Mathematical Sciences: Homotopy Theory and Its Applications

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Professor Ravenel wishes to continue his investigation of the applications of complex cobordism to homotopy theory. Professor Neisendorfer plans to study the product decompositions of double loop spaces of Moore spaces and, more generally, of the double loop spaces of simply connected finite complexes. He also plans to study the computation of the mod p homology of certain function spaces. Both investigations are efforts to expand the scope of some standard algebraic techniques for analyzing and classifying high- dimensional manifolds. Manifolds themselves are natural geometric objects which arise in theoretical physics and elsewhere, often as the solution sets of ordinary or differential equations.