Classification of the cohomology rings of finite Hopf spaces

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The summary of reserch results is as follows.1. We constructed p-th order mod p unstable cohomology operations for any odd prime p. Then, by using the operation, we studied the action of the Steenrod operations on the cohomology of the mod p finite Hopf spaces. We gave a lecture on a part of our resutl at the Japan-America Mathematics Institute at the Johns Hopkins University held at March 2000.2. In order to apply the above p-th order operation to the cohomology of Hopf spaces, we introduced iterated H-deviation for maps between Hopf spaces, which is an extension of the H-deviation.3. We studied conditions for mod p finite Hopf spaces to be quase p-regular. Our result is a considered as a generalization of the result by Kumpel for the p-regularity of mod p finite Hopf spaces. Our result includes the results by Harper, McClearly and Wilkerson.4. O^^-shima determined the group structure of the set of self homotopy equivalences for the exceptional group G_2. While Morisugi determined the one for the classical groups SU (3), Sp (2).5. Shimomura studied the υ^<-1>_2BP-localized homotopy groups of the spheres localized at prime 2 or 3. Komatsu studied orbit closure decompositions of tiling spaces by the generalized projection method. Tsukiyama studied the group of homotopy equivalence classes of S^1-bundles.