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Structural aspects of twin and pure twin groups. / Bardakov, Valeriy; Singh, Mahender; Vesnin, Andrei.

в: Geometriae Dedicata, Том 203, № 1, 01.12.2019, стр. 135-154.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

Harvard

Bardakov, V, Singh, M & Vesnin, A 2019, 'Structural aspects of twin and pure twin groups', Geometriae Dedicata, Том. 203, № 1, стр. 135-154. https://doi.org/10.1007/s10711-019-00429-1

APA

Bardakov, V., Singh, M., & Vesnin, A. (2019). Structural aspects of twin and pure twin groups. Geometriae Dedicata, 203(1), 135-154. https://doi.org/10.1007/s10711-019-00429-1

Vancouver

Bardakov V, Singh M, Vesnin A. Structural aspects of twin and pure twin groups. Geometriae Dedicata. 2019 дек. 1;203(1):135-154. doi: 10.1007/s10711-019-00429-1

Author

Bardakov, Valeriy ; Singh, Mahender ; Vesnin, Andrei. / Structural aspects of twin and pure twin groups. в: Geometriae Dedicata. 2019 ; Том 203, № 1. стр. 135-154.

BibTeX

@article{297cb99288e8484190866424f033926e,
title = "Structural aspects of twin and pure twin groups",
abstract = " The twin group T n is a Coxeter group generated by n- 1 involutions and the pure twin group PT n is the kernel of the natural surjection of T n onto the symmetric group on n letters. In this paper, we investigate structural aspects of twin and pure twin groups. We prove that the twin group T n decomposes into a free product with amalgamation for n> 4. It is shown that the pure twin group PT n is free for n= 3 , 4 , and not free for n≥ 6. We determine a generating set for PT n , and give an upper bound for its rank. We also construct a natural faithful representation of T 4 into Aut (F 7 ). In the end, we propose virtual and welded analogues of these groups and some directions for future work. ",
keywords = "Coxeter group, Doodle, Eilenberg–Maclane space, Free group, Hyperbolic plane, Pure twin group, Twin group",
author = "Valeriy Bardakov and Mahender Singh and Andrei Vesnin",
year = "2019",
month = dec,
day = "1",
doi = "10.1007/s10711-019-00429-1",
language = "English",
volume = "203",
pages = "135--154",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer Netherlands",
number = "1",

}

RIS

TY - JOUR

T1 - Structural aspects of twin and pure twin groups

AU - Bardakov, Valeriy

AU - Singh, Mahender

AU - Vesnin, Andrei

PY - 2019/12/1

Y1 - 2019/12/1

N2 - The twin group T n is a Coxeter group generated by n- 1 involutions and the pure twin group PT n is the kernel of the natural surjection of T n onto the symmetric group on n letters. In this paper, we investigate structural aspects of twin and pure twin groups. We prove that the twin group T n decomposes into a free product with amalgamation for n> 4. It is shown that the pure twin group PT n is free for n= 3 , 4 , and not free for n≥ 6. We determine a generating set for PT n , and give an upper bound for its rank. We also construct a natural faithful representation of T 4 into Aut (F 7 ). In the end, we propose virtual and welded analogues of these groups and some directions for future work.

AB - The twin group T n is a Coxeter group generated by n- 1 involutions and the pure twin group PT n is the kernel of the natural surjection of T n onto the symmetric group on n letters. In this paper, we investigate structural aspects of twin and pure twin groups. We prove that the twin group T n decomposes into a free product with amalgamation for n> 4. It is shown that the pure twin group PT n is free for n= 3 , 4 , and not free for n≥ 6. We determine a generating set for PT n , and give an upper bound for its rank. We also construct a natural faithful representation of T 4 into Aut (F 7 ). In the end, we propose virtual and welded analogues of these groups and some directions for future work.

KW - Coxeter group

KW - Doodle

KW - Eilenberg–Maclane space

KW - Free group

KW - Hyperbolic plane

KW - Pure twin group

KW - Twin group

UR - http://www.scopus.com/inward/record.url?scp=85062792034&partnerID=8YFLogxK

U2 - 10.1007/s10711-019-00429-1

DO - 10.1007/s10711-019-00429-1

M3 - Article

AN - SCOPUS:85062792034

VL - 203

SP - 135

EP - 154

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 1

ER -

ID: 18860761