Mathematical Sciences: Homotopy Theory and Its Applications

数学科学：同伦理论及其应用

• 批准号: 8903178
• 负责人: Douglas Ravenel
• 金额: $ 24.28万
• 依托单位: University of Rochester
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903178&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Homotopy; Theory; Its

Professor Ravenel wishes to continue his investigation of the applications of complex cobordism to homotopy theory. Professor Neisendorfer plans to study the product decompositions of double loop spaces of Moore spaces and, more generally, of the double loop spaces of simply connected finite complexes. He also plans to study the computation of the mod p homology of certain function spaces. Both investigations are efforts to expand the scope of some standard algebraic techniques for analyzing and classifying high- dimensional manifolds. Manifolds themselves are natural geometric objects which arise in theoretical physics and elsewhere, often as the solution sets of ordinary or differential equations.

Ravenel教授希望继续调查复杂的共同体对同型理论的应用。 Neisendorfer教授计划研究摩尔空间的双环空间的产品分解以及更普遍的简单连接有限复合物的双环空间的产品分解。 他还计划研究某些功能空间的MOD P同源性的计算。 两项研究都是为了扩大某些标准代数技术的范围，用于分析和分类高维流形。 歧管本身是自然的几何对象，通常是在理论物理和其他地方出现的，通常是普通或微分方程的解决方案集。