Homotopy normality of Lie groups

1. 古河道,靖国神社。我们考虑李群的同伦正规性时，采用了比McCarty和James提出的定义更弱的定义。我们改进了他们的结果，并研究了特殊李群的情况。进一步，我们确定了例外李群的包含图诱导的上同图mod p。接下来，我们利用计算机软件Mathematica给出了一个阿蒂亚-托德数公式的程序。然后给出了Kervaire-Milnor数的估计。Ohkawa Tetsusuke。Handel的结果表明无点cw -配合物的同伦范畴是平衡的。Dyer和Roitberg的结果表明，连通的点状cw -配合物的同伦范畴是平衡的。本文给出了对这些事实的直接平行证明，即证明了无点cw -配合物的同伦范畴与连通点cw -配合物的同伦范畴是平衡的。已知n流形到实射影空间P（2n）的每个映射与嵌入是同伦的。我们证明了这是最好的可能。证明使用了Stiefel-Whitney类。

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.