A new family of links topologically, but not smoothly, concordant to the Hopf link

Abstract

We give new examples of 2-component links with linking number one and unknotted components that are topologically concordant to the positive Hopf link, but not smoothly so - in fact they are not smoothly concordant to the positive Hopf link with a knot tied in the first component. Such examples were previously constructed by Cha-Kim-Ruberman-Strle; we show that our examples are distinct from theirs.

v1 is 7 pages, 7 figures; v2 is 10 pages, 11 figures, includes a computation of a multivariable Alexander polynomial as suggested by Jim Davis (Remark 2.2) and addresses why some other natural candidates do not work (Remark 2.7), to appear in the Tim Cochran memorial issue of J. Knot Theory Ramifications