Knotoids and knots in the thickened torus


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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.

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Ph. Korablev

Chelyabinsk State University; Krasovskiĭ Institute of Mathematics and Mechanics

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Email: korablev@csu.ru
俄罗斯联邦, Chelyabinsk; Ekaterinburg

Ya. May

Chelyabinsk State University

Email: korablev@csu.ru
俄罗斯联邦, Chelyabinsk

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