Аннотация:
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 $i\neq j$.
Ключевые слова:Kishino knot, knot in thickened surface, virtual knot, genus of the knot.