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:

Category:Terminology related to knot theory