Mathematical Sciences: Some Problems in Geometric Topology

数学科学：几何拓扑中的一些问题

• 批准号: 9003746
• 负责人: Steven Ferry
• 金额: $ 12.45万
• 依托单位: SUNY at Binghamton
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003746&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Problems; Geometric

Ferry will study a number of topics in controlled topology and differential geometry. Most of these problems bear on the problem, "How much control is enough to force simple homotopy equivalence between polyhedra or homeomorphism between topological manifolds?" An interesting testing ground for controlled theories is on the borderline between topology and differential geometry, where there are problems which are obviously controlled in some way but for which there is no obvious control space. Ferry has already solved one such problem by, in some sense, letting the problem construct its own control space. He plans to explore further ramifications of these techniques.

费里将研究受控拓扑和微分几何中的许多主题。 这些问题大多数都涉及这样的问题：“多少控制足以迫使多面体之间的简单同伦等价或拓扑流形之间的同胚？” 受控理论的一个有趣的试验场位于拓扑学和微分几何之间的边界，其中存在明显以某种方式控制的问题，但没有明显的控制空间。 从某种意义上说，费里已经通过让问题构建自己的控制空间来解决这样一个问题。 他计划探索这些技术的进一步影响。