Mathematical Sciences: Function Spaces, Homotopy Theory, and Group Cohomology

数学科学：函数空间、同伦论和群上同调

• 批准号: 9013139
• 负责人: Frederick Cohen
• 金额: $ 22.22万
• 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: 1991
• 资助国家: 美国
• 起止时间: 1991-03-01 至 1995-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9013139&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Function; Spaces; Homotopy

There are two faculty investigators in the projects described below, F. R. Cohen and S. Gitler, as well as two of their graduate students involved in thesis research. All of the research concerns algebraic techniques in topology. F. R. Cohen intends to consider problems in classical homotopy theory and some offshoots to the cohomology of certain discrete groups. Three of the main projects involve (1) improving his bounds on the exponent of a mod-2-to-the-r Moore space, r at least 2, and trying to extend some results to the case when r is 1, (2) a study of the Whitehead product involving spaces of rational functions together with their interplay with Cayley-Dickson algebras, and (3) the cohomology and stable structure for the classifying space of certain discrete groups called mapping class groups. Some of these problems involve configuration spaces and are part of joint work with S. Gitler and L. Taylor (University of Notre Dame). S. Gitler intends to consider several problems centered on mapping spaces, their cohomology, and their relationship to homotopy theory. For example, he intends to study maps (X,Y) and their cohomology for "good" spaces X and Y. Setting Y equal to a space in the omega-spectrum for Morava K-theory, K(n), one gets useful examples of spaces with periodic homotopy groups. Gitler intends to study applications of these spaces.

项目中有两名教员调查员 如下所述，F. R. Cohen和S.吉特勒，以及两个 他们的研究生参与论文研究。 所有 研究涉及拓扑学中的代数技术。 F. R.科恩打算考虑问题，在古典 同伦理论和某些上同调的一些分支 离散群体 三个主要项目涉及（1） 改进了他关于模2到r的摩尔指数的界 空间，r至少为2，并试图将一些结果扩展到 当r为1时，（2）研究Whitehead乘积， 有理函数空间及其与 Cayley-Dickson代数的上同调和稳定性 一类离散群的分类空间的结构 称为映射类组。 其中一些问题涉及 配置空间，并与S. Gitler 和L.泰勒（圣母大学）。 S. Gitler打算考虑几个问题， 映射空间，它们的上同调，以及它们与 同伦理论 例如，他打算研究地图（X，Y）和 它们对于“好”空间X和Y的上同调。 设Y等于a 在Morava K-理论的ω-谱中的空间，K（n），得到 具有周期同伦群的空间的有用例子。 Gitler 他打算研究这些空间的应用。