2011 Fiscal Year Final Research Report
Cohomological dimension theory in coarse geometry
| Project/Area Number |
21540075
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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 | Waseda University (2011)
Shizuoka University (2009-2010) |
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Principal Investigator |
KOYAMA Akira 早稲田大学, 理工学術院, 教授 (40116158)
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| Co-Investigator(Renkei-kenkyūsha) |
HOSAKA Tetsuya 静岡大学, 理学部, 准教授 (50344908)
CHINEN Naotsugu 広島工業大学, 工学部, 准教授 (20370067)
EDA Katsuya 早稲田大学, 理工学術院, 教授 (90015826)
YAGASAKI Tatsuhiko 京都工芸繊維大学, 工芸科学研究科, 教授 (40191077)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 位相幾何 / Coarse幾何 / コホモロジー次元論 |
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| Research Abstract |
As we started to investigate coarse geometry from the viewpoint of asymptotic dimension theory, we faced an important problem related to embedding problems. Namely, we investigated the problem what kind of n-dimensional compact metric spaces can be embedded into a product of n one-dimensional compact metric spaces. First, we tried to determine a class of n-dimensional topological and generalized manifolds which can be embedded into a product of n one-dimensional compact metric spaces by using geometric structures and the rank of 1-dimensional cohomology groups. Next, we applied this method to arbitrary n-dimensional compact metric spaces to determine embeddability and succeeded to give a criterion by using the triviality of n-dimensional Cech cohomology groups and the rank of 1-dimensional Cech cohomology groups.
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Research Products
(12 results)
