On homotopy aspects and cablings of virtual pure braid groups

2018/08/29 by Valeriy G. Bardakov, Bardakov, Valeriy G., Roman Mikhailov +3
Computer Science · Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1808.09786

openalex publication_date 2018/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By exploring simplicial structure of pure virtual braid groups, we give new connections between the homotopy groups of the 3-sphere and the virtual braid groups that are related to the theory of Brunnian virtual braids. The group structure of VP_n with n > 4 is determined by VP₃, VP₄ and virtual cablings given by iterated degeneracy operations on the generators and defining relations. The complete proofs will be published in the two forthcoming papers.

Related

• On virtual cabling and structure of 4-strand virtual pure braid group
• Virtual Braids
• Algebraic structures among virtual singular braids
• Lifting theorem for the virtual pure braid groups
• On the pure virtual braid group PV₃