Smooth concordance of links topologically concordant to the Hopf link (Q2893260)

The authors consider the question of when a 2-component link is smoothly concordant to the Hopf link. A theorem of M. Freedman shows that a knot with trivial Alexander polynomial is topologically concordant to the trivial knot. Later J. Davis showed that a 2-component link with trivial Alexander polynomial is topologically concordant to the Hopf link. This result does not hold in the smooth category due to the existence of smooth non-slice knots with trivial Alexander polynomial. In this paper it is shown that there is a 2-component link with trivial Alexander polynomial which has unkotted components and is not smoothly concordant to any link that is the connected sum of the Hopf link and a split link. Infinitely many smooth concordance classes of such links are constructed, and these links are shown to be not smoothly concordant to the Hopf link with knots tied in its components in a certain way.