Mathematical Sciences: Rational Homotropy Theory

数学科学：有理同异性理论

• 批准号: 8711536
• 负责人: David Anick
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 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: 1987-07-15 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8711536&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Rational; Homotropy; Theory

David Anick will continue his research in rational homotopy theory, both for its intrinsic interest and for its applications to integral homotopy. The principal methods will be the use of algebraic models for spaces (Quillen, Sullivan, Adams-Hilton); loop space decompositions (Hilton-Milnor, Cohen-Moore- Neisendorfer, Selick); and Poincare series (Roos-Lofwall, Felix- Thomas-Halperin). True applications of such examinations of the algebraic tools of topology require first, applications of the tools to geometric topological problems, and then, applications of the results to, for example, theoretical physics.

David Anick将继续他对有理同伦理论的研究，包括它的内在兴趣和它在积分同伦中的应用。主要的方法将是使用空间的代数模型(Quillen，Sullivan，Adams-Hilton)；循环空间分解(Hilton-Milnor，Cohen-Moore-Neisendorfer，Selick)；以及Poincare系列(Roos-Lofwall，Felix-Thomas-Halperin)。拓扑学的这种代数工具的真正应用首先需要将这些工具应用于几何拓扑问题，然后将结果应用于例如理论物理。