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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
5 answers
2k views

Examples of manifolds with effective circle actions?

I would like to know examples of smooth compact connected manifolds, on which there exists an effective smooth circle action preserving a positive smooth volume, besides the simple example: $[0,1]^d \ …
Mostafa's user avatar
  • 403
3 votes
1 answer
1k views

Is it possible to define a structure of differentiable manifold on the Hilbert cube $[0,1]^\...

Is it possible to define a structure of differentiable (smooth) manifold on the Hilbert cube $[0,1]^\mathbb{N}$ ? Has it been done in the literature? In textbooks, only the Banach case is treated, …
Mostafa's user avatar
  • 403