Mathematical Sciences: Mod Z and Rational Cohomology of Finite H-Spaces

数学科学：有限 H 空间的 Mod Z 和有理上同调

• 批准号: 8700984
• 负责人: James Lin
• 金额: $ 8.95万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8700984&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Mod; Rational; Cohomology

The investigator will study relations between the mod Z and rational cohomology of a finite H-space. New information obtained by the investigator about the mod Z cohomology should severely restrict the rational cohomology and also the action of the Steenrod algebra. The investigator will also study various relations between homotopy associativity and homotopy commutativity. These are significant topics in algebraic topology, a discipline which seeks a calculus for treating qualitative geometric properties such as connectedness and knottedness. It underlies much important work in other fields, e.g. the analysis of stability of solutions to differential equations.

研究者将研究mod Z和 有限H-空间的有理上同调。 新信息 研究者获得的关于模Z上同调的结果应该 严格限制了有理上同调， 斯廷罗德代数 研究人员还将研究各种 同伦结合性与同伦的关系 交换性 这些都是代数拓扑学中的重要课题， 一门寻求用微积分来处理定性问题的学科 几何性质，如连通性和打结性。 它 在其他领域的许多重要工作的基础，例如分析 微分方程解的稳定性。