Link (knot theory)

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The Borromean rings, a link with three components each equivalent to the unknot.

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

A Hopf link spanned by an annulus (image created with povray).

More formally, a link is a subspace of 3-dimensional Euclidean space (or often the 3-sphere) whose connected components are homeomorphic to circles. A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory.

The simplest nontrivial example of a link with more than one component is called the Hopf link, which consists of two circles (or unknots) linked together once. Borromean rings form a link with three components each equivalent to the unknot. The three loops are collectively linked despite the fact that no two of them are directly linked.

[edit] See also

• Linking coefficient
• Linking number
• Hyperbolic link
• Braid

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