Link invariants derived from multiplexing of crossings

Abstract

We introduce the multiplexing of a crossing, replacing a classical crossing of a virtual link diagram with a mixture of classical and virtual crossings.

For integers $m_i$ $\left(i=1,\dots ,n\right)$ and an ordered $n$–component virtual link diagram $D$, a new virtual link diagram $D\left(m_1,\dots ,m_n\right)$ is obtained from $D$ by the multiplexing of all crossings. For welded isotopic virtual link diagrams $D$ and $D^{\prime }$, the virtual link diagrams $D\left(m_1,\dots ,m_n\right)$ and $D^{\prime }\left(m_1,\dots ,m_n\right)$ are welded isotopic. From the point of view of classical link theory, it seems very interesting that new classical link invariants are obtained from welded link invariants via the multiplexing of crossings.