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Dear all, this is perhaps a bit a vague question, but some references would already be very helpfull. So let $G$ be a finitely generated group and choose some finite set of generators. This allows to ...

Let $M$ be a (Hausdorff) smooth compact manifold and $G$ a Lie group acting smoothly on $M$. If $G$ is compact then, by Mostow-Palais theorem, there exists an equivariant smooth embedding $M\to {\...