The virtual and universal braids
Tom 184 / 2004
Fundamenta Mathematicae 184 (2004), 1-18
MSC: Primary 20F36; Secondary 20F05, 20F10.
DOI: 10.4064/fm184-0-1
Streszczenie
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 quotients the singular braid group, virtual braid group, welded braid group, and classical braid group.
