| Project/Area Number |
24740053
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群) |
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Principal Investigator |
KAWAMOTO Yusuke 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工, 総合教育学群, 准教授 (10531759)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | ループ空間 / ホップ空間 / 高位ホモトピー可換性 / 巡回多面体 / 置換結合多面体 / ベキ写像 / 高位ホモトピー結合性 / 多面体 |
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| Outline of Final Research Achievements |
The concept of higher homotopy commutativity was first studied by Sugawara in the case of topological monoids. In the present study, we constructed a new higher homotopy commutativity for the (loop) multiplications of loop spaces (higher homotopy associative Hopf spaces) using cyclohedra constructed by Bott and Taubes. We also gave combinatorial decompositions of permuto-associahedra constructed by Kapranov into unions of product spaces of cyclohedra. Then the cyclohedron can be regarded as a subspace of the permuto-associahedron. From the decompositions, we also studied relations between the new concept of higher homotopy commutativity and another one represented by the permuto-associahedra.
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