Mathematical Sciences: Problems in Classical Knot Theory

数学科学：经典结理论中的问题

• 批准号: 9001801
• 负责人: Charles Livingston
• 金额: $ 4.2万
• 依托单位: Indiana University
• 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: 1990-07-15 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001801&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Classical; Knot

The principal investigator is currently addressing two areas of research. The first is the application of Casson-Gordon type invariants to problems in link concordance, and, in particular, to questions relating to boundary linking. A second area of research is the study of periodic knots and symmetries of manifolds. Both areas require the development of algebraic tools for describing knots and links and for distinguishing truly distinct knots and links from ones which are merely differently presented. Application of such tools to classify knots and links to within some natural equivalence is a major goal.

首席调查员目前正在处理两个研究领域。第一个是Casson-Gordon类型不变量在链接一致性问题中的应用，特别是关于边界链接的问题。第二个研究领域是研究流形的周期纽结和对称性。这两个领域都需要开发代数工具来描述节点和链接，并将真正不同的节点和链接与仅以不同方式表示的节点和链接区分开来。应用这样的工具将结和链接分类到某种自然等价性是一个主要目标。