2001 Fiscal Year Final Research Report Summary
Homotopy normality of Lie groups
| Project/Area Number |
10640073
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Aichi University of Education |
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Principal Investigator |
FURUKAWA Yasukuni Aichi University of Education, Prof., 教育学部, 教授 (90024033)
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| Co-Investigator(Kenkyū-buntansha) |
UEMURA Hideaki Aichi University of Education, Ass. Prof., 教育学部, 助教授 (30203483)
YASUI Tsutomu Kagoshima University/Faculty of Edu.,Prof., 教育学部, 教授 (60033891)
OHKAWA Tetsusuke Hiroshima InstofTech.Fac.of Engineering, Ass. Prof., 工学部, 助教授 (60116548)
TAKEUCHI Yoshihiro Aichi University of Education, Ass. Prof., 教育学部, 助教授 (10206956)
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| Project Period (FY) |
1998 – 2001
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| Keywords | Lie group / Atiyah Todd number / Milnor Kervaire number / Cohomology ring / CW Complex / homotopy category / manifold / embedding problem |
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| Research Abstract |
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.
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