On the pure virtual braid group $PV_3$

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

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arXiv · 0906.1743

On the pure virtual braid group $PV_3$

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

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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.

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BibTeX RIS

V. G. Bardakov, R. Mikhailov, V. V. Vershinin, J. Wu. 2009-06-09. On the pure virtual braid group $PV_3$. https://arxiv.org/abs/0906.1743

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