Mathematical Sciences: Classification Problems in Geometric Topology

本文旨在结合几何方法和稳定同伦理论对某些类型的流形进行分类。特别地，他给出了正标量曲率度量存在的充要条件，并给出了Dupin超曲面和完全交的微分同态分类。具有良好几何性质的流形的分类和希腊人一样古老。这里考虑的房产更现代，但基本理念大同小异。

The investigator intends to focus on classifying certain kinds of manifolds using a combination of geometric methods and stable homotopy theory. In particular, he would like to find necessary and sufficient conditions for the existence of positive scalar curvature metrics, and give a diffeomorphism classification of Dupin hypersurfaces and complete intersections. Classification of manifolds with nice geometric properties is as old as the Greeks. Here the properties under consideration are more modern, but the basic idea is much the same.