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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1237–1244 (Mi semr991)  

Geometry and topology

Classification of low complexity knotoids

Ph. G. Korablevab, Y. K. Maya, V. V. Tarkaevab

a Chelyabinsk State University, Br. Kashirinykh str., 192, 454000, Chelyabinsk, Russia
b N.N. Krasovsky Institute of Mathematics and Meckhanics, str. S. Kovalevskoy, 4, 620990, Ekaterinburg, Russia

Abstract: As the main result of the paper we present the complete classification of all prime knotoids with positive height and at most 5 crossings. We prove that there exist exactly 31 knotoids of this type. The proof is based on the complete table of knots in the thickened torus and the correspondence between knotoids in the two dimensional sphere and knots in the thickened torus.

Keywords: knotoid, classification, crossing number, height of knotoid, table.

Funding Agency Grant Number
Russian Science Foundation 16–11–10291


DOI: https://doi.org/10.17377/semi.2018.15.100

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Bibliographic databases:

Document Type: Article
UDC: 515.162.8
MSC: 57M25
Received August 15, 2018, published October 23, 2018

Citation: Ph. G. Korablev, Y. K. May, V. V. Tarkaev, “Classification of low complexity knotoids”, Sib. Èlektron. Mat. Izv., 15 (2018), 1237–1244

Citation in format AMSBIB
\Bibitem{KorMayTar18}
\by Ph.~G.~Korablev, Y.~K.~May, V.~V.~Tarkaev
\paper Classification of low complexity knotoids
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1237--1244
\mathnet{http://mi.mathnet.ru/semr991}
\crossref{https://doi.org/10.17377/semi.2018.15.100}


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