Some Problems in Geometric Topology

几何拓扑中的一些问题

• 批准号: 9971296
• 负责人: Steven Ferry
• 金额: $ 8.38万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-06-01 至 2003-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971296&HistoricalAwards=false
• 关键词: Some; Problems; Geometric; Topology

Proposal: DMS-9971296PI: Steve FerryAbstract: Our main effort will go into using the methods of controlled surgery theory to study of the geometric properties of the exotic homology manifolds discovered by Bryant, Mio, Weinberger, and the author. The most pressing questions in this area concern the existence of exotic homology manifolds which are homogeneous and the existence of exotic homology manifolds which have contractible universal covers. Construction of an exotic homogeneous homology manifold would give a counterexample to the well-known Bing-Borsuk conjecture, while an exotic aspherical homology manifold would give a counterexample to either the integral Novikov conjecture or the well-known conjecture that every Poincare duality group is the fundamental group of some aspherical manifold.We also plan to use methods from controlled topology to study the Gromov-Lawson conjecture and to study the classification of high-dimensional wild topological embeddings in codimension two.

提案：DMS-9971296PI：Steve Ferry 摘要：我们的主要工作将是使用控制手术理论的方法来研究 Bryant、Mio、Weinberger 和作者发现的奇异同调流形的几何性质。该领域最紧迫的问题涉及同质的奇异同调流形的存在性以及具有可收缩的通用覆盖的奇异同调流形的存在性。构造一个奇异的齐次同调流形将为著名的 Bing-Borsuk 猜想提供反例，而一个奇异的非球面同调流形将为积分诺维科夫猜想或众所周知的猜想（每个庞加莱对偶群是一些非球面流形的基本群。我们还计划使用受控拓扑的方法来研究格罗莫夫-劳森猜想和研究高维野拓扑嵌入的分类在余维二中。