For example, an unknotted loop has as its minimal energy a round circle. They hope that looking at energies will give a way to distinguish between different knots and links. A particularly nice class of links is the class Hopf links. These are links composed of particular great circles on the three-sphere which come from the Hopf fibration, defined as follows. Equivalently, they are points on the three-sphere such that the ratio of the two complex coordinates is constant.
Hopf circles turn out to be great circles of the three-sphere.
In fact, each point on the three-sphere is contained in exactly one Hopf circle. This division into Hopf circles is called the Hopf fibration. Any two Hopf circles link exactly once. Thus a collection of Hopf circles form a link. For Hopf links, the associated energy depends only on the distance between loops in four-space, since each loop in the link is itself a round circle.