Large Scale Geometry, Topology, and Rigidity in Geometric Group Theory

几何群论中的大尺度几何、拓扑和刚性

• 批准号: 9704640
• 负责人: Benson Farb
• 金额: $ 6.2万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-08-01 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704640&HistoricalAwards=false
• 关键词: Large; Scale; Geometry; Topology; Rigidity

9704640 Farb Farb's project is in the area of geometric group theory. A new geometric/topological approach to rigidity questions for lattices in semisimple Lie groups, generalizing Mostow rigidity, has been developed by several authors, including Farb. He plans to continue his work with L. Mosher in bringing these new ideas and themes to bear on understanding quasi-isometries of broader classes of groups arising in combinatorial group theory. He will also work on characterizing a broad class of finitely generated groups by certain dynamics they exhibit. Finally, Farb will study the geometry of deformation spaces of discrete subgroups of rank-one Lie groups over local fields. Geometric group theory is a mixture of geometry, topology, algebra, and algorithms. Farb's project in this area is an attempt to understand the relationship between the symmetries exhibited by a space and its geometric structure on very large scales. ***

小行星9704640 法布的项目是在该地区的几何群论。 一个新的几何/拓扑方法刚性问题的格在半单李群，推广Mostow刚性，已开发的几个作者，包括Farb。 他计划继续他的工作与L。莫舍在把这些新的想法和主题承担理解准等距的更广泛的类群体产生的组合群论。 他还将致力于通过他们表现出的某些动态来描述一大类由非线性生成的群体。 最后，Farb将研究局部域上秩一李群的离散子群的变形空间的几何。 几何群论是几何、拓扑、代数、 和算法 法布在这一领域的项目是一种尝试， 在非常大的尺度上，空间所表现出的对称性与其几何结构之间的关系。 ***