2009/08/22 by Jianguo Cao, Jian Ge, Cao, Jianguo +1
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.0908.3229
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.