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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 975–980
(Mi semr542)
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This article is cited in 1 scientific paper (total 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.
Received December 3, 2014, published December 13, 2014
Citation:
Ph. G. Korablev, “Infinite series of Kishino type knots”, Sib. Èlektron. Mat. Izv., 11 (2014), 975–980
Linking options:
https://www.mathnet.ru/eng/semr542 https://www.mathnet.ru/eng/semr/v11/p975
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Abstract page: | 145 | Full-text PDF : | 58 | References: | 31 |
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