Knot (mathematics)
In mathematics, a knot is an embedding of a circle in 3-dimensional space, considered up to continuous deformations (isotopies). This is basically equivalent to a conventional knot with the ends of the string joined together to prevent it from becoming undone. The study of such objects forms a branch of mathematics called knot theory.
The simplest knot, called the unknot, is just a standard circle embedded in R3. It the ordinary sense of the word, the unknot is not "knotted" at all. The simplest nontrivial knots are the trefoil knot and the figure-eight knot.
Several knots, possibly tangled together, are called links. Knots are links with with a single component.
In higher dimensions, circles are always unknotted, so one considers embeddings of spheres, always in codimension 2.
See also:
de:Knoten (Topologie)