Mathematical Sciences: Transformation Groups and Low-Dimensional Topology

数学科学：变换群和低维拓扑

• 批准号: 8800391
• 负责人: Allan Edmonds
• 金额: $ 4.57万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8800391&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Transformation; Groups; Low

Symmetry plays an important role in geometry and topology and can best be treated in systematic fashion through introduction of the theory of groups. The existence and classification of finite groups of symmetries of manifolds of dimensions less than five will be studied, with particular emphasis on group actions on four-dimensional manifolds. Here breakthroughs by S. Donaldson and M. Freedman in recent years have produced powerful new methods that opened up a host of formerly inaccessible problems.

对称性在几何学和拓扑学中占有重要地位 最好的治疗方法是 介绍了群论。 的存在和 流形对称性有限群的分类 将研究小于5的维度，特别是 重点是四维流形上的群作用。 这里 突破S。唐纳森和M.弗里德曼近年来 产生了强大的新方法， 以前无法解决的问题。