On virtual cabling and a structure of 4-strand virtual pure braid group

Valeriy G. Bardakov; Jie Wu

doi:10.1142/S021821652042002X

On virtual cabling and a structure of 4-strand virtual pure braid group

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

Аннотация

This paper is dedicated to cabling on virtual braids. This construction gives a new generating set for the virtual pure braid group VPn. We define simplicial group VP∗ and its simplicial subgroup T∗ which is generated by VP₂. Consequently, we describe VP₄ as HNN-extension and find presentation of T₂ and T₃. As an application to classical braids, we find a new presentation of the Artin pure braid group P₄ in terms of the cabled generators.

Язык оригинала	английский
Номер статьи	2042002
Число страниц	32
Журнал	Journal of Knot Theory and its Ramifications
Том	29
Номер выпуска	10
DOI	https://doi.org/10.1142/S021821652042002X
Состояние	Опубликовано - сен 2020

Доступ к документу

10.1142/S021821652042002X

Другие файлы и ссылки

Link to publication in Scopus

Цитировать

@article{1b01efc625854645bed98862a42b74e4,

title = "On virtual cabling and a structure of 4-strand virtual pure braid group",

abstract = "This paper is dedicated to cabling on virtual braids. This construction gives a new generating set for the virtual pure braid group VPn. We define simplicial group VP∗ and its simplicial subgroup T∗ which is generated by VP2. Consequently, we describe VP4 as HNN-extension and find presentation of T2 and T3. As an application to classical braids, we find a new presentation of the Artin pure braid group P4 in terms of the cabled generators.",

keywords = "Homotopy group, Simplicial group, Virtual braid group, Virtual cabling, virtual cabling, virtual braid group, simplicial group",

author = "Bardakov, {Valeriy G.} and Jie Wu",

year = "2020",

month = sep,

doi = "10.1142/S021821652042002X",

language = "English",

volume = "29",

journal = "Journal of Knot Theory and its Ramifications",

issn = "0218-2165",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "10",

}

TY - JOUR

T1 - On virtual cabling and a structure of 4-strand virtual pure braid group

AU - Bardakov, Valeriy G.

AU - Wu, Jie

PY - 2020/9

Y1 - 2020/9

N2 - This paper is dedicated to cabling on virtual braids. This construction gives a new generating set for the virtual pure braid group VPn. We define simplicial group VP∗ and its simplicial subgroup T∗ which is generated by VP2. Consequently, we describe VP4 as HNN-extension and find presentation of T2 and T3. As an application to classical braids, we find a new presentation of the Artin pure braid group P4 in terms of the cabled generators.

AB - This paper is dedicated to cabling on virtual braids. This construction gives a new generating set for the virtual pure braid group VPn. We define simplicial group VP∗ and its simplicial subgroup T∗ which is generated by VP2. Consequently, we describe VP4 as HNN-extension and find presentation of T2 and T3. As an application to classical braids, we find a new presentation of the Artin pure braid group P4 in terms of the cabled generators.

KW - Homotopy group

KW - Simplicial group

KW - Virtual braid group

KW - Virtual cabling

KW - virtual cabling

KW - virtual braid group

KW - simplicial group

UR - http://www.scopus.com/inward/record.url?scp=85093956926&partnerID=8YFLogxK

U2 - 10.1142/S021821652042002X

DO - 10.1142/S021821652042002X

M3 - Article

AN - SCOPUS:85093956926

VL - 29

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 10

M1 - 2042002

ER -

On virtual cabling and a structure of 4-strand virtual pure braid group

Аннотация

Доступ к документу

Другие файлы и ссылки

Fingerprint

Цитировать