Mathematical Sciences: K-Theory of Group Rings, a Conjectureof Hambleton-Taylor-Williams, and Isospectral Deformations of Nilmanifolds

数学科学：群环的 K 理论、Hambleton-Taylor-Williams 的猜想以及 Nilmanifolds 的等谱变形

• 批准号: 9000271
• 负责人: David Webb
• 金额: $ 3.24万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9000271&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; Group; Rings

This project is concerned with problems in algebraic K- theory and geometric analysis. The principal investigator will study the G-theory of group rings of finite groups. He will study a conjecture of Hambleton, Taylor and Williams for which he has already established several special cases. He will also work on determining to what extent the geometry of a Riemannian manifold is determined by the spectrum of the Laplace operator. This research is concerned with algebraic K-theory. In a broad sense algebraic K-theory concerns the evolution of concepts from linear algebra such as basis and vector space. This work has implications for algebraic geometry and geometric analysis, and promises to make interesting connections between a number of different areas of mathematics.

这个项目涉及代数K- 理论和几何分析。主要研究者将 研究有限群的群环的G-理论。他将研究 汉布尔顿、泰勒和威廉姆斯的猜想， 目前已经有几个特殊案例。他还将致力于 确定黎曼流形的几何 由拉普拉斯算子的谱决定。 本研究涉及代数K理论。中 广义代数K-理论关注概念的演化 从线性代数，如基础和向量空间。这项工作 代数几何和几何分析的影响， 希望能在一些 不同的数学领域。