| Project/Area Number |
11640083
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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 | KOCHI UNIVERSITY |
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Principal Investigator |
HEMMI Yutaka Faculty of Science, KOCHI UNIVERSITY Professor, 理学部, 教授 (70181477)
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| Co-Investigator(Kenkyū-buntansha) |
OSHIMA Hideaki Ibaraki University Faculty of Science, Professor, 理学部, 教授 (70047372)
KOMATSU Kazushi Faculty of Science, KOCHI UNIVERSITY Research Associate, 理学部, 助手 (00253336)
SHIMOMURA Katsumi Faculty of Science, KOCHI UNIVERSITY Professor, 理学部, 教授 (30206247)
TSUKIYAMA Kouzou Shimane University Faculty of Education, Professor, 教育学部, 教授 (20093651)
MORISUGI Kaoru Wakayama University Faculty of Education, Professor, 教育学部, 教授 (00031807)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | Hopf spaces / iterated H-deviation / Steenrod operations / higher order operations / quasi p-regular / homotopy groups of spheres / self homotopy equivalences / Moore space / mod p cohomology / Moore space / 同変ホモトピー |
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| Research Abstract |
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.
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