Definition:Knot (Knot Theory)

Definition
Let $Y$ be a manifold and $X \subset Y$ a submanifold of $Y$.

Let $i: X \to Y$ be an inclusion, i.e. a mapping such that $i \left({X}\right) = X$.

Then a knotted embedding is an embedding $\phi: X \to Y$ (or the image of such an embedding) such that $\phi \left({X}\right)$ is not freely homotopic to $i \left({X}\right)$.