%0 Journal Article
%T On the pure virtual braid group $PV_3$
%A V. G. Bardakov
%A R. Mikhailov
%A V. V. Vershinin
%A J. Wu
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0906.1743v1