Mathematical Sciences: Studies in Geometric Topology

弗洛伊德教授计划从事几何群论和拓扑学方面的工作。为了在非正曲流形的几何群论方面取得一些进展，他计划研究有限图上有限群的图融合积。这将是与沃尔特·帕里的联合工作。他打算继续他对双曲群增长函数的研究，使计算机成为研究增长函数的更有效的工具。他的另一个研究课题是与Edwin E.Floyd的一个联合项目，该项目是通过有限群的欧几里得作用来构造(并计算)有限群的分类空间的同调。奎因教授计划研究几何拓扑学，以及代数和几何的相关课题。具体地说，他计划完成K理论和L理论的受控版本的开发。这有望得到关于从同源基团到K-和L-基团的组装图的信息。反过来，这应该允许进一步计算无限挠群的K-群和L-群，特别是李群的离散子群。它还应该阐明分层空间的拓扑结构，如群行动的代数簇和商。简而言之，Floyd和Quinn正在研究被称为流形的几何对象(球体、环面和其他更高连接的对象)的基本结构以及它们的对称性质，这些性质可以用群来代数描述。

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.