Seminar | Institute of Mathematical Sciences
Time：14:00-15:00, June 5, Wednsday
Location：Room S407, IMS
Speaker: Huihong Jiang, Shanghai Jiaotong University
Abstract: A manifold is said to be of finite topological type if it is homeomorphic to the interior of a compact manifold with boundary; otherwise, infinite topological type. Jiping Sha and Zhongmin Shen has asked if a complete Riemannian manifold with nonnegative Ricci curvature and quadratically asymptotically nonnegative sectional curvature is of finite topological type or not. Actually it is true provided with certain control over the volume growth or diameter growth. Recently, we have constructed some examples with nonnegative Ricci curvature, quadratically asymptotically nonnegative curvature and infinite topological type in dimension bigger than or equal to 5. Thus the answer to Sha and Shen's question is exactly NO in high dimension. In this talk, I will explain the construction of these examples. This a joint work with Yi-Hu Yang.