split link
{{short description|Concept in mathematical knot theory}}
{{For|the connecting link (or split link) of a Roller chain |Master link}}
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.{{citation|title=Knots and Links|first=Peter R.|last=Cromwell|publisher=Cambridge University Press|year=2004|isbn=9780521548311|at=Definition 4.1.1, p. 78|url=https://books.google.com/books?id=djvbTNR2dCwC&pg=PA78}}. 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.{{citation|title=An Introduction to Knot Theory|series=Graduate Texts in Mathematics|volume=175|first=W. B. Raymond|last=Lickorish|authorlink=W. B. R. Lickorish|publisher=Springer|year=1997|isbn=9780387982540|page=32|url=https://books.google.com/books?id=PhHhw_kRvewC&pg=PA32}}. A split link has many connected, non-alternating link diagrams.