Mathematical Sciences: Rational Homotropy Theory

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David Anick will continue his research in rational homotopy theory, both for its intrinsic interest and for its applications to integral homotopy. The principal methods will be the use of algebraic models for spaces (Quillen, Sullivan, Adams-Hilton); loop space decompositions (Hilton-Milnor, Cohen-Moore- Neisendorfer, Selick); and Poincare series (Roos-Lofwall, Felix- Thomas-Halperin). True applications of such examinations of the algebraic tools of topology require first, applications of the tools to geometric topological problems, and then, applications of the results to, for example, theoretical physics.