Homotopy normality of Lie groups

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1. Furukawa,Yasukuni.We considerd the homotopynormality of Lie groups by adopting a weaker definitio than those proposed by McCarty and James. We improved their results, and investigated the case of the exceptional Lie groups. Further,we determined the cohomology maps mod p induced by the inclusion maps of the exceptional Lie groups.Next,we presented a program of Atiyah-Todd number formula by the computer software Mathematica.and then gave an estimation of the Kervaire-Milnor number.2. Ohkawa,Tetsusuke.A result of Handel shows that the homotopy category of unpointed CW-complexes is balanced. The results of Dyer and Roitberg show that the homotopy category of connected pointed CW-complexes is balanced.Here, we presented a direct and parallel proof of these facts, I.e., we proved that the homotopy category of unpointed CW-complexes and the homotopy category of connected pointed CW-complexes are balanced.3.Yasui,Tsutomu.It is known that each map of an n-manifold to real projective space P(2n) is homotopic to an embedding. We proved that this is best possible. The proof uses Stiefel-Whitney classes.