2009 Fiscal Year Final Research Report
Research on homotopical properties of Lie groups
| Project/Area Number |
18540064
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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 | Ibaraki University |
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Principal Investigator |
OSHIMA Hideaki Ibaraki University, 理学部, 教授 (70047372)
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| Project Period (FY) |
2006 – 2009
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| Keywords | リー群 / ホモトピー / ホモトピー群 / べき零指数 / 自己写像 / 写像空間 |
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| Research Abstract |
For a Lie group G, I studied on homotopy groups of the function space of self maps of G. I proved that for any natural number n there exists G of which the nilpotency class of the 0-th homotopy group is greater than n. When G is SU(3) or Sp(2), I and coauthers determined the n-th homotopy group of the function space for 0<n<12. I calculated a quotient group of the group of homotopy classes of self homotopy equivalences of SO(4).
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