Hopf link

The Hopf link is the link isotopy class of the two coordinate circles in the three-sphereUnder stereographic projection it has the familiar two-crossing diagram of two circles linked once. Both components are unknots, and their linking number is $+1$ or $-1$ depending on their orientations. Each component is a meridian of a knot of the other. The specific standard link type is part of the definition: the same component knot types and linking number do not in general determine a link.

Its link exterior is $T^2\times [0,1]$. Indeed, removing small neighborhoods of the two coordinate circles leaves both complex arguments free while $|z_1|$ varies in a closed interval. This product explains why exchanging the two meridians and longitudes gives the zero surgery on the Hopf link computation.

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.