Mathematical Sciences: Presidential Young Investigator Award

数学科学：总统青年研究员奖

• 批准号: 9158090
• 负责人: John Luecke
• 金额: $ 27.5万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1999-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9158090&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Presidential; Young; Investigator

This Presidential Young Investigator Award will enhance support for John E. Luecke's research in Dehn Surgery on Links, a topic in the topology of three-dimensional manifolds. A link in a 3-dimensional manifold, M, is a collection of circles embedded in M. A knot is a link of one component. The work this year will have two aspects: (1) understanding when a non-hyperbolic manifold results from Dehn surgery on a knot with hyperbolic complement, (2) generalizing results about Dehn surgery on knots to results about Dehn surgery on links with more than one component. Manifolds are natural objects of study, being spaces which are locally but in general not globally like Euclidean space. The case of three dimensions is the lowest dimension for which the closed manifolds have not been fully classified. Knots and links are also natural objects, about which it is surprising how basic are some of the questions still unanswered.

这一总统青年调查员奖将提高 支持John E。Luecke在Dehn Surgery on Links的研究， 三维流形拓扑学的主题。 中的链接 一个三维流形，M，是一个嵌入的圆的集合， in M. 结是一个组件的连接。 今年的工作 将有两个方面：（1）理解当一个非双曲 双曲结Dehn手术的多种结果 补充，（2）推广Dehn手术结的结果 关于Dehn手术的结果与不止一个 成分 流形是自然的研究对象，是空间， 是局部的，但一般不像欧几里得空间那样是全局的。 三维的情况是最低维， 闭流形还没有完全分类。 结和 链接也是自然对象，令人惊讶的是， 一些基本的问题仍然没有答案。