Knot

Definition

A knot is defined as an embedding of $S^{1}$ in $S^{3}$. In other words, it is a choice of submanifold of $S^{3}$ which is homeomorphic to $S^{1}$.

The term knot is also sometimes used more generally to study the problem of how a compact submanifold can live inside a bigger manifold.

A list of terminology related to the theory of knots is available at: