Perelman's collapsing theorem for 3manifolds
Abstract
We will simplify the earlier proofs of Perelman's collapsing theorem of 3manifolds given by ShioyaYamaguchi and MorganTian. Among other things, we use Perelman's semiconvex analysis of distance functions to construct the desired local Seifert fibration structure on collapsed 3manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3manifolds. Our proof of Perelman's collapsing theorem is almost selfcontained. We believe that our proof of this collapsing theorem is accessible to nonexperts and advanced graduate students.
 Publication:

arXiv eprints
 Pub Date:
 August 2009
 arXiv:
 arXiv:0908.3229
 Bibcode:
 2009arXiv0908.3229C
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Geometric Topology;
 53C23;
 53C20
 EPrint:
 v1: 5 pictures v2: 2 pictures added v3: 9 pictures total v4: added one more graph, This final version was refereed and accepted for publication in "The Journal of Geometric Analysis"