Mathematical Sciences: Topology and Its Connections to Geometry and Modular Representation Theory

数学科学：拓扑及其与几何和模表示理论的联系

• 批准号: 9101415
• 负责人: Mark Mahowald
• 金额: $ 42.55万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101415&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topology; Its; Connections

This project deals with homotopy theory and its applications to several related areas. Friedlander works on the homotopy type of certain algebraic varieties, and also studies the representation theory of mod-p Lie algebras and the cohomology of groups of Lie type. Additionally, he plans to continue his study of algebraic K-theory. Mahowald works on intrinsic questions in stable and unstable homotopy theory. His main emphasis is on periodic structures in the homotopy groups of spheres. Priddy studies relations between modular representation theory and the stable homotopy type of finite and infinite groups. The cohomology of groups and stable splittings of classifying spaces are central to his work. In short, all three investigators are working with highly sophisticated algebraic tools for studying geometric structures. On the one hand, they improve our understanding of the tools. On the other hand, they apply the tools to answer geometric questions about spaces.

这个项目涉及同伦理论及其应用 几个相关领域。 弗里德兰德研究同伦类型 某些代数簇，并研究了表示 模p李代数理论与李群的上同调 类型. 此外，他计划继续他的研究代数 K理论 Mahowald致力于解决稳定和 不稳定同伦理论 他的主要重点是定期 球面同伦群中的结构。 普里迪研究 模表示理论与稳定 有限群和无限群的同伦类型。 的上同调 分类空间的群和稳定分裂是 他的作品 简而言之，所有三名调查人员都在高度合作， 用于研究几何结构的复杂代数工具。 一方面，它们提高了我们对工具的理解。 对 另一方面，他们应用这些工具来回答几何问题 关于空间。