Homotopy Theory and Its Applications

同伦理论及其应用

• 批准号: 9802852
• 负责人: Stephen Mitchell
• 金额: $ 22.11万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9802852&HistoricalAwards=false
• 关键词: Homotopy; Theory; Its; Applications

9802852 Mitchell This project addresses problems in three distinct but closely related areas of homotopy theory: (1) homotopy fixed point spectra arising from the action of closed subgroups of the Morava stabilizer group on the Landweber exact spectrum whose coefficient ring is the functions on the Lubin-Tate moduli space of lifts (Devinatz); (2) multiplicative stable homotopy theory, the homotopy theory of operads, Andre-Quillen homology of algebras over simplicial operads (Goerss); and (3) etale homotopy type of rings of algebraic integers, with a view to applications in Iwasawa theory and algebraic K-theory (Mitchell). The broader goal of the project is to further our understanding of homotopy theory, the branch of topology concerned with those properties of higher-dimensional surfaces and other geometric objects that remain invariant under deformation. There are some surprising and rather mysterious connections between homotopy theory and seemingly unrelated fields such as number theory and algebraic geometry, and it is these connections that the investigators hope to elucidate. ***

9802852 Mitchell本项目研究了同伦理论中三个不同但密切相关的领域的问题：(1)由Morava稳定群的闭子群作用于Landweber精确谱产生的同伦不动点谱，Landweber精确谱的系数环是升力的Lubin-Tate模空间上的函数（Devinatz）；(2)乘法稳定同伦理论，操作数的同伦理论，简单操作数上代数的Andre-Quillen同伦（Goerss）；(3)代数整数环的半同伦类型，并在Iwasawa理论和代数k理论（Mitchell）中的应用。该项目更广泛的目标是进一步加深我们对同伦理论的理解，同伦理论是拓扑的一个分支，关注高维表面和其他几何物体在变形下保持不变的性质。同伦理论与数论和代数几何等看似无关的领域之间存在着一些令人惊讶的、相当神秘的联系，而研究者希望阐明的正是这些联系。＊＊＊