knot
In mathematics, a knot is an embedding of the circle S1 into three-dimensional Euclidean space, R3 (also known as E3). Often two knots are considered equivalent if they are isotopic. A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed — there are no ends to tie or untie on a mathematical knot. Physical properties such as friction and thickness also do not apply, although there are mathematical definitions of a knot that take such properties into account. The term knot is also applied to embeddings of S j in Sn, especially in the case j = n − 2. The branch of mathematics that studies knots is known as knot theory, and has many simple relations to graph theory.
embedding of a circle in R³
link embedding