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arXiv · 0908.3229

Perelman's collapsing theorem for 3-manifolds

Jianguo Cao·Jian Ge
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Abstract

We will simplify the earlier proofs of Perelman's collapsing theorem of 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's semi-convex analysis of distance functions to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theorem is almost self-contained. We believe that our proof of this collapsing theorem is accessible to non-experts and advanced graduate students.

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Jianguo Cao, Jian Ge. 2010-05-18. Perelman's collapsing theorem for 3-manifolds. https://arxiv.org/abs/0908.3229

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