| Project/Area Number |
19540108
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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 | Okinawa National College of Technology |
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Principal Investigator |
CHINEN Naotsugu Okinawa National College of Technology, 工学部, 准教授 (20370067)
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| Co-Investigator(Kenkyū-buntansha) |
KOYAMA Akira 静岡大学, 創造科学技術大学院, 教授 (40116158)
TOMOYASU Kazuo 都城工業高等専門学校, 一般科目理科, 准教授 (10332107)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 位相幾何 / 距離に依存するコンパクト化 / asymptotic次元 / 写像によるカラーリング / 幾何学的群論 / Higsonコンパクト化 / Smirnovコンパクト化 / トポロジー / 幾何学 / コンパクト化 / CAT(0) / aymptotic次元 / Smirnov / Higson / 写像によるcoloring |
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| Research Abstract |
We investigate coarse geometric properties of unbounded metric spaces that contains asymptotic dimension, colorings for maps, and topological properties of remainders of Higson and Smirnov compactifications. We prove that all proper CAT(0) spaces that are homeomorphic to the plane have asymptotic 2-dimension. This result is the first one step of the solution of a question "Does every CAT(0) group have finite asymptotic dimension?".
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