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Pré-Publication, Document De Travail Année : 2009

On the pure virtual braid group $PV_3$

V. G. Bardakov
  • Fonction : Auteur
R. Mikhailov
  • Fonction : Auteur
Jie Wu

Résumé

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.

Dates et versions

hal-00803753 , version 1 (22-03-2013)

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Citer

V. G. Bardakov, R. Mikhailov, Vladimir Vershinin, Jie Wu. On the pure virtual braid group $PV_3$. 2009. ⟨hal-00803753⟩
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