The Borromean rings, a link with three components each equivalent to the unknot. In Mathematics, the Borromean rings consist of three topological Circles which are linked and form a Brunnian link, i

In mathematics, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Mathematics, a knot is an Embedding of a Circle in 3-dimensional Euclidean space, R 3 considered up to continuous deformations

A Hopf link spanned by an annulus.

More formally, a link is a subspace of 3-dimensional Euclidean space (or often the 3-sphere) whose connected components are homeomorphic to circles. In Topology and related areas of Mathematics, a subspace of a Topological space X is a Subset S of X which is In Mathematics, a 3-sphere is a higher-dimensional analogue of a Sphere. In Topology and related branches of Mathematics, a connected space is a Topological space which cannot be represented as the disjoint union of Topological equivalence redirects here see also Topological equivalence (dynamical systems. Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory. In Mathematics, knot theory is the area of Topology that studies mathematical knots While inspired by knots which appear in daily life in shoelaces

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. In mathematical Knot theory, the Hopf link, named after Heinz Hopf, is the simplest nontrivial link with more than one component The unknot arises in the mathematical theory of knots. Intuitively the unknot is a closed loop of rope without a Knot in it Borromean rings form a link with three components each equivalent to the unknot. In Mathematics, the Borromean rings consist of three topological Circles which are linked and form a Brunnian link, i The three loops are collectively linked despite the fact that no two of them are directly linked.

Trefoil knot linked with a circle. In Knot theory, the trefoil knot is the simplest nontrivial knot.

More generally

A link frequently refers to any submanifold of the sphere Sⁿ diffeomorphic to a disjoint union of a finite number of spheres, S^j. "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe

See also

• Linking number
• Hyperbolic link
• Braid theory
• Unlink