This paper is devoted to the proof of the orbifold theorem: If O is a compact connected orientable irreducible and topologically atoroidal 3-orbifold with nonempty ramification locus, then O is geometric (i.e. has a metric of constant curvature or is Seifert fibred).As a corollary, any smooth orientationpreserving nonfree finite group action on S 3 is conjugate to an orthogonal action.
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Boileau et al. (2005) studied this question.
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