Email this article Knotoids and knots in the thickened torus
- Authors: Korablev P.G.1,2, May Y.K.1
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Affiliations:
- Chelyabinsk State University
- Krasovskiĭ Institute of Mathematics and Mechanics
- Issue: Vol 58, No 5 (2017)
- Pages: 837-844
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171452
- DOI: https://doi.org/10.1134/S003744661705010X
- ID: 171452
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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.
About the authors
Ph. G. Korablev
Chelyabinsk State University; Krasovskiĭ Institute of Mathematics and Mechanics
Author for correspondence.
Email: korablev@csu.ru
Russian Federation, Chelyabinsk; Ekaterinburg
Ya. K. May
Chelyabinsk State University
Email: korablev@csu.ru
Russian Federation, Chelyabinsk
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