On the pure virtual braid group $PV_3$
Geometric Topology
2009-06-10 v1 Group Theory
Abstract
In this article, we investigate various properties of the pure virtual braid group PV_3. From its canonical presentation, we obtain a free product decomposition of PV_3. As a consequence, we show that PV_3 is residually torsion free nilpotent, which implies that the set of finite type invariants in the sense of Goussarov-Polyak-Viro is complete for virtual pure braids with three strands. Moreover we prove that the presentation of PV_3 is aspherical. Finally we determine the cohomology ring and the associated graded Lie algebra of PV_3.
Cite
@article{arxiv.0906.1743,
title = {On the pure virtual braid group $PV_3$},
author = {V. G. Bardakov and R. Mikhailov and V. V. Vershinin and J. Wu},
journal= {arXiv preprint arXiv:0906.1743},
year = {2009}
}
Comments
19 pages, 1 figure