The classical sphere theorem states that any compact simply connected manifold with sectional curvature between 1 and 4 is homeomorphic to a sphere. Brendle and Schoen recently solved the long standing open conjecture that it is actually diffeomorphic to a sphere. I will discuss this result and various related sphere theorem. The method uses the Ricci flow and is based on recent work by Boehm and Wilking.
Geometry-Topology Reading Seminar
Tuesday, October 9, 2007 - 10:30am
Wolfgang Ziller
University of Pennsylvania