The virtual and universal braids

Valerij G. Bardakov

Fundamenta Mathematicae (2004)

  • Volume: 184, Issue: 1, page 1-18
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Valerij G. Bardakov. "The virtual and universal braids." Fundamenta Mathematicae 184.1 (2004): 1-18. <http://eudml.org/doc/283356>.

@article{ValerijG2004,
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 quotients the singular braid group, virtual braid group, welded braid group, and classical braid group.},
author = {Valerij G. Bardakov},
journal = {Fundamenta Mathematicae},
keywords = {knot theory; singular knots; virtual knots; virtual braid groups; singular braid monoids; free groups; automorphisms; word problem; semidirect products},
language = {eng},
number = {1},
pages = {1-18},
title = {The virtual and universal braids},
url = {http://eudml.org/doc/283356},
volume = {184},
year = {2004},
}

TY - JOUR
AU - Valerij G. Bardakov
TI - The virtual and universal braids
JO - Fundamenta Mathematicae
PY - 2004
VL - 184
IS - 1
SP - 1
EP - 18
AB - 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.
LA - eng
KW - knot theory; singular knots; virtual knots; virtual braid groups; singular braid monoids; free groups; automorphisms; word problem; semidirect products
UR - http://eudml.org/doc/283356
ER -

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