I'm looking for some reference for the following statement I noticed on wiki:
It says that the slice theorem can be used to prove that the orbit space is a manifold when the group is compact and action is free. Where I can find a proof of this?
Also, is it necessary that the group is compact? Don't we also need to require the action to be proper (for quotient space to be Haursdorff)? Is the group or the manifold necessarily finite dimensional to make the quotient a manifold? What is the general statement of this one?
Any comment is appreciated.