Embeddings and Group Actions

DMS-0201695约翰·R·克莱恩这份提案包含两个项目。第一个是研究与一个流形在另一个流形上的光滑嵌入空间相关的各种同伦理论问题。这些问题包括嵌入的障碍理论、链接现象、压缩问题和分裂问题。第二个程序是研究具有有限群的驯服作用的拓扑流形的等变结构集的一种新方法。新的内容是利用Poincare嵌入来分析等变结构和等变结构之间的差异。流形是一个局部欧几里得的拓扑空间。拓扑学中的一个基本问题是枚举一个流形到另一个流形的嵌入。所有这些嵌入的集合形成了一个拓扑空间。这个建议的第一部分是研究嵌入空间的各种拓扑方面。第二部分是关于具有有限对称群的流形的分类。

DMS-0201695John R. KleinThis proposal contains two programs. The first is to study a variety of homotopy theoretic problems associated with space of smooth embeddings of one manifold in another. Among these problems are obstruction theory for embeddings, linking phenomena, compression problems and splitting questions. The second program is a new approach to the study of the equivariant structure sets of topological manifolds equipped with a tame action of a finite group. The new ingredient is to use Poincare embeddings to analyse the difference between the equivariant structures and the isovariant ones.A manifold is a topological space which is locally euclidean. A fundamental problem in topology is to enumerate the embeddings one manifold into another one. The set of all such embeddings forms a topological space. The first part of this proposal is to study various topological aspects of the space of embeddings. The second part concerns the classification of manifolds equipped with a finite group of symmetries.