In the mathematical field of knot theory, an unlink is a link that is equivalent (under ambient isotopy) to finitely many disjoint circles in the plane.
The two-component unlink, consisting of two non-interlinked unknots, is the simplest possible unlink.
Related Image Collections
Add Image
We don't have any YouTube videos related to Unlink yet.
You can add one yourself here.
We don't have any PDF documents related to Unlink yet.
You can add one yourself here.
We don't have any Books related to Unlink yet.
You can add one yourself here.
We don't have any archived web articles related to Unlink yet.
Properties
- 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 the unknot.
- The link group of an n-component unlink is the free group on n generators, and is used in classifying Brunnian links.
Examples
- 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.
- Taizo Kanenobu has shown that for all n > 1 there exists a hyperbolic link of n components such that any proper sublink is an unlink (a Brunnian link). The Whitehead link and Borromean rings are such examples for n = 2, 3.2
See also
Further reading
- Kawauchi, A. A Survey of Knot Theory. Birkhauser.
References
Kanenobu, Taizo (1986), "Hyperbolic links with Brunnian properties", Journal of the Mathematical Society of Japan, 38 (2): 295–308, doi:10.2969/jmsj/03820295, MR 0833204 /wiki/Doi_(identifier) ↩
Kanenobu, Taizo (1986), "Hyperbolic links with Brunnian properties", Journal of the Mathematical Society of Japan, 38 (2): 295–308, doi:10.2969/jmsj/03820295, MR 0833204 /wiki/Doi_(identifier) ↩