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Klein群及其变形，与Klein群相关的自同构形和Eichler上同调，以及与Riemann曲面的Fuchsian和Kleian一致化有关的附属参数。伯纳德·马斯基特还将在克莱恩集团工作。特别地，他将研究Kleian群的特殊类的构造，Fuchsian群和Klein群的变形的参数空间，以及Teichmuller模群的基本域。Kra要考虑的许多问题都涉及尖点形式空间的几何意义。这涉及到选择相对庞加莱级数的有限支撑集的问题。由Maskit进行的TeichMuller模群基本域的计算涉及到几何和动力学问题。