Geometrization of 3-dimensional orbifolds

Details Geometrization of 3-dimensional orbifolds Geometrization of 3-dimensional orbifolds

2000-10-18

arxiv.org/abs/math/0010184v3

Mathematics

Geometric Topology

Revised version (one single paper instead of the previous 2)

Scientific paper

The purpose of this article is to give a proof of the Orbifold Theorem
announced by Thurston in late 1981: If $O$ is a compact, connected, orientable,
irreducible and topologically atoroidal 3-orbifold with non-empty ramification
locus, then $O$ is geometric. As a corollary, any smooth orientation preserving
non-free finite group action on $S^3$ is conjugate to an orthogonal action.

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