Consider $G$ lie group and $M$ riemannian manifold, what does it mean to say that that the points in M/G corresponding to the orbit G(p) and G(q) are in the same path component of M/G?
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1Are you asking for a clarification of path components, or looking for some results that follow from this assumption? – bliipbluup Dec 01 '20 at 16:10
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I am actually trying to understand the final part of the Principal Orbit Theorem, in the part that $M_{pric} / G$ is connected in $M / G$ – Toy Dec 01 '20 at 17:12
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$M_{pric}$ is the set of principal points, – Toy Dec 01 '20 at 17:13