Link groups of Kishino knot stacks
Blake K Winter

TL;DR
This paper introduces a new class of links called stacks derived from virtual links, and demonstrates that their fundamental groups can distinguish Kishino knots from unknots and each other, also computing their Jones polynomials.
Contribution
It presents a novel method for constructing link groups from virtual links called stacks, which can detect nontrivial and nonclassical virtual knots like Kishino knots.
Findings
Groups distinguish all Kishino knots from the unknot
Groups differentiate Kishino knots from each other
Jones polynomials of Kishino knots are computed
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.
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Taxonomy
TopicsDupuytren's Contracture and Treatments · Oral and gingival health research
