Link (knot theory)

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is a collection of knots which do not intersect,
but which may be linked (or knotted) together.

A knot can be described as a link with one component.
Links and knots are studied in a branch of mathematics called knot theory.

Implicit in this definition is that there is a trivial reference link, usually called the unlink,
but the word is also sometimes used in context where there is no notion of a trivial link.

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Frequently the word link is used to describe any submanifold of the sphere S^n diffeomorphic to
a disjoint union of a finite number of spheres, S^j.

In full generality, the word link is essentially the same as the word knot โ€“
the context is that one has a submanifold M of a manifold N (considered to be trivially embedded)
and a non-trivial embedding of M in N, non-trivial in the sense that
the 2nd embedding is not isotopic to the 1st.
If M is disconnected, the embedding is called a link (or said to be linked).
If M is connected, it is called a knot.