2013 Fiscal Year Final Research Report
Study of Hopf spaces by using higher order cohomology operations
| Project/Area Number |
23540093
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 高知大学, 教育研究部自然科学系, 教授 (70181477)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAMOTO Yusuke 防衛大学校, 総合教育学群, 准教授 (10531759)
MORISUGI Kaoru 和歌山大学, 教育学部, 特任教授 (00031807)
YAMAGUCHI Toshihiro 高知大学, 教育研究部自然科学系, 教授 (90346700)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 非安定高位コホモロジー作用素 / ホップ空間 / 高位ホモトピー結合性 / Long Toda積 / cyclohedron / 高位ホモトピー可換性 |
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| Research Abstract |
It is known that the non trivial p-component of the homotopy group of 2n+1 dimensional sphere occurs in dimension 2n+2i(p-1)-1 for n<i<p. The generators for the case of n=1 is given by the composition of the Toda's alpha elements, but for n>1 we showed that they are given by the Toda bracket or higher Toda brackets. We studied higher cohomology operatons detecting these generators. For 3-sphere we showed that it is the secoandary operation which has been useful in studying higher homotopy associativity of Hopf spaces
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