拓扑研讨班：Topological classification of manifolds with positive isotropic curvature

中国科学院数学与系统科学研究院

数学研究所

学术报告

拓扑研讨班

Speaker: 黄红 教授（北京师范大学）

Title: Topological classification of manifolds with positive isotropic curvature
Time&Venue: 2024年12月4日（星期三） 14:15-15:15 & 南楼N818

Abstract: In this talk I will discuss the topological classification of compact manifolds with positive isotropic curvature. This curvature condition was introduced by Micallef and Moore in 1988, and played an important role in the proof of the differentiable sphere theorem by Brendle and Schoen. First I’ll briefly survey some of the previous works by various authors on Riemannian manifolds with positive isotropic curvature. Then I’ll introduce my recent work on the topological classification of compact manifolds of dimension n ≥ 12 with positive isotropic curvature. The main tool is Ricci flow with surgery, which was used by Perelman to attack the Poincare conjecture and Thurston’s geometrization conjecture. Techniques from topology are also used extensively.