2009 Fiscal Year Final Research Report
A study of stable Hopf invariants and Hopf constructions
| Project/Area Number |
19540106
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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 | Fukuoka University |
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Principal Investigator |
ODA Nobuyuki Fukuoka University, 理学部, 教授 (80112283)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIGURO kenshi 福岡大学, 理学部, 教授 (00268971)
IWASE Norio 九州大学, 大学院・数理学研究院, 教授 (60213287)
TORII Takeshi 岡山大学, 大学院・自然科学研究科, 准教授 (30341407)
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| Co-Investigator(Renkei-kenkyūsha) |
HIRASHIMA Yasumasa 関西大学, システム理工学部, 准教授 (80047399)
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| Project Period (FY) |
2007 – 2009
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| Keywords | トポロジー |
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| Research Abstract |
Formulas are obtained among box brackets and matrix Toda brackets. Generalizations of classical formulas by Toda are obtained including relations with the Hopf invariants. A class of spaces is defined which is closely connected with the LS category. Relations between the class and covering spaces are clarified which are useful to study examples. Topologies of function spaces which are defined by the exponential topology are studied. Exponential homeomorphisms are proved which hold for any topological spaces and applications of the theorem are obtained.
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