Homotopical Algebra and its Geometric Applications

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Akira Kono, the head investigator and Hiroaki Hamanaka, an investigator defined the unstable K-theory of a space X as the homotopy set [X, U(n)] and proved certain properties of it. Using the unstable K-theory they classified the homotopy types of gauge groups of principal SU(2)-bundles over the 6 dimensional sphere and SU(3)-bundles over the 4 dimensional sphere.Akira Kono and Hideaki Oshima proved the self homotopy group [G, G] is not commutative for simple Lie group G of rank not less than 2. Hiroaki Hamanaka proved the nilpotent class of the self homotopy group of SU(n) is not less than 2 if n is greater than 4.Akira Kono and Yasuhiko Kamiyama, an investigator determined the cohomology of the moduli space of SO(n)-instantons with instanton number 1.Akira Kono proved a certain property of the Stiefel-Whitney classes of representations of exceptional Lie groups