Mathematical Sciences: Loop Spaces and Classical Homotopy Theory

数学科学：循环空间和经典同伦理论

• 批准号: 8702608
• 负责人: Frederick Cohen
• 金额: $ 12.42万
• 依托单位: University of Kentucky
• 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=8702608&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Loop; Spaces; Classical

The principal investigator is studying several related areas. A number of problems are connected to the classical distributivity formula obtained from the Hilton-Milnor theorem. Problem one here is a reformulation of the strong form of the Kervaire invariant, the first step being the analysis of zero divisors in Dickson's analogues of the Cayley numbers. The second problem is the analysis of a simpler, stable distributivity law. One direction is a certain stable analogue of Barratt's finite exponent conjecture. In a related project, he continues some of his past work on the homology of configuration spaces. These investigations are mainly attempts to understand and perfect algebraic techniques. Specifically, the techniques permit calculations concerning qualitative properties of geometric manifolds, e.g. connectedness, knottedness, the fixed- point property, and so forth.

首席研究员正在研究几个相关的 地区 许多问题都与经典的 由Hilton-Milnor定理得到的分配率公式。 这里的问题一是重新表述了 Kervaire不变量，第一步是零的分析 Dickson的Cayley数的类似物中的因子。 的 第二个问题是分析一个更简单、稳定的 分配律 一个方向是某种稳定的类比 Barratt有限指数猜想 在一个相关的项目中， 他继续他过去的一些工作， 配置空间 这些调查主要是试图了解和 完美的代数技巧 具体来说，技术 允许计算有关的定性性质 几何流形，例如连通性，knottedness，固定的， 点属性等等。