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- Title
On virtual cabling and a structure of 4-strand virtual pure braid group.
- Authors
Bardakov, Valeriy G.; Wu, Jie
- Abstract
This paper is dedicated to cabling on virtual braids. This construction gives a new generating set for the virtual pure braid group VP n . We define simplicial group VP ∗ and its simplicial subgroup T ∗ which is generated by VP 2 . Consequently, we describe VP 4 as HNN-extension and find presentation of T 2 and T 3 . As an application to classical braids, we find a new presentation of the Artin pure braid group P 4 in terms of the cabled generators.
- Subjects
HOMOTOPY groups; GROUPOIDS
- Publication
Journal of Knot Theory & Its Ramifications, 2020, Vol 29, Issue 10, pN.PAG
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S021821652042002X