Split link
≈ 2 min read
Names in other languages
No names in other languages are held for this entry yet.
Article bodies are English and are not machine-translated. A name in another language is not a translation of the article.
In the mathematical field of knot theory, a split link is a link that has a (topological) 2-sphere in its complement separating one or more link components from the others. A split link is said to be splittable, and a link that is not split is called a non-split link or not splittable. Whether a link is split or non-split corresponds to whether the link complement is reducible or irreducible as a 3-manifold. A link with an alternating diagram, i.e. an alternating link, will be non-split if and only if this diagram is connected. This is a result of the work of William Menasco. A split link has many connected, non-alternating link diagrams.
In the mathematical field of knot theory, a split link is a link that has a (topological) 2-sphere in its complement separating one or more link components from the others. A split link is said to be splittable, and a link that is not split is called a non-split link or not splittable. Whether a link is split or non-split corresponds to whether the link complement is reducible or irreducible as a 3-manifold. A link with an alternating diagram, i.e. an alternating link, will be non-split if and only if this diagram is connected. This is a result of the work of William Menasco. A split link has many connected, non-alternating link diagrams. ==References==
Text derived from https://en.wikipedia.org/w/index.php?oldid=1197282803 under CC BY-SA 4.0; modifications have been made.