On invariants of multiplexed virtual links

Abstract

For a virtual knot $K$ and an integer $r$ with $r\geq2$, we introduce a method of constructing an $r$-component virtual link $L(K;r)$, which we call the $r$-multiplexing of $K$. Every invariant of $L(K;r)$ is an invariant of $K$. We give a way of calculating three kinds of invariants of $L(K;r)$ using invariants of $K$. As an application of our method, we also show that Manturov's virtual $n$-colorings for $K$ can be interpreted as certain classical $n$-colorings for $L(K;2)$.