Mathematical Sciences: Controlled Topology of Manifolds

数学科学：流形的受控拓扑

• 批准号: 8701314
• 负责人: C. Bruce Hughes
• 金额: $ 3.13万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701314&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Controlled; Topology; Manifolds

Manifolds are the main object of study in topology. They are the spaces which are locally homeomorphic to euclidean spaces. Often a manifold E comes equipped with a map p:E--B onto another manifold which is locally a product projection. Such a map is called a bundle projection. The controlled topology of E is the study of certain classical topics in the topology of manifolds on which restrictions are placed reflecting the bundle structure on E. These restrictions usually take the form of metric control measured in B. This project is concerned with the study of controlled homotopy equivalences, controlled simple homotopy theory, and controlled pseudo-isotopies. These technical investigations are important because manifolds are ubiquitous in topology, geometry, analysis, even mathematical physics.

歧管是拓扑研究的主要对象。 它们是对欧几里得空间本地同构的空间。 通常，歧管E配备了映射p：e-b到另一个是局部产品投影的歧管上。 这样的地图称为捆绑投影。 E的受控拓扑结论是对歧管拓扑中某些经典主题的研究，在其上放置了反映E的限制。这些限制通常采用B中测量的度量控制的形式。该项目与受控同型等额的研究有关，对受控的同型等值，受控的简单同型理论和受控的Pseudo pseudo-Esopopies。 这些技术研究很重要，因为流形在拓扑，几何，分析甚至数学物理学中无处不在。