题目👮🏿‍♂️：A Survey on Cheeger-Gromoll's Soul Theorem and the Most Recent Developments

报告人：胥世成 教授 （首都师范大学） 

地点：腾讯会议室

时间：2021年8月17日 9:30-10:30

摘要: It is a survey talk on the Cheeger and Gromoll's well-known Soul Theorem, which states that any noncompact complete manifold M with nonnegative sectional curvature contains a compact totally geodesic submanifold Σ in M, called the soul of M, whose normal bundle is diffeomorphic to M. As a consequence, all the topology of M is concentrated in Σ, therefore is of finite type. Cheeger and Gromoll also conjectured that if M is of strictly positive curvature at one point, then the soul is also a point (thus M is diffeomorphic to the Euclidean space). The solution of this Soul Conjecture is one of G. Perelman's famous works, where some essential geometric structures from M to the soul were established. The soul theorem provides a guideline in understanding of manifolds with various curvatures, e.g., why the unsolved Milnor conjecture is reasonalble for nonnegative Ricci curvature. Many works have been invoked by Cheeger-Gromoll and Perelman's work.

腾讯会议🧍🫴🏽：https://meeting.tencent.com/s/vjvTdiIhDfQv

会议 ID🔑：412 296 324

All are welcome!