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.

流形是拓扑学的主要研究对象。 他们 是局部同胚于欧几里得的空间 空间. 通常流形E配备有映射p：E--B到 另一个流形是局部的乘积投影。 这样的 映射称为束投影。 E的受控拓扑 是研究拓扑学中的某些经典主题， 流形，在其上放置限制以反映丛 E.这些限制通常采取以下形式： 在B中测量的公制控制。 该项目涉及 受控同伦等价、受控单 同伦理论和受控伪同位素。 这些 技术调查是重要的，因为流形是 在拓扑学、几何学、分析学甚至数学中无处不在 物理学