Research on algebraic topology and its geometric applications

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We considered the problems in unstable homotopy theory about compact Lie groups and their classifying spaces, free loop groups and gauge groups. We solved the problems of mod p decomposition of non simply connected Lie groups and relations between the cohomology of the classifying space of free loop groups and related algebraic groups. We considered about higher homotopy commutativities and assosiativities of Hopf spaces and determined the connecting map of the evaluation fiber sequence. We also solved the problem of the commutativity of the localized self homotopy groups in many cases.