Mathematical Sciences: Classification Problems in Geometric Topology

主要研究者打算专注于分类 某些类型的可微流形或群作用 使用手术和稳定的方法相结合的歧管 同伦理论 特别是，他想研究 一类齐性空间的同构分类及 完整的交叉点，给出四个稳定的分类- 流形的谱不变量，并确定关系 球面对合和Mahowald根不变量之间的关系 这些分类问题都涉及提取几何 关于流形的代数信息，或者 集体行动的问题。

The principal investigator intends to focus on classifying certain kinds of differentiable manifolds or group actions on manifolds using a combination of methods from surgery and stable homotopy theory. In particular, he would like to study the diffeomorphism classification of certain homogeneous spaces and complete intersections, give a stable classification of four- manifolds by spectral invariants, and determine the relationship between spherical involutions and Mahowald root invariants. These classification questions all involve extracting geometric information from algebraic information about the manifolds or group actions in question.