Mathematical Sciences: Cohomology, Automorphic Forms of Kleinian Groups and Projective Structures

数学科学：上同调、克莱因群的自守形式和射影结构

• 批准号: 8918944
• 负责人: Dipendra Sengupta
• 金额: $ 2.45万
• 依托单位: Elizabeth City State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-03-01 至 1993-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8918944&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cohomology; Automorphic; Forms

The two investigators will study Kleinian groups on 3- manifolds and their related cohomology. Maskit's cohomological classification of geometrically finite Kleinian groups will be further studied. Sullivan and Marden's theory of stable Kleinian groups will be analyzed using Gardiner and Kra's cohomological conditions. The investigators will also institute a year honors course for two students to prepare them for graduate study of Kleinian groups. Motions of three-dimensional hypersurfaces which permute a finite number of subdomains will be investigated. Geometers and topologists have shown intense interest in these "Kleinian groups" since Thurston classified such hypersurfaces using hyperbolic geometry. In addition, the two investigators will institute a one year honors course for two students. The goal of this course will be to prepare these students for graduate study in mathematics. Kleinian groups will be used as a rich source of examples for their study.

两位研究人员将在3- 流形及其相关的上同调。 Maskit上同调 几何有限Kleinian群的分类将是 进一步研究。 Sullivan和马尔登的稳定克莱因理论 将使用加德纳和Kra的上同调 条件 调查人员还将设立一年荣誉 两名学生的课程，为他们的研究生学习做准备 克莱因群 置换a的三维超曲面的运动 将研究有限数目的子域。 几何和 拓扑学家们对这些"克莱因" 群"，因为Thurston使用 双曲几何 此外，两名调查人员还将 为两名学生开设为期一年的荣誉课程。 的目标 本课程将为这些学生的研究生学习做准备 在数学上。 克莱因团体将被用作丰富的 为他们的学习提供例子。