Geodesic
Infinite series of Kishino type knots
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 975-980

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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. 
@article{SEMR_2014_11_a46,
     author = {Ph. G. Korablev},
     title = {Infinite series of {Kishino} type knots},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {975--980},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a46/}
}
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Ph. G. Korablev. Infinite series of Kishino type knots. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 975-980. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a46/