 Zero surgery on the Hopf link

The Hopf link exterior is $T^2\times I$. Each component's Seifert longitude is the other's meridian. Filling the two boundary tori along these longitudes therefore attaches solid tori with meridians intersecting once on a common torus, recovering the standard genus-one splitting of the three-sphere. Merely specifying two linked unknots without specifying their link type does not force this answer.