Mathematical Sciences: Homotopy Theory and Its Applications

数学科学：同伦理论及其应用

• 批准号: 8901307
• 负责人: Stephen Mitchell
• 金额: $ 3.7万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901307&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Homotopy; Theory; Its

Professor Mitchell plans to investigate the implications for algebraic K-theory of recent developments in homotopy theory. In particular, he plans to study aspects of algebraic K-theory connected with the Lichtenbaum-Quillen conjectures from the point of view of higher periodicity in homotopy theory, using the spectacular work of Devinatz, Hopkins and Smith; the point being that by work of Thomason there shouldn't be any higher periodicity in algebraic K-theory. In a related project he plans to study periodic self-maps of finite complexes, the problem of realizing subalgebras of the Steenrod algebra geometrically, and stable splittings obtained from the modular representation theory of symmetric groups. These investigations will help to integrate two of the major algebraic machines for investigating geometric spaces, namely homotopy theory, which has been advancing particularly rapidly in recent years, and algebraic K-theory, also the scene of intense current exploration.

米切尔教授计划研究 同伦理论的最新发展的代数K理论。 在 特别是，他计划研究代数K理论的各个方面， 与Lichtenbaum-Quillen的关系， 在同伦理论中的更高的周期性的观点，使用 德维纳茨、霍普金斯和史密斯的杰作;关键在于 根据托马森的工作，不应该再高了 代数K理论中的周期性 在他计划的一个相关项目中 为了研究有限复形的周期自映射， 几何上实现Steenrod代数的子代数，以及 由模表示理论得到的稳定分裂 对称群。 这些调查将有助于整合 研究几何的两种主要代数机器 空间，即同伦理论，它一直在推进 近年来尤其迅速，而代数K理论， 也是一个紧张的探险现场。