In the mathematical
field of knot theory
, the unlink
is a link
that is equivalent (under ambient isotopy
) to finitely many disjoint circles in the plane.
- An n-component link L ⊂ S3 is an unlink if and only if there exists n disjointly embedded discs Di ⊂ S3 such that L = ∪i∂Di.
- A link with one component is an unlink if and only if it is isotopic to the unknot.
- The Hopf link is a simple example of a link with two components that is not an unlink.
- The Borromean rings form a link with three components that is not an unlink; however, any two of the rings considered on their own do form a two-component unlink.
- Kanenobu has shown that for all n > 1 there exists a hyperbolic link of n components such that any proper sublink is an unlink. The Whitehead link and Borromean rings are such examples for n = 2, 3.