Mathematical Sciences: Homotopy Theory at Large Primes

数学科学：大素数同伦论

• 批准号: 8912842
• 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: 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=8912842&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Homotopy; Theory; Large

Professor Anick intends to extend his resarch in rational homotopy theory to the study of homotopy theory at large primes. The principal methods will be the use of H-spaces and exponents (Cohen-Moore-Neisendorfer, Gray, Selick); algebraic models for spaces (Dwyer, Felix-Halperin, Quillen); and V1-homotopy (Mahowald, R. Thompson). Homotopy thoery is one of the standard algebraic techniques for dealing with geometric questions. Typically one starts with such a question, translates it into its algebraic counterpart, calculates concerning the algebra which has been introduced, and then translates the results back into the language of geometry. None of these steps has a cookbook recipe, of course, but this is often the type of argument one attempts to construct.

Anick教授打算将他对有理同伦理论的研究扩展到大素数同伦理论的研究。 主要方法是使用 H 空间和指数（Cohen-Moore-Neisendorfer、Gray、Selick）；空间代数模型（Dwyer、Felix-Halperin、Quillen）；和 V1-同伦（Mahowald，R. Thompson）。 同伦理论是处理几何问题的标准代数技术之一。 通常，人们从这样一个问题开始，将其翻译成对应的代数，计算所引入的代数，然后将结果翻译回几何语言。 当然，这些步骤都没有食谱食谱，但这通常是人们试图构建的论点类型。