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: