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How can we deduce the three dimensional spherical space form conjecture from the Poincare conjecture? More precisely, how can we deduce using the Poincare conjecture that every free action of a finite group on $\mathbb{S}^3$ is equivalent to an orthogonal group action. If the proof is involved, then kindly suggest some readable reference for a beginner.

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You can't deduce this from the Poincare conjecture, but it follows from the geometrization conjecture/theorems for manifolds and orbifolds. I assume (though I haven't checked) Morgan-Tian talk about this.

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  • $\begingroup$ Many thanks. Though I have accepted your answer as final, I would appreciate if someone suggests some short article regarding my question as I am not an expert in this area. $\endgroup$
    – kelly
    Commented Jan 21, 2012 at 5:05

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