Ph. G. Korablev, Ya. K. May, “Knotoids and knots in the thickened torus”, Sibirsk. Mat. Zh., 2017, Volume 58, Number 5,Pages <nobr>1080

This article is cited in 6 papers

Knotoids and knots in the thickened torus

Ph. G. Korablev^ab, Ya. K. May^a

^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.

UDC: 515.162.32

MSC: 35R30

Received: 09.03.2017

DOI: 10.17377/smzh.2017.58.510