Mathematical Sciences: Geometrical Structures on Manifolds and Deformations of Discrete Groups

数学科学：流形的几何结构和离散群的变形

• 批准号: 8902619
• 负责人: William Goldman
• 金额: $ 12.93万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-15 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902619&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometrical; Structures; Manifolds; Mathematical; Sciences; Geometrical; Structures; Manifolds

William Goldman plans to continue his investigation into the deformation theory of discrete groups and geometric structures. This investigation is currently divided into five (closely related) topics: 1) the deformation theory of flat bundles over Kahler manifolds, and relations with symplectic geometry, 2) real projective structures on surfaces, 3) affinely flat manifolds, including flat Lorentz manifolds, 4) the deformation space of flat PSL(2,R)-bundles over surfaces, relations with (possibly singular) geometric structures, and 5) complex hyperbolic Kleinian groups. Goldman and his students have developed graphics software particularly suited to their problems to run on a SUN work- station, and more will be done along these lines also.

威廉·戈德曼（William Goldman）计划继续调查离散群体和几何结构的变形理论。 This investigation is currently divided into five (closely related) topics: 1) the deformation theory of flat bundles over Kahler manifolds, and relations with symplectic geometry, 2) real projective structures on surfaces, 3) affinely flat manifolds, including flat Lorentz manifolds, 4) the deformation space of flat PSL(2,R)-bundles over surfaces, relations with (possibly singular) geometric结构和5）复杂的双曲线kleinian组。 高盛（Goldman）和他的学生开发了特别适合在太阳工作站运行的问题，并且还将按照这些方式完成更多工作。