Links with nontrivial Alexander polynomial which are topologically concordant to the Hopf link

TL;DR

This paper constructs infinitely many 2-component links with unknotted components that are topologically concordant to the Hopf link but not smoothly concordant to links with trivial Alexander polynomial, highlighting differences between topological and smooth concordance.

Contribution

It introduces new examples of links demonstrating the distinction between topological and smooth concordance related to Alexander polynomial invariants.

Findings

Existence of infinitely many such links

Links are pairwise non-concordant

Links are topologically but not smoothly concordant to the Hopf link

Abstract

We give infinitely many $2$-component links with unknotted components which are topologically concordant to the Hopf link, but not smoothly concordant to any $2$-component link with trivial Alexander polynomial. Our examples are pairwise non-concordant.