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Knotoids and knots in the thickened torus

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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.

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Authors and Affiliations

  1. Chelyabinsk State University, Chelyabinsk, Russia

    Ph. G. Korablev & Ya. K. May

  2. Krasovskiĭ Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Ph. G. Korablev

Authors
  1. Ph. G. Korablev
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  2. Ya. K. May
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Corresponding author

Correspondence to Ph. G. Korablev.

Additional information

Original Russian Text Copyright © 2017 Korablev Ph.G. and May Ya.K.

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 5, pp. 1080–1090, September–October, 2017; DOI: 10.17377/smzh.2017.58.510.

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Korablev, P.G., May, Y.K. Knotoids and knots in the thickened torus. Sib Math J 58, 837–844 (2017). https://doi.org/10.1134/S003744661705010X

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  • DOI: https://doi.org/10.1134/S003744661705010X

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