Hopf link

The Hopf link consists of two unknots with linking number

\pm 1

. Each component is a meridian of a knot of the other.

Table of contents
- Zero surgery on the Hopf link Hopf link

Zero surgery on the Hopf link ( $S_{0, 0}^{3} (Hopf) ≅ S^{3}$ )

 0  0

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.