On invariants of multiplexed virtual links

Abstract

For a virtual knot [Formula: see text] and an integer [Formula: see text] with [Formula: see text], we introduce a method of constructing an [Formula: see text]-component virtual link [Formula: see text], which we call the [Formula: see text]-multiplexing of [Formula: see text]. Every invariant of [Formula: see text] is an invariant of [Formula: see text]. We give a way of calculating three kinds of invariants of [Formula: see text] using invariants of [Formula: see text]. As an application of our method, we also show that Manturov’s virtual [Formula: see text]-colorings for [Formula: see text] can be interpreted as certain classical [Formula: see text]-colorings for [Formula: see text].