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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 975–980 (Mi semr542)  

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
Full-text PDF (168 kB) Citations (1)
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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
Document Type: Article
UDC: 515.162.8
MSC: 57M27
Language: Russian
Citation: Ph. G. Korablev, “Infinite series of Kishino type knots”, Sib. Èlektron. Mat. Izv., 11 (2014), 975–980
Citation in format AMSBIB
\Bibitem{Kor14}
\by Ph.~G.~Korablev
\paper Infinite series of Kishino type knots
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 975--980
\mathnet{http://mi.mathnet.ru/semr542}
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  • https://www.mathnet.ru/eng/semr542
  • https://www.mathnet.ru/eng/semr/v11/p975
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Full-text PDF :58
    References:31
     
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