The virtual and universal braids
Group Theory
2007-05-23 v1 Geometric Topology
Abstract
We study the structure of the virtual braid group. It is shown that the virtual braid group is a semi--direct product of the virtual pure braid group and the symmetric group. Also, it is shown that the virtual pure braid group is a semi--direct product of free groups. From these results we obtain a normal form of words in the virtual braid group. We introduce the concept of a universal braid group. This group contains the classical braid group and has as its quotient groups the singular braid group, virtual braid group, welded braid group, and classical braid group.
Keywords
Cite
@article{arxiv.math/0407400,
title = {The virtual and universal braids},
author = {Valerij G. Bardakov},
journal= {arXiv preprint arXiv:math/0407400},
year = {2007}
}
Comments
20 pages, 5 figures