2009 Fiscal Year Final Research Report
Reconstruction of generalized cohomology theories by means of the notion of continuous functors
| Project/Area Number |
19540087
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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 | Okayama University |
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Principal Investigator |
SHIMAKAWA Kazuhisa Okayama University, 大学院・自然科学研究科, 教授 (70109081)
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| Co-Investigator(Kenkyū-buntansha) |
MIMURA Mamoru 岡山大学, 名誉教授 (70026772)
OKUYAMA Shingo 香川高等専門学校, 情報工学科 (50290812)
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| Co-Investigator(Renkei-kenkyūsha) |
TORII Takeshi 岡山大学, 大学院・自然科学研究科, 准教授 (30341407)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 位相幾何学 / ホモトピー論 / 一般コホモロジー |
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| Research Abstract |
We constructed a category of topological spaces which satisfies the properties suitable for developing homotopy theory, and used it to establish a method for defining generalized cohomology theories by means of the notion of bivariant functors. In comparison with the conventional construction given by spectra, our new construction is more systematic and is easier to extend to categories other than that of topological spaces ; hence we may expect it to be applied to a variety of problems.
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