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Parity, virtual closure and minimality of knotoids. / Gügümcü, N.; Kauffman, L. H.

In: Journal of Knot Theory and its Ramifications, Vol. 30, No. 11, 2150076, 01.10.2021.

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

Harvard

Gügümcü, N & Kauffman, LH 2021, 'Parity, virtual closure and minimality of knotoids', Journal of Knot Theory and its Ramifications, vol. 30, no. 11, 2150076. https://doi.org/10.1142/S0218216521500760

APA

Gügümcü, N., & Kauffman, L. H. (2021). Parity, virtual closure and minimality of knotoids. Journal of Knot Theory and its Ramifications, 30(11), [2150076]. https://doi.org/10.1142/S0218216521500760

Vancouver

Gügümcü N, Kauffman LH. Parity, virtual closure and minimality of knotoids. Journal of Knot Theory and its Ramifications. 2021 Oct 1;30(11):2150076. doi: 10.1142/S0218216521500760

Author

Gügümcü, N. ; Kauffman, L. H. / Parity, virtual closure and minimality of knotoids. In: Journal of Knot Theory and its Ramifications. 2021 ; Vol. 30, No. 11.

BibTeX

@article{5cd7cc7213894d8f8e8e63f629c4b0ed,
title = "Parity, virtual closure and minimality of knotoids",
abstract = "In this paper, we study parity in planar and spherical knotoids in relation to virtual knots. We introduce a planar version of the parity bracket polynomial for planar knotoids. We show that the virtual closure map (a map from the set of knotoids in S2 to the set of virtual knots of genus at most one) is not surjective, by utilizing the surface bracket polynomial of virtual knots. We give specific examples of virtual knots that are not in the image of the virtual closure map. Turaev conjectured that minimal diagrams of knot-type knotoids have zero height. We prove this conjecture by using the results of Nikonov and Manturov induced by parities of virtual knots. ",
keywords = "crossing number, Knotoids, parity, virtual knots",
author = "N. G{\"u}g{\"u}mc{\"u} and Kauffman, {L. H.}",
note = "The first author's work was supported by the Dorothea Schlozer Postdoctoral Program for Women Scientists by the University of Goettingen. The second author's work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (contract no. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation). Publisher Copyright: {\textcopyright} 2021 World Scientific Publishing Company.",
year = "2021",
month = oct,
day = "1",
doi = "10.1142/S0218216521500760",
language = "English",
volume = "30",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "11",

}

RIS

TY - JOUR

T1 - Parity, virtual closure and minimality of knotoids

AU - Gügümcü, N.

AU - Kauffman, L. H.

N1 - The first author's work was supported by the Dorothea Schlozer Postdoctoral Program for Women Scientists by the University of Goettingen. The second author's work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (contract no. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation). Publisher Copyright: © 2021 World Scientific Publishing Company.

PY - 2021/10/1

Y1 - 2021/10/1

N2 - In this paper, we study parity in planar and spherical knotoids in relation to virtual knots. We introduce a planar version of the parity bracket polynomial for planar knotoids. We show that the virtual closure map (a map from the set of knotoids in S2 to the set of virtual knots of genus at most one) is not surjective, by utilizing the surface bracket polynomial of virtual knots. We give specific examples of virtual knots that are not in the image of the virtual closure map. Turaev conjectured that minimal diagrams of knot-type knotoids have zero height. We prove this conjecture by using the results of Nikonov and Manturov induced by parities of virtual knots.

AB - In this paper, we study parity in planar and spherical knotoids in relation to virtual knots. We introduce a planar version of the parity bracket polynomial for planar knotoids. We show that the virtual closure map (a map from the set of knotoids in S2 to the set of virtual knots of genus at most one) is not surjective, by utilizing the surface bracket polynomial of virtual knots. We give specific examples of virtual knots that are not in the image of the virtual closure map. Turaev conjectured that minimal diagrams of knot-type knotoids have zero height. We prove this conjecture by using the results of Nikonov and Manturov induced by parities of virtual knots.

KW - crossing number

KW - Knotoids

KW - parity

KW - virtual knots

UR - http://www.scopus.com/inward/record.url?scp=85124013054&partnerID=8YFLogxK

U2 - 10.1142/S0218216521500760

DO - 10.1142/S0218216521500760

M3 - Article

AN - SCOPUS:85124013054

VL - 30

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 11

M1 - 2150076

ER -

ID: 35464233