Mathematical Sciences: Connections Between Geometry, Topology, and K-Theory

数学科学：几何、拓扑和 K 理论之间的联系

• 批准号: 8800657
• 负责人: Mark Mahowald
• 金额: $ 38.21万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8800657&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Connections; Between; Geometry

This research project is concerned with homotopy theory and how it impinges on several related areas. Friedlander works on the interface of algebraic geometry and algebraic topology. His investigations involve algebraic groups, algebraic geometry and algebraic k-theory. The common theme is the exploitation of relationships between algebraic geometry and homotopy theory. Priddy's current interest is in the emerging area of homotopy theory which uses modular representation theory and invariant theory. Stable splittings of spaces are an important example of such applications. Mahowald's work is primarily in stable homotopy theory and also in the unstable homotopy of spheres.

本研究项目涉及同伦理论及其对几个相关领域的影响。弗里德兰德致力于代数几何和代数拓扑的结合。他的研究涉及代数群、代数几何和代数k理论。共同的主题是利用代数几何和同伦理论之间的关系。Priddy目前的兴趣是在新兴的同伦理论领域，它使用模表示理论和不变理论。稳定的空间分割是这类应用的一个重要例子。Mahowald的工作主要集中在稳定同伦理论和球的不稳定同伦上。