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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
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.
Received: 09.03.2017
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
Linking options:
https://www.mathnet.ru/eng/smj2920 https://www.mathnet.ru/eng/smj/v58/i5/p1080
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Abstract page: | 201 | Full-text PDF : | 87 | References: | 33 | First page: | 6 |
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