Mathematical Sciences: Research in Topology

数学科学：拓扑研究

• 批准号: 8901213
• 负责人: Sylvain Cappell
• 金额: $ 18.01万
• 依托单位: New York 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=8901213&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Topology

8901213 Cappell This project includes research problems in a variety of areas of geometrical topology. These include singular spaces and their characteristic classes, transformation groups and H-spaces, some questions in low-dimensional topology and nonlinear similarity. Among the specific problems are questions related to the role of K-homology characteristic classes on singular spaces and methods of computing them; characteristic classes on singular algebraic varieties and methods of computing them; Alexander polynomials of nonisolated singularities; replacement of fixed points of group actions; de Rham's problem on similarity of matrices. These topics concern the possible reduction to a certain amount of computation of questions about knottedness, connectedness, and so forth. The ultimate subject matter of topology is the latter, but systematic treatment requires the introduction of algebraic concepts such as groups and rings and of techniques for computing with them.

8901213卡佩尔这个项目包括几何拓扑学各个领域的研究问题。这些问题包括奇异空间及其特征类、变换群和H-空间、低维拓扑和非线性相似中的一些问题。这些具体问题包括：奇异空间上K-同调特征类的作用及其计算方法；奇异代数簇上的特征类及其计算方法；非孤立奇点的Alexander多项式；群作用的不动点的替换；关于矩阵相似性的De Rham问题。这些主题涉及到关于结点、连通性等问题的可能减少到一定计算量的问题。拓扑学的最终主题是后者，但系统的处理需要引入代数概念，如群和环，以及用它们进行计算的技术。