Mathematical Sciences: Deformations of Complex Structures

数学科学：复杂结构的变形

• 批准号: 8701774
• 负责人: Irwin Kra
• 金额: $ 25.95万
• 依托单位: SUNY at Stony Brook
• 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: 1987-06-01 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701774&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Deformations; Complex; Structures

Irwin Kra will continue his research on Kleinian groups and their deformations, the automorphic forms and Eichler cohomology associated with Kleinian groups, and the accessory parameters associated with Fuchsian and Kleinian uniformizations of Riemann surfaces. Bernard Maskit will also work on Kleinian groups. In particular he will study constructions of special classes of Kleinian groups, parameter spaces of deformations of Fuchsian and Kleinian groups, and fundametal domains for the Teichmuller modular group. Many of the problems to be considered by Kra involve the geometric significance of the spaces of cusp forms. This is related to the problem of choosing finite spanning sets of relative Poincare series. The calculations of fundamental domains for Teichmuller modular groups, to be carried out by Maskit, are related to problems in both geometry and dynamics.

Irwin Kra 将继续研究克莱因群及其变形、与克莱因群相关的自守形式和艾希勒上同调，以及与黎曼曲面的 Fuchsian 和 Kleinian 均匀化相关的辅助参数。伯纳德·马斯基特 (Bernard Maskit) 还将致力于克莱因群的研究。特别是，他将研究克莱因群特殊类的构造、Fuchsian 群和克莱因群变形的参数空间以及 Teichmuller 模群的基础域。 Kra 要考虑的许多问题都涉及尖点形式空间的几何意义。这与选择相对庞加莱级数的有限生成集的问题有关。由 Maskit 进行的 Teichmuller 模群基本域的计算涉及几何和动力学问题。