2023/06/15 by John M. Sullivan, Sullivan, John M., Max Zahoransky von Worlik +1
Chemistry · Materials Science · Mathematics · #57K10 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Organoboron and organosilicon chemistry #Supramolecular Self-Assembly in Materials
paper · pdf · doi:10.48550/arxiv.2306.09110
openalex publication_date 2023/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a framework to analyze knots and links in an unmarked solid torus. We discuss invariants that detect when such links are equivalent under an ambient homeomorphism, and show that the multivariable Alexander polynomial is such in invariant. We compute, for links with low wrapping number, bounds on the degree of a Dehn twist needed to transform one into the other that depend on the dichromatic Kauffman polynomial. Finally, we use this to give a classification of all non-split links up to 6 crossings in the unmarked solid torus.