A circle pair is a one dimensional shape constructed from a pair of two disconnected circles. This shape is found as the boundary of some higher dimensional shapes, such as the two-dimensional tube.
Knot Theory[]
In knot theory, embeddings of the circle pair into the Euclidean realm make up the 2-component links. These are distinct in that no link can be smoothly deformed into another without intersecting itself at some point
Unlink[]
The simplest link, the unlink, is the link made up of a circle pair where the components are completely disconnected and seperate.
The unlink can be seperated out into two distinct unknots.
Hopf Link[]
The Hopf link is the simplest nontrivial link, made up of a circle pair where the two circles are linked together exactly once but are otherwise undistorted.
The Hopf link can be seperated out into two distinct unknots.
Solomon's Knot[]
Solomon's knot is a link made up of a circle pair in which the circles are doubly linked.
Solomon's knot can be seperated out into two distinct unknots
Whitehead Link[]
The Whitehead link is a link made up of a circle pair, with one of the circles twisted into a figure-eight shape intertwined with a larger circle which goes through the two loops of the figure-eight.
The Whitehead link can be seperated out into two distinct unknots; the inner knot, twisted into a figure-eight shape, is only unable to be deformed into an unknot normally because it is linked with the outer knot which constrains it.