Mathematical Sciences: Homotopy Theory at Large Primes

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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.