# Definition:Normal Bundle

## Definition

Let $M$ be a differentiable manifold.

Let $p \in M$ be a point in $M$.

Let $N_p M$ be the normal space at $p$.

The normal bundle of $M$ is the disjoint union of all the normal spaces of $M$:

$\displaystyle N M = \coprod_{p \mathop \in M} N_p M$