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Representations of virtual braids by automorphisms and virtual knot groups. / Bardakov, Valeriy G.; Mikhalchishina, Yuliya A.; Neshchadim, Mikhail V.

In: Journal of Knot Theory and its Ramifications, Vol. 26, No. 1, 1750003, 01.01.2017.

Research output: Contribution to journal › Article › peer-review

Harvard

Bardakov, VG, Mikhalchishina, YA & Neshchadim, MV 2017, 'Representations of virtual braids by automorphisms and virtual knot groups', Journal of Knot Theory and its Ramifications, vol. 26, no. 1, 1750003. https://doi.org/10.1142/S0218216517500031

APA

Bardakov, V. G., Mikhalchishina, Y. A., & Neshchadim, M. V. (2017). Representations of virtual braids by automorphisms and virtual knot groups. Journal of Knot Theory and its Ramifications, 26(1), [1750003]. https://doi.org/10.1142/S0218216517500031

Vancouver

Bardakov VG, Mikhalchishina YA, Neshchadim MV. Representations of virtual braids by automorphisms and virtual knot groups. Journal of Knot Theory and its Ramifications. 2017 Jan 1;26(1):1750003. doi: 10.1142/S0218216517500031

Author

Bardakov, Valeriy G. ; Mikhalchishina, Yuliya A. ; Neshchadim, Mikhail V. / Representations of virtual braids by automorphisms and virtual knot groups. In: Journal of Knot Theory and its Ramifications. 2017 ; Vol. 26, No. 1.

BibTeX

@article{3a56baf4297645efaf46184143fb12df,
title = "Representations of virtual braids by automorphisms and virtual knot groups",
abstract = "In the present paper, a new representation of the virtual braid group VBn into the automorphism group of free product of the free group and free abelian group is constructed. This representation generalizes the previously constructed ones. The fact that the previously known representations are not faithful for n ≥ 4 is verified. Using representations of VBn, a virtual link group is defined. Also representations of the welded braid group WBn are constructed and the welded link group is defined.",
keywords = "Braids, representations by automorphisms, virtual braids, INVARIANTS, LINKS, ALEXANDER GROUPS",
author = "Bardakov, {Valeriy G.} and Mikhalchishina, {Yuliya A.} and Neshchadim, {Mikhail V.}",
year = "2017",
month = jan,
day = "1",
doi = "10.1142/S0218216517500031",
language = "English",
volume = "26",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "1",

}

RIS

TY - JOUR

T1 - Representations of virtual braids by automorphisms and virtual knot groups

AU - Bardakov, Valeriy G.

AU - Mikhalchishina, Yuliya A.

AU - Neshchadim, Mikhail V.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In the present paper, a new representation of the virtual braid group VBn into the automorphism group of free product of the free group and free abelian group is constructed. This representation generalizes the previously constructed ones. The fact that the previously known representations are not faithful for n ≥ 4 is verified. Using representations of VBn, a virtual link group is defined. Also representations of the welded braid group WBn are constructed and the welded link group is defined.

AB - In the present paper, a new representation of the virtual braid group VBn into the automorphism group of free product of the free group and free abelian group is constructed. This representation generalizes the previously constructed ones. The fact that the previously known representations are not faithful for n ≥ 4 is verified. Using representations of VBn, a virtual link group is defined. Also representations of the welded braid group WBn are constructed and the welded link group is defined.

KW - Braids

KW - representations by automorphisms

KW - virtual braids

KW - INVARIANTS

KW - LINKS

KW - ALEXANDER GROUPS

UR - http://www.scopus.com/inward/record.url?scp=84995803043&partnerID=8YFLogxK

U2 - 10.1142/S0218216517500031

DO - 10.1142/S0218216517500031

M3 - Article

AN - SCOPUS:84995803043

VL - 26

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 1

M1 - 1750003

ER -

ID: 10320736