февр. 2022

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