2014 Fiscal Year Final Research Report
On the homotopy properties of the Quillen complex of a symmetric group
| Project/Area Number |
23540024
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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 |
Algebra
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| Research Institution | Dokkyo Medical University |
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Principal Investigator |
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| Research Collaborator |
SAWABE Masato 千葉大学, 教育学部, 准教授
ODA Fumihito 近畿大学, 理工学部, 准教授
KONO Susumu 大阪大学, 理学研究科
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | キリン複体 / 部分群複体 / 順序複体 / ホモトピー性質 / 有限位相空間 |
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| Outline of Final Research Achievements |
I obtained some new informations on homotopy properties of the Quillen complex of a genereal finite group, of course, including a symmetric group, from a topological point of view. As a result, it follows that the Quillen complex of a symmetric group is equivariant homotopy equivalent to the Quillen complex of its alternative group whose dimension is more than five. Besides, I contributed to create a new equivariant theory by finding the relation to the finite topological space theory.
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| Free Research Field |
変換群論
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