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Graduate Student Geometry-Topology Seminar

Wednesday, October 17, 2007 - 12:00pm

Chenxu He

University of Pennsylvania

Location

University of Pennsylvania

3C6 DRL

Recently S. Brendle and R. Schoen first proved the differential sphere theorem which states that a compact simply-connected Riemannian manifold with 1/4-pinched sectional curvature is diffeomorphic to the sphere. Independently L. Ni and J. Wolfson gave a different and shorter proof using the complex sectional curvature instead of the isotropic curvature. Both proofs use the method developed by C. Boehm and B. Wilking. Moreover, Ni and Wolfson proved the more general case. In this talk, we will present Ni and Wolfson's proof on the case of the 1/4-pinched curvature.