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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].

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Fixed points of the action of an algebraic group

Angelo's conjectural statement is proven in Fogarty, J.; Norman, P. "A fixed-point characterization of linearly reductive groups." MR0485896 (not enough reputation to post this as comment, sorry)
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