Mathematical Sciences: Transformation Groups on Manifolds and Varieties

数学科学：流形和簇上的变换群

• 批准号: 8703538
• 负责人: Ted Petrie
• 金额: $ 17.2万
• 依托单位: Rutgers University New Brunswick
• 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: 1987-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703538&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Transformation; Groups; Manifolds

This project deals with smooth actions of compact Lie groups on manifolds and algebraic actions of algebraic groups on affine varieties. Here are two of the many problems in the algebraic setting: Are conjugacy classes of algebraic actions of a finite (reductive) group on a non-singular variety V countable? In the case V is complex n-space, is this number finite? Among the aims of the project in the smooth setting: Give information on the equivariant surgery obstructions for an equivariant normal map in the non-free case (in favorable cases) in terms of fixed point data, and provide conditions which guarantee these obstructions vanish (i.e. give vanishing theorems). Group actions are ubiquitous in nature. Understanding them is akin to understanding dynamical systems.

该项目研究流形上紧李群的光滑作用和仿射簇上代数群的代数作用。 以下是代数环境中的众多问题中的两个：非奇异簇 V 上的有限（还原）群的代数作用的共轭类是否可数？ 如果 V 是复数 n 空间，这个数字是有限的吗？ 该项目在平滑设置中的目标之一是：以定点数据的形式给出非自由情况下（在有利情况下）等变法线图的等变手术障碍的信息，并提供保证这些障碍消失的条件（即给出消失定理）。 群体行动本质上是普遍存在的。 理解它们类似于理解动力系统。