2010 Fiscal Year Final Research Report
Study of Hopf spaces and p-compact groups
| Project/Area Number |
20540080
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kochi University |
|---|
Principal Investigator |
HEMMI Yutaka Kochi University, 教育研究部・自然科学系, 教授 (70181477)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MORISUGI Kaoru 和歌山大学, 教育学部, 教授 (00031807)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
TSUKIYAMA Kouzou 島根大学, 教育学部, 教授 (20093651)
SHIMOMURA Katsumi 高知大学, 教育研究部自然科学系, 教授 (30206247)
YAMAGUCHI Toshihiro 高知大学, 教育研究部自然科学系, 准教授 (90346700)
|
|---|
| Project Period (FY) |
2008 – 2010
|
| Keywords | ホップ空間 / 空間の既約分解 / アトミック空間 / p正則性 / 準p正則性 / 高位Toda積 / ホモトピー群 |
|---|
| Research Abstract |
Spaces are assumed to be simply connected and localized at a fixed odd prime p. We assume that the homology of each Hopf space has no p torsion, and the mod p cohomology ring of it is finite. We first completed the classification of irreducible Hopf spaces with rank less than or equal to five. Then, by using this result, we determined the irreducible decomposition of Hopf spaces satisfying the condition that the difference between the maximum and the minimum dimensions of the generators is less that 8(p-1). In the course of studying this problem we showed that some low dimensional unstable homotopy groups of spheres are generated by elements given by long Toda bracket of alpha elements. Moreover we extended a known fact on quasi p regularity of quaternionic Stiefel manifolds and real Stiefel manifolds.
|
