2009 Fiscal Year Final Research Report
Coarse geometry and compactifications that are metric-dependent, with relation to Novikov conjecture
| 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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| 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 |
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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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