Mathematical Sciences: Studies in Geometric Topology

数学科学：几何拓扑研究

• 批准号: 8902199
• 负责人: William Floyd
• 金额: $ 16.51万
• 依托单位: Virginia Polytechnic Institute and State University
• 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: 1989-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902199&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Geometric; Topology

Professor Floyd plans to work in geometric group theory and topology. In an attempt to make some progress on the geometric group theory of nonpositively curved manifolds, he plans to study graph amalgamation products of finite groups over finite graphs. This will be joint work with Walter Parry. He intends to continue his research on the growth functions of hyperbolic groups and make the computer a more effective tool for studying growth functions. His other research topic is a joint project with Edwin E. Floyd on constructing (and computing the homology of) classifying spaces of finite groups via their Euclidean actions. Professor Quinn plans to work in geometric topology, and related topics in algebra and geometry. Specifically he plans to complete the development of controlled versions of K- and L-theory. This is expected to yield information about assembly maps from homology groups to K- and L- groups. In turn this should allow further computations of K- and L- groups of infinite groups with torsion, especially discrete subgroups of Lie groups. It should also shed light on the topological structure of stratified spaces, like algebraic varieties and quotients of group actions. In short, Floyd and Quinn are investigating the fundamental structure of geometric objects known as manifolds (spheres, toruses, and other more highly connected objects) as well as their symmetry properties, which can be described algebraically by groups.

弗洛伊德教授计划从事几何群论的研究 和拓扑学。 为了取得一些进展， 非正曲流形的几何群论 研究有限群的图合并积的计划 在有限图上 这将是与沃尔特·帕里的合作。 他打算继续他的研究的增长功能， 双曲群，使计算机成为更有效的工具 来研究生长函数。 他的另一个研究课题是 与Edwin E.弗洛伊德关于构建（和 计算有限群的分类空间的同调 通过他们的欧几里得行为。 奎因教授计划在几何拓扑工作， 代数和几何的相关主题。 具体来说，他计划 完成受控版本的K-和 L理论 预计这将产生有关组件的信息 从同调群映射到K-和L-群。 这进而 应该允许进一步计算K-和L-群， 有挠的无限群，尤其是 李群。 它还应该阐明拓扑 分层空间的结构，如代数簇和 集体行动的后果。 简而言之，弗洛伊德和奎因正在调查 几何物体的基本结构称为流形 （球体、圆环体和其他高度连接的对象）作为 以及它们的对称性， 代数地分组。