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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2014 Volume 11, Pages 975–980 (Mi semr542)

This article is cited in 1 paper

Geometry and topology

Infinite series of Kishino type knots

Ph. G. Korablev

Chelyabinsk State University

Abstract: We construct an infinite series of nontrivial virtual knots $\mathcal{K}_n$, $n \geqslant 2$. Each knot in this series is a connected sum of trivial virtual knots. We prove that for each $n$ the genus of $\mathcal{K}_n$ is equal to $n$. As a consequence, two knots $\mathcal{K}_i$ and $\mathcal{K}_j$ are non-equivalent iff $i\neq j$.

Keywords: Kishino knot, knot in thickened surface, virtual knot, genus of the knot.

UDC: 515.162.8

MSC: 57M27

Received December 3, 2014, published December 13, 2014



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