| 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)
田原 賢一 愛知教育大学, 教育学部, 教授 (00024026)
安本 太一 愛知教育大学, 教育学部, 助教授 (00231647)
小谷 健司 愛知教育大学, 教育学部, 助教授 (60273299)
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| Project Period (FY) |
1998 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1999: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1998: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Lie group / Atiyah Todd number / Milnor Kervaire number / Cohomology ring / CW Complex / homotopy category / manifold / embedding problem / Milnor-Kervaire数 / Atiyah-Todd数 / シミュレーション / ベルヌーイ数 / 微分可能構造 / 例外リー群 / Bernoulli数 / ホモトピー正規性 / スペクトル系列 / コホモロジー作用素 / 古典リー群 / ホモロジー環 / 外積代数 |
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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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