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 this group is able to distinguish five Kishino knots from the unknot using a stacked pair. However, for two other Kishino knots, the group and quandle of any stack invariant will be free with a number of generators equal to the number of copies in the stack, although the Jones polynomial of the stacks is able to detect their nontriviality.