On the pure virtual braid group PV₃

2009/06/09 by В. Г. Бардаков, Roman Mikhailov, Bardakov, V. G. +5 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0906.1743

openalex publication_date 2009/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we investigate various properties of the pure virtual braid group PV₃. From its canonical presentation, we obtain a free product decomposition of PV₃. As a consequence, we show that PV₃ 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 PV₃ is aspherical. Finally we determine the cohomology ring and the associated graded Lie algebra of PV₃.

Citations

• On Basis-Conjugating Automorphisms of Free Groups

Cited by

• Multi-virtual braid groups

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