Spaces of Embeddings

小行星9971293 设P和N是流形，其中P是紧的。 本文分析了E（P，N）= P到N的嵌入空间的同伦类型。 目标是建立嵌入空间的“多重析取”结果。 多重析取的应用包括： 1. E（P，N）的同伦群的有限生成 当N是欧几里得空间时， 2.边界主义的理论障碍，嵌入超越 亚稳范围，和 3.对高阶连接现象的研究。 流形是具有齐性性质的空间：它们局部“看起来像”欧几里德空间。 流形是数学研究的基本对象。 研究它们的一种方法是试图确定一个流形何时“坐在”另一个流形中。 这就产生了“嵌入”的概念。具体地说，流形P在流形N中的嵌入是一个从P到N的函数，使得P中没有两个点通过该函数映射到N中的同一点。 从P到N的所有嵌入的集合形成一个拓扑空间E（P，N），称为"嵌入空间“.这个项目的目标是通过引入代数拓扑领域的技术来更好地理解空间E（P，N）。

9971293Klein Let P and N be manifolds, where P is compact. This project analysesthe homotopy type of E(P,N) = the space of embeddings from P to N. Theaim will be to establish ``multiple disjunction'' results for spaces ofembeddings. Applications of multiple disjunction are to include: 1. the finite generation of the homotopy groups of E(P,N) in positive degrees when N is euclidean space, 2. bordism theoretic obstructions to embedding beyond the metastable range, and 3. the study of higher order linking phenomena. Manifolds are spaces having a homogeneity property: they locally``look like'' euclidean space. Manifolds are fundamental objects ofmathematical research. One approach to studying them is to try to decidewhen one manifold ``sits inside'' another one. This gives rise to thenotion of ``embedding.'' Specifically, an embedding of a manifold P ina manifold N is a function from P to N such that no two points of P aremapped via the function to the same point of N. The set of all embeddingsfrom P to N forms a topological space E(P,N), called the ``embeddingspace.'' The goal of this project is to understand better the spaceE(P,N) by importing techniques from the field of algebraic topology.***