Finite Groups and Periodic Theories in Stable Homotopy

稳定同伦中的有限群和周期理论

• 批准号: 8701089
• 负责人: Nicholas Kuhn
• 金额: $ 2.55万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1988-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701089&HistoricalAwards=false
• 关键词: Finite; Groups; Periodic; Theories; Stable

The study of complex cobordism and related cohomology theories is a long standing and well respected area of algebraic topology. Another area has been that of (finite) group theoretic constructions, becoming, in its most modern form, equivariant stable homotopy theory. Results in recent years, most spectacularly the proofs of Segal's Burnside ring conjecture and Ravenel's nilpotence conjecture, have dramatically begun to bring to fruition these two branches of stable homotopy theory. Historically, these branches have been basically independent of each other. An exception is Atiyah's theorem relating K*(BG) (a bordism type of object) to the complex representation ring of G. There are now indications of much more widespread interrelations. This is the subject of Kuhn's recent and current research. It is hard to say where the study of such intricate algebraic patterns will lead, but the history of mathematics strongly suggests that mastering them will have repercussions elsewhere, either in use of the patterns themselves or of the techniques developed for treating them.

复配边与相关上同调的研究 理论是一个长期存在和备受尊敬的领域代数 topology. 另一个领域是（有限）群论 结构，成为，在其最现代的形式，等变 稳定同伦理论 近年来，大多数 特别是Segal的伯恩赛德环猜想的证明和 拉文埃尔的零猜想，已经戏剧性地开始 稳定同伦理论的这两个分支 从历史上看，这些分支机构基本上是独立的 彼此的关系。 一个例外是关于K *（BG）的Atiyah定理 （一种边界类型的对象）到的复表示环 G. 现在有迹象表明， 相互关系 这是库恩最近和当前的主题， research. 很难说这种复杂的研究 代数模式将引领潮流，但数学史 强烈表明掌握它们会产生影响 在其他地方，无论是在使用模式本身或 为治疗它们而开发的技术。