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| Lifting Theorem for the Virtual Pure Braid Groups |
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Citation： |
Valeriy G. BARDAKOV,Jie WU.Lifting Theorem for the Virtual Pure Braid Groups[J].Chinese Annals of Mathematics B,2025,46(1):85~114 |
| Page view： 163
Net amount： 149 |
Authors： |
Valeriy G. BARDAKOV; Jie WU |
Foundation： |
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 and the Start-up Research Fund from Yanqi
Lake Beijing Institute of Mathematical Sciences and Applications. |
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| Abstract： |
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 P4, then they can find presentation of V Pn for 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 Pn in semi-direct product of free groups in the cabled generators. |
Keywords： |
Virtual braid group Pure braid group Simplicial group Virtual cabling |
Classification： |
20F36, 55Q40, 18G31 |
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