Definition

Smooth Manifold

Lie Groups and Lie Algebras · lie-groups.tex

A topological $n$-manifold $M$ (Definition~Topological Manifold) is a smooth manifold if it is equipped with a maximal smooth atlas: a collection of charts $(U_\alpha, \varphi_\alpha)$ covering $M$ such that all transition maps $\varphi_\beta \circ \varphi_\alpha^{-1}$ are smooth.

Depends on

Topological Manifold

Used in

Tangent Space
Smooth Map and Diffeomorphism
Lie Group

Dependency Graph

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