Mathematical Sciences: Mod Z and Rational Cohomology of Finite H-Spaces

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The investigator will study relations between the mod Z and rational cohomology of a finite H-space. New information obtained by the investigator about the mod Z cohomology should severely restrict the rational cohomology and also the action of the Steenrod algebra. The investigator will also study various relations between homotopy associativity and homotopy commutativity. These are significant topics in algebraic topology, a discipline which seeks a calculus for treating qualitative geometric properties such as connectedness and knottedness. It underlies much important work in other fields, e.g. the analysis of stability of solutions to differential equations.