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Groups of the virtual trefoil and Kishino knots. / Bardakov, Valeriy G.; Mikhalchishina, Yuliya A.; Neshchadim, Mikhail V.

In: Journal of Knot Theory and its Ramifications, Vol. 27, No. 13, 1842009, 01.11.2018.

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

Harvard

Bardakov, VG, Mikhalchishina, YA & Neshchadim, MV 2018, 'Groups of the virtual trefoil and Kishino knots', Journal of Knot Theory and its Ramifications, vol. 27, no. 13, 1842009. https://doi.org/10.1142/S0218216518420099

APA

Bardakov, V. G., Mikhalchishina, Y. A., & Neshchadim, M. V. (2018). Groups of the virtual trefoil and Kishino knots. Journal of Knot Theory and its Ramifications, 27(13), [1842009]. https://doi.org/10.1142/S0218216518420099

Vancouver

Bardakov VG, Mikhalchishina YA, Neshchadim MV. Groups of the virtual trefoil and Kishino knots. Journal of Knot Theory and its Ramifications. 2018 Nov 1;27(13):1842009. doi: 10.1142/S0218216518420099

Author

Bardakov, Valeriy G. ; Mikhalchishina, Yuliya A. ; Neshchadim, Mikhail V. / Groups of the virtual trefoil and Kishino knots. In: Journal of Knot Theory and its Ramifications. 2018 ; Vol. 27, No. 13.

BibTeX

@article{d7d5c7aa50a34b2f84e98fad4c736d98,
title = "Groups of the virtual trefoil and Kishino knots",
abstract = "In the paper [13], for an arbitrary virtual link L, three groups G1,r(L), r > 0, G2(L) and G3(L) were defined. In the present paper, these groups for the virtual trefoil are investigated. The structure of these groups are found out and the fact that some of them are not isomorphic to each other is proved. Also, we prove that G3 distinguishes the Kishino knot from the trivial knot. The fact that these groups have the lower central series which does not stabilize on the second term is noted. Hence, we have a possibility to study these groups using quotients by terms of the lower central series and to construct representations of these groups in rings of formal power series. It allows to construct an invariants for virtual knots.",
keywords = "Braids, Kishino knot, representations by automorphisms, virtual braids, INVARIANTS, LINKS",
author = "Bardakov, {Valeriy G.} and Mikhalchishina, {Yuliya A.} and Neshchadim, {Mikhail V.}",
year = "2018",
month = nov,
day = "1",
doi = "10.1142/S0218216518420099",
language = "English",
volume = "27",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "13",

}

RIS

TY - JOUR

T1 - Groups of the virtual trefoil and Kishino knots

AU - Bardakov, Valeriy G.

AU - Mikhalchishina, Yuliya A.

AU - Neshchadim, Mikhail V.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - In the paper [13], for an arbitrary virtual link L, three groups G1,r(L), r > 0, G2(L) and G3(L) were defined. In the present paper, these groups for the virtual trefoil are investigated. The structure of these groups are found out and the fact that some of them are not isomorphic to each other is proved. Also, we prove that G3 distinguishes the Kishino knot from the trivial knot. The fact that these groups have the lower central series which does not stabilize on the second term is noted. Hence, we have a possibility to study these groups using quotients by terms of the lower central series and to construct representations of these groups in rings of formal power series. It allows to construct an invariants for virtual knots.

AB - In the paper [13], for an arbitrary virtual link L, three groups G1,r(L), r > 0, G2(L) and G3(L) were defined. In the present paper, these groups for the virtual trefoil are investigated. The structure of these groups are found out and the fact that some of them are not isomorphic to each other is proved. Also, we prove that G3 distinguishes the Kishino knot from the trivial knot. The fact that these groups have the lower central series which does not stabilize on the second term is noted. Hence, we have a possibility to study these groups using quotients by terms of the lower central series and to construct representations of these groups in rings of formal power series. It allows to construct an invariants for virtual knots.

KW - Braids

KW - Kishino knot

KW - representations by automorphisms

KW - virtual braids

KW - INVARIANTS

KW - LINKS

UR - http://www.scopus.com/inward/record.url?scp=85057408680&partnerID=8YFLogxK

U2 - 10.1142/S0218216518420099

DO - 10.1142/S0218216518420099

M3 - Article

AN - SCOPUS:85057408680

VL - 27

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 13

M1 - 1842009

ER -

ID: 17669108