Classification of small links in the unmarked solid torus

Abstract

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.