## A simple proof of Perelman's collapsing theorem for 3-manifolds

**Speaker(s): ** Prof. Jianguo Cao( Notre Dame University)

**Time: ** 00:00-00:00 June 7, 2010

**Venue: ** 北京大学资源大厦1328教室

报告题目：A simple proof of Perelman's collapsing theorem for 3-manifolds

报告人： Prof. Jianguo Cao( Notre Dame University)

报告时间：6月7日（周一） 下午 15：30－16：30

报告地点：北京大学资源大厦1328教室

摘要:In this lecture, we will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. A version of Perelman's collapsing theorem states: ``A sufficiently collapsing 3-manifold with curvature bounded below is a graph-manifold". This result can be viewed as an extension of the implicit function theorem. Among other things, we use Perelman's critical point theory of Alexandrov spaces to construct the desired local Seifert fibration structure on sufficiently 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. A version of Geometrization Conjecture asserts that any closed 3-manifold admits a piecewise locally homogeneous metric.

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PS： 茶点时间为：15:00-15:30