Synthetic research on the relationship among various equivalence relations of singularities
| Project/Area Number |
20540075
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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 | Hyogo University of Teacher Education |
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Principal Investigator |
KOIKE Satoshi Hyogo University of Teacher Education, 大学院・学校教育研究科, 教授 (60161832)
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| Co-Investigator(Kenkyū-buntansha) |
FUKUI Toshizumi 埼玉大学, 理学部, 教授 (90218892)
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| Co-Investigator(Renkei-kenkyūsha) |
SHIOTA Masahiro 名古屋大学, 大学院・多元数理科学研究科, 教授 (00027385)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 微分トポロジー / 特異点論 / ブロー解析同値 / リプシッツ同値 / 点列選択性性質 / C^1同値 / 実ツリーモデル / 半直線-(SSP)条件 / 曲率集中化問題 / C^r同値 / 点列選択性条件 / 定義可能集合 / オーミニマル構造 / 実閉体 / 層化理論 / Lojasiewicz不等式 / ミルナー半経一様性 / Whitney条件(a) |
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| Research Abstract |
T.C.Kuo introduced the notion of blow-analytic equivalence as a desirable equivalence relation for real analytic singularities. In this research, we have proved that C^1 equivalence implies blow-analytic one. This is a negative result to the conjecture given by Kuo and other many real singularitists. In addition, we have proved that the directional dimension of definable sets in o-minimal structure over general real closed field is a Lipschitz invariant, generalizing the Lipschitz invariant I introduced in order to show that blow-analytic equivalence does not always imply Lipschitz one.
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Report
(4 results)
Research Products
(35 results)
