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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 5, Pages 1080–1090
DOI: https://doi.org/10.17377/smzh.2017.58.510 (Mi smj2920) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Knotoids and knots in the thickened torus

Ph. G. Korablevab, Ya. K. Maya

a Chelyabinsk State University, Chelyabinsk, Russia
b Krasovskiĭ Institute of Mathematics and Mechanics, Ekaterinburg, Russia
Full-text PDF (351 kB) Citations (6)
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DOI: https://doi.org/10.17377/smzh.2017.58.510
Abstract: We study the relationship between knotoids and knots in the direct product of the two-dimensional torus and an interval. Each knotoid on the sphere can be lifted to a knot of geometric degree 1 in the thickened torus. We prove that lifting is a bijection on the set of prime knotoids of complexity greater than 1.
Keywords: knotoid, knot in the thickened torus, complexity of a knotoid, multiplication of knotoids.
Funding agency Grant number
Russian Science Foundation 16-11-10291
The authors were supported by the Russian Science Foundation (Grant 16-11-10291).
Received: 09.03.2017
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 5, Pages 837–844
DOI: https://doi.org/10.1134/S003744661705010X
Bibliographic databases:
Document Type: Article
UDC: 515.162.32
MSC: 35R30
Language: Russian
Citation: Ph. G. Korablev, Ya. K. May, “Knotoids and knots in the thickened torus”, Sibirsk. Mat. Zh., 58:5 (2017), 1080–1090; Siberian Math. J., 58:5 (2017), 837–844
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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