Mathematical Sciences: 4-Manifolds, Groups Actions, and Scalar Curvature

数学科学：4-流形、群作用和标量曲率

• 批准号: 8901583
• 负责人: Slawomir Kwasik
• 金额: $ 4.75万
• 依托单位: Tulane University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901583&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Manifolds; Groups; Actions

The main purpose of this research project is to study symmetries of manifolds, with particular attention paid to symmetries of 4-dimensional manifolds. The problems to be studied vary from general questions concerning the geometric structure of exotic space forms and 4-dimensional manifolds to many specific problems connected with the existence of symmetric and asymmetric manifolds. The broad spectrum of methods which will be employed in this research include the techniques of surgery and homotopy theory, transformation groups, differential geometry and gauge theory. Since manifolds are very natural geometric objects, including spheres and tori, for example, and since symmetry is a very natural geometric property, techniques for treating symmetry of manifolds are important to cultivate.

本研究项目的主要目的是研究流形的对称性，特别是四维流形的对称性。所要研究的问题从关于奇异空间形式和四维流形的几何结构的一般问题到与对称和非对称流形的存在有关的许多具体问题。在这项研究中将使用的广泛的方法包括手术和同伦理论，变换群，微分几何和规范理论的技术。由于流形是非常自然的几何对象，包括球体和环面，而且对称性是非常自然的几何属性，因此处理流形的对称性的技术是重要的培养。