Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Finite type invariants for knotoids. / Manouras, Manousos; Lambropoulou, Sofia; Kauffman, Louis H.
в: European Journal of Combinatorics, Том 98, 103402, 12.2021.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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