On the pure virtual braid group $PV_3$

Details On the pure virtual braid group $PV_3$ On the pure virtual braid group $PV_3$

2009-06-09

arxiv.org/abs/0906.1743v1

Mathematics

Geometric Topology

19 pages, 1 figure

Scientific paper

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.

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