In mathematics, autonomous system is a dynamic equation on a smooth manifold.

A Lie group is a group in the category of smooth manifolds.

For example, the set of real numbers R is a smooth manifold.

All oriented smooth manifolds of dimension 4 or less are spin.

Let be any regular value of , so that the level set is a smooth manifold.

For a smooth manifold of dimension in (clearly we need ).

They apply in ways similar to, but more complicated than, Morse functions on smooth manifolds.

But if the stabilizer groups change we cannot expect a smooth manifold any longer.

A more involved example comes from differential topology, in which we have the notion of a smooth manifold.

Therefore X is a smooth manifold via transport of structure.