Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, April 27, 2015 - 12:00 to 13:00

Location:

Gilk 115

Guest Speaker:

Zheting Dong

Institution:

Graduate Student

Abstract:

The soul theorem of Riemannian geometry largely reduced the study of non-compact complete Riemannian manifolds with non-negative curvature to the study of compact submanifolds. The soul theorem was published in 1972 by Cheeger and Gromoll, and in 1994 Perelman proved a significant conjecture based on the soul theorem. In this talk we will briefly outline the proof of the soul theorem, mainly focusing on the existence of the soul (a submanifold) and its properties. The proof is constructive, hence has great applicational value. We will end with the statement of the soul conjecture proved by Perelman.