Link groups of Kishino knot stacks

Abstract

For any virtual link, a class of new links can be defined called stacks, in which copies of the virtual link are placed on top of one another. The resulting virtual link depends only on the virtual isotopy class of the original link, and the fundamental group of such a link may be used to detect whether the link is nontrivial and whether it is nonclassical in some cases. We show that the groups constructed using this method are sufficient to distinguish all the Kishino knots from the unknot and from one another, as well as calculating their Jones polynomials.