Mathematical Sciences: Homotopy Theory at Large Primes

Anick教授打算将他对有理同伦理论的研究扩展到对大素数同伦理论的研究。主要的方法将是使用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，一个人从这样一个问题开始，把它转换成代数对应的问题，计算已经引入的代数，然后把结果转换回几何语言。当然，这些步骤都没有食谱，但这通常是人们试图构建的参数类型。

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.