| Project/Area Number |
25400087
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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 | Kyoto University |
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Principal Investigator |
Kishimoto Daisuke 京都大学, 理学(系)研究科(研究院), 准教授 (60402765)
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| Co-Investigator(Renkei-kenkyūsha) |
KONO Akira 同志社大学, 理工学部, 教授 (00093237)
IRIYE Kouyemon 大阪府立大学, 大学院理学研究科, 教授 (40151691)
IWASE Norio 九州大学, 大学院数理学研究院, 教授 (60213287)
KURIBAYASHI Katsuhiko 信州大学, 理学部, 教授 (40249751)
TAMAKI Dai 信州大学, 理学部, 教授 (10252058)
TSUKUDA Shuichi 琉球大学, 理学部, 准教授 (50305182)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 代数トポロジー / ホモトピー論 / ゲージ群 / ポリヘドラルプロダクト / polyhedral product / Samelson積 / Stanley-Reisner環 / 組み合わせ論 |
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| Outline of Final Research Achievements |
Homotopy noncommutativity of the loop product of loop spaces was studied through gauge groups and polyhedral products. As for gauge groups, the mod p decomposition, the classification of homotopy types of gauge groups corresponding to principal bundles with non-simply connected structure groups, and the classification of A_\infty types were achieved. Particularly, in the classification of A_\infty types, a new method to detect higher order Whitehead products by using Lanne T-functor was developed. As for polyhedral products, the fat wedge filtration was introduced, and through analyzing its structure, the homotopy types of polyhedral products were described. As is application. a topological proof of Golodness of certain simplicial complexes, which has been studied in combinatorial commutative algebra, was given.
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