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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

8 votes

Manifolds with polynomial transition maps

Let me develop Robert Bryant's answer : if $M$ is a simply-connected manifold of dimension $n$ with a polynomial atlas, then there exists a local isomorphism $M \rightarrow \mathbb{R}^n$. Conversely, …
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