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.
Graduate Student Geometry-Topology Seminar
Wednesday, October 17, 2007 - 12:00pm
Chenxu He
University of Pennsylvania