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Finite type invariants for knotoids. / Manouras, Manousos; Lambropoulou, Sofia; Kauffman, Louis H.

In: European Journal of Combinatorics, Vol. 98, 103402, 12.2021.

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

Harvard

Manouras, M, Lambropoulou, S & Kauffman, LH 2021, 'Finite type invariants for knotoids', European Journal of Combinatorics, vol. 98, 103402. https://doi.org/10.1016/j.ejc.2021.103402

APA

Manouras, M., Lambropoulou, S., & Kauffman, L. H. (2021). Finite type invariants for knotoids. European Journal of Combinatorics, 98, [103402]. https://doi.org/10.1016/j.ejc.2021.103402

Vancouver

Manouras M, Lambropoulou S, Kauffman LH. Finite type invariants for knotoids. European Journal of Combinatorics. 2021 Dec;98:103402. doi: 10.1016/j.ejc.2021.103402

Author

Manouras, Manousos ; Lambropoulou, Sofia ; Kauffman, Louis H. / Finite type invariants for knotoids. In: European Journal of Combinatorics. 2021 ; Vol. 98.

BibTeX

@article{cf6fee6cf97345509e708d1848903f8c,
title = "Finite type invariants for knotoids",
abstract = "We extend the theory of Vassiliev (or finite type) invariants for knots to knotoids using two different approaches. Firstly, we take closures on knotoids to obtain knots and we use the Vassiliev invariants for knots, proving that these are knotoid isotopy invariant. Secondly, we define finite type invariants directly on knotoids, by extending knotoid invariants to singular knotoid invariants via the Vassiliev skein relation. Then, for spherical knotoids we show that there are non-trivial type-1 invariants, in contrast with classical knot theory where type-1 invariants vanish. We give a complete theory of type-1 invariants for spherical knotoids, by classifying linear chord diagrams of order one, and we present examples arising from the affine index polynomial and the extended bracket polynomial.",
author = "Manousos Manouras and Sofia Lambropoulou and Kauffman, {Louis H.}",
note = "Funding Information: Kauffman's work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University, Russia (contract no.14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation ). Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",
year = "2021",
month = dec,
doi = "10.1016/j.ejc.2021.103402",
language = "English",
volume = "98",
journal = "European Journal of Combinatorics",
issn = "0195-6698",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Finite type invariants for knotoids

AU - Manouras, Manousos

AU - Lambropoulou, Sofia

AU - Kauffman, Louis H.

N1 - Funding Information: Kauffman's work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University, Russia (contract no.14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation ). Publisher Copyright: © 2021 Elsevier Ltd

PY - 2021/12

Y1 - 2021/12

N2 - We extend the theory of Vassiliev (or finite type) invariants for knots to knotoids using two different approaches. Firstly, we take closures on knotoids to obtain knots and we use the Vassiliev invariants for knots, proving that these are knotoid isotopy invariant. Secondly, we define finite type invariants directly on knotoids, by extending knotoid invariants to singular knotoid invariants via the Vassiliev skein relation. Then, for spherical knotoids we show that there are non-trivial type-1 invariants, in contrast with classical knot theory where type-1 invariants vanish. We give a complete theory of type-1 invariants for spherical knotoids, by classifying linear chord diagrams of order one, and we present examples arising from the affine index polynomial and the extended bracket polynomial.

AB - We extend the theory of Vassiliev (or finite type) invariants for knots to knotoids using two different approaches. Firstly, we take closures on knotoids to obtain knots and we use the Vassiliev invariants for knots, proving that these are knotoid isotopy invariant. Secondly, we define finite type invariants directly on knotoids, by extending knotoid invariants to singular knotoid invariants via the Vassiliev skein relation. Then, for spherical knotoids we show that there are non-trivial type-1 invariants, in contrast with classical knot theory where type-1 invariants vanish. We give a complete theory of type-1 invariants for spherical knotoids, by classifying linear chord diagrams of order one, and we present examples arising from the affine index polynomial and the extended bracket polynomial.

UR - http://www.scopus.com/inward/record.url?scp=85112496411&partnerID=8YFLogxK

U2 - 10.1016/j.ejc.2021.103402

DO - 10.1016/j.ejc.2021.103402

M3 - Article

AN - SCOPUS:85112496411

VL - 98

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

M1 - 103402

ER -

ID: 33979391