Applications of centers of mass configuration spaces to homotopy theory
| Project/Area Number |
18540092
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | University of the Ryukyus |
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Principal Investigator |
KAMIYAMA Yasuhiko University of the Ryukyus, 理学部, 教授 (10244287)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,890,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥690,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | 重心配置空間 / クモの巣装置 / モーメント角複体 / 多角形 / モジュライ空間 / モース関数 / パーフェクト / 最良 / チェイン複体 / ホモロジー / 重心 / 配置空間 / パワーショベル / ロボット / ホモロジー分解 / コンピュータ計算 / 位相的複雑さ / ループ空間 / 超平面 / 可換図式 / 予想 / ホモトピー同値 / 局所係数ホモロジー / ホモトピーファイバー / 整係数ホモロジー / ねじれ群 / 結節マシン / 安定ホモトピー同値 / ホモトピーコリミット |
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| Research Abstract |
Homotopy theory is a topology which studies continuous maps between two spaces. Traditionally, problems in homotopy theory have been solved by ad hoc methods. In the present research, I defined the "centers of mass" configuration spaces and posed a conjecture about its property. I elucidated that if our conjecture was proved, then not only many known results are reproved in an integral way, but also we can prove unsolved problems.
The merit of our research is as follows. The complement of hyperplanes in the Euclidean space is a computable object. Since our configuration space is a kind of such a complement, our conjecture is far more accessible than the traditional way to construct continuous maps.
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Report
(6 results)
Research Products
(39 results)
