Mathematical Sciences: Some Problems in Geometric Topology

数学科学：几何拓扑中的一些问题

• 批准号: 8911718
• 负责人: Steven Ferry
• 金额: $ 4.52万
• 依托单位: SUNY at Binghamton
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8911718&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Problems; Geometric

The principal investigator will work on several problems in manifold theory. He plans to continue his work on topological rigidity with S. Weinberger (University of Chicago) and his work with his colleague Erik Peterson on controlled surgery. He is also interested in characterizing open subsets of Euclidean space topologically. In a thesis under his direction, Ms. T. Engel will study families of deformations in a situation where topological rigidity does not hold. These problems come down to probing the fundamental structure of the space in which we live and that of other abstractions of the physical world. How do these abstractions differ, and what is common to them all? To what extent do their basic properties follow from a few underlying assumptions without the possibility of any variation?

首席研究员将研究流形理论中的几个问题。 他计划继续与 S. Weinberger（芝加哥大学）一起研究拓扑刚性，并与同事 Erik Peterson 一起研究控制手术。 他还对描述欧几里得空间的开子集的拓扑特征感兴趣。 在他指导下的一篇论文中，T. Engel 女士将研究拓扑刚性不成立的情况下的变形族。 这些问题归根结底都是为了探索我们所生活的空间的基本结构以及物理世界的其他抽象概念的基本结构。 这些抽象有何不同，它们有何共同点？ 它们的基本属性在多大程度上遵循一些基本假设而没有任何变化的可能性？