Mathematical Sciences: Deformations of Complex Structures

数学科学：复杂结构的变形

• 批准号: 9003361
• 负责人: Irwin Kra
• 金额: $ 15.56万
• 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: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003361&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Deformations; Complex; Structures

Two investigators will study Kleinian groups and Teichmuller spaces. One will analyze deformation spaces and cohomology of Kleinian groups, moduli of Riemann surfaces and their explicit representations, automorphic forms, and projective structures. The second will continue his investigation into the structure of Kleinian groups and hyperbolic 3-orbifolds emphasizing the classification of geometrically finite groups and combination theorems. The two investigators will work toward solving several problems related to the study of Kleinian groups. An example of such a group would be a collection of motions of the plane which preserve a periodic tiling. As elements of a group these must satisfy several axioms including one which requires the existence of an inverse element associated with each element of the group. If one element translates the plane by two units to the "right," its inverse element would translate the plane two units to the "left." The study of such motions has led mathematicians to the solutions of problems involving crystal structures.

两名研究人员将研究Kleinian群和Teichmuller群 空间. 一个将分析变形空间和上同调 Kleinian群，Riemann曲面的模及其显式 表示、自守形式和投射结构。 第二个将继续他的调查结构， Kleinian群和双曲3-orbifold强调了 几何有限群的分类与组合 定理 两位调查人员将致力于解决几个 与Kleinian群研究有关的问题。 的示例 这样的一组运动是平面运动的集合， 保持周期性的平铺。 作为一个组的元素，这些必须 满足几个公理，包括一个要求存在 一个逆元素与每个元素的组。 如果一个元素将平面向右平移两个单位， 它的逆元素会将平面平移两个单位， “左边。“对这种运动的研究使数学家们 涉及晶体结构的问题的解决方案。