Lifting Theorem for the Virtual Pure Braid Groups

Lifting Theorem for the Virtual Pure Braid Groups Full article

Journal

Chinese Annals of Mathematics. Series B
ISSN: 0252-9599

Output data

Year: 2025, Volume: 46, Number: 1, Pages: 85-114 Pages count : 30 DOI: 10.1007/s11401-025-0005-4

Tags

Virtual braid group, Pure braid group, Simplicial group, Virtual cabling

Authors

Bardakov Valeriy G. ^1,2,3 , Wu Jie ^4,5

Affiliations

1	Sobolev Institute of Mathematics
2	Tomsk State University
3	Novosibirsk State Agrarian University
4	School of Mathematical Sciences, Center of Topology and Geometry Based Technology Hebei Normal University
5	Beijing Institute of Mathematical Sciences and Applications

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0009

In this article the authors prove theorem on Lifting for the set of virtual pure braid groups. This theorem says that if they know presentation of virtual pure braid group VP4, then they can find presentation of V Pn for arbitrary n > 4. Using this theorem they f ind the set of generators and defining relations for simplicial group T∗ which was defined in [Bardakov, V. G. and Wu, J., On virtual cabling and structure of 4-strand virtual pure braid group, J. Knot Theory and Ram., 29(10), 2020, 1–32]. They find a decomposition of the Artin pure braid group Pn in semi-direct product of free groups in the cabled generators.

Bardakov V.G. , Wu J.
Lifting Theorem for the Virtual Pure Braid Groups
Chinese Annals of Mathematics. Series B. 2025. V.46. N1. P.85-114. DOI: 10.1007/s11401-025-0005-4 WOS Scopus РИНЦ OpenAlex

Submitted:	May 30, 2022
Published print:	Jan 16, 2025
Published online:	Mar 4, 2025

Web of science:	WOS:001437278700008
Scopus:	2-s2.0-86000087315
Elibrary:	81542603
OpenAlex:	W4408108661

DB	Citing
Web of science	1
Scopus	1