Mathematical Sciences: Some Problems in Geometric Topology

数学科学：几何拓扑中的一些问题

• 批准号: 8702991
• 负责人: Steven Ferry
• 金额: $ 5.57万
• 依托单位: University of Kentucky
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702991&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Problems; Geometric

Ferry plans to study problems in several areas of geometric topology. The problems are concerned with constructing closed manifolds containing a given open manifold as a codimension-zero submanifold, characterizing open subsets of Euclidean space, studying which open manifolds may be deformed into each other via Hurewicz fibrations, and finding when a map with acyclic homotopy fiber is homotopic to a map with acyclic point-inverses. Understanding 3-manifolds is particularly valuable, since they are the natural setting for studying many questions about our physical habitat.

费里计划研究几何学的几个领域的问题， topology. 这些问题与构建封闭的 包含给定开流形作为余维零的流形 子流形，表征欧几里得空间的开子集， 研究哪些开流形可以通过 Hurewicz纤维化及无圈同伦映射的判定 纤维是同伦的一个地图与非循环点逆。 理解三维流形特别有价值，因为 它们是研究许多问题的自然背景， 我们的物理栖息地