Smooth manifold

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Note: It's worth looking at Motivation for smooth manifolds

Definition

A smooth manifold is[1] a pair [ilmath](M,\mathcal{A})[/ilmath] where [ilmath]M[/ilmath] is a topological [ilmath]n[/ilmath]-manifold and [ilmath]\mathcal{A} [/ilmath] is a smooth structure on [ilmath]M[/ilmath]

We may now talk about "smooth manifolds"

Notes

Specifying smooth atlases

Because of the huge number of charts that'd be in a smooth structure there's little point in even trying to explicitly define one, see:

Other names

  • Smooth manifold structure
  • Differentiable manifold structure
  • [ilmath]C^\infty[/ilmath] manifold structure

See also

References

  1. Introduction to smooth manifolds - John M Lee - Second Edition
  2. Ker60 in Introduction to smooth manifolds - John M Lee - Second Edition