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.



Three dimensional spherical space form
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](https://arxiv.org/abs/0809.4040) talk about this.


