Lifting Theorem for the Virtual Pure Braid Groups  

作　　者：Valeriy G.BARDAKOV Jie WU 

机构地区：[1]Sobolev Institute of Mathematics,4 Acad,Koptyug Avenue,630090,Novosibirsk,Russia [2]Tomsk State University,Pr.Lenina,36,Tomsk,634050,Russia [3]Novosibirsk State Agrarian University,Dobrolyubova street,160,Novosibirsk,630039,Russia [4]School of Mathematical Sciences,Center of Topology and Geometry Based Technology Hebei Normal University,Shijiazhuang 050024,China [5]Beijing Institute of Mathematical Sciences and Applications,Beijing 101408,China

出　　处：《Chinese Annals of Mathematics,Series B》2025年第1期85-114,共30页数学年刊(B辑英文版)

基　　金：supported by the National Natural Science Foundation of China(No.11971144);the State Contract of the Sobolev Institute of Mathematics;SB RAS(No.I.1.5,FWNF-2022-0009);the High-level Scientific Research Foundation of Hebei Province;the Start-up Research Fund from Yanqi Lake Beijing Institute of Mathematical Sciences and Applications。

摘　　要：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 V P_(4),then they can find presentation of V Pnfor arbitrary n>4.Using this theorem they find 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 P_(n)in semi-direct product of free groups in the cabled generators.

关 键 词：Virtual braid group Pure braid group Simplicial group Virtual cabling 

分 类 号：O17[理学—数学]