Mathematical Sciences: Group Proposal in Topology

数学科学：拓扑学小组提案

• 批准号: 9423300
• 负责人: J May
• 金额: $ 56.67万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9423300&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Group; Proposal; Topology

9423300 May This project encompasses research in a wide variety of topics in topology and related areas of algebra, algebraic K-theory and algebraic geometry. One focus is global algebraic structures in stable homotopy theory, with applications to such topics as cobordism, topological Hochschild homology, and algebraic K-theory. Another is the study of algebraic and topological vector bundles and of Hochschild homology for algebraic varieties. Another is the study of analytic and combinatorial torsion invariants of manifolds. Research in algebraic and geometric topology at the University of Chicago has for many years explored areas both internal to topology and areas on the borders between topology and algebraic geometry and differential geometry. Ideas developed here, for example the notion of an operad, have been used in diverse fields, from mathematical physics to combinatorial group theory. Graduate students and postdocs involved in the project leave Chicago with especially broad interdisciplinary training and background. ***

9423300 5月这个项目涵盖了拓扑学以及代数、代数K理论和代数几何相关领域的各种主题的研究。其中一个焦点是稳定同伦理论中的整体代数结构，并应用于余边论、拓扑Hochschild同调和代数K-理论等主题。另一个是研究代数向量丛和拓扑向量丛以及代数簇的Hochschild同调。另一个是流形的解析不变量和组合扭转不变量的研究。多年来，芝加哥大学在代数和几何拓扑学方面的研究一直在探索拓扑学的内部区域以及拓扑学与代数几何和微分几何之间的边界区域。在这里形成的想法，例如歌剧的概念，已经被用于从数学物理到组合群论的不同领域。参与该项目的研究生和博士后带着特别广泛的跨学科培训和背景离开了芝加哥。***