Unrestricted virtual braids, fused links and other quotients of virtual braid groups

TL;DR

This paper investigates the structure of unrestricted virtual braid groups, their relation to fused links, and explores properties of related braid groups including flat virtual and virtual Gauss braids, focusing on their algebraic features.

Contribution

It introduces the structure of unrestricted virtual braid groups, examines their connections with fused links, and studies properties like linearity of related braid groups.

Findings

Unrestricted virtual braid groups have a specific algebraic structure.

Relations between virtual braids and fused links are characterized.

Linearity of flat virtual and virtual Gauss braid groups is analyzed.

Abstract

We consider the group of unrestricted virtual braids, describe its structure and explore its relations with fused links. Also, we define the groups of flat virtual braids and virtual Gauss braids and study some of their properties, in particular their linearity.