2011 Fiscal Year Final Research Report
Symmetry from the homotopical viewpoint
| Project/Area Number |
21540068
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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 | Chiba University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
IWASE Norio 九州大学, 大学院・数理学研究院, 教授 (60213287)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 位相幾何学 |
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| Research Abstract |
Study of symmetry has been one of the major subjects in geometry for centuries. In our study we investigated symmetry from the homotopy theoretical viewpoint. As in the other geometrical theories, the symmetry of a space is described by a certain set of automorphisms. Our main result in this study is that the algebraic structure of the automorphisms is closely related to the linear groups in algebra. This result is valid for quite general spaces and hence it is thought as a fundamental result of the field.
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