The virtual and universal braids

@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 -