The virtual and universal braids

Tom 184 / 2004

Valerij G. Bardakov 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.

Autorzy

  • Valerij G. BardakovSobolev Institute of Mathematics
    Novosibirsk 630090, Russia
    e-mail

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