The virtual and universal braids

Details The virtual and universal braids The virtual and universal braids

2004-07-23

arxiv.org/abs/math/0407400v1

Mathematics

Group Theory

20 pages, 5 figures

Scientific paper

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.

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