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.

费里计划研究几何拓扑几个领域的问题。 这些问题涉及构建包含给定开流形作为余维零子流形的闭流形、描述欧几里得空间的开子集、研究哪些开流形可以通过 Hurewicz 纤维变形到彼此，以及查找何时具有非循环同伦纤维的映射与具有非循环点逆的映射同伦。 了解三流形特别有价值，因为它们是研究有关我们的物理栖息地的许多问题的自然环境。