On the pure virtual braid group $PV_3$

J. Wu; R. Mikhailov; V. G. Bardakov; V.V. Vershinin

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arxiv 0906.1743 v1 pith:465OM6UJ submitted 2009-06-09 math.GT math.GR

On the pure virtual braid group PV₃

V. G. Bardakov , R. Mikhailov , V.V. Vershinin , J. Wu This is my paper

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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.

On the pure virtual braid group PV₃

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