Mathematical Sciences: Low-dimensional Manifolds and Knot Theory

数学科学：低维流形和结理论

• 批准号: 8701366
• 负责人: Cameron Gordon
• 金额: $ 13.59万
• 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: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701366&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Low; dimensional; Manifolds

Gordon will continue to investigate problems in the topology of low-dimensional manifolds, particularly those related to knot theory. Two topics which will receive attention are the Dehn surgery construction on knots and links, and Heegaard splittings. Both of these are relevant to many fundamental questions concerning the structure of 3-dimensional manifolds. In fact investigations of knots have begun to find applications in organic chemistry, in addition to their connections with other parts of mathematics, particularly representation theory of operator algebras.

戈登将继续研究低维流形的拓扑问题，特别是那些与纽结理论有关的问题。将受到关注的两个话题是关于结和环的Dehn手术结构，以及Heegaard分裂。这两个问题都与有关三维流形结构的许多基本问题有关。事实上，对纽结的研究已经开始在有机化学中找到应用，除了它们与数学的其他部分，特别是算子代数的表示理论的联系之外。