2010 Fiscal Year Final Research Report
Topology of the group of diffeomorphisms and the spaces of embeddings of manifolds
| Project/Area Number |
21840002
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Hokkaido University |
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Principal Investigator |
WATANABE Tadayuki Hokkaido University, 大学院・理学研究院, 助教 (70467447)
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| Project Period (FY) |
2009 – 2010
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| Keywords | ファイバー束 / 微分同相 / 埋め込み / Morse / 理論 / 代数的K理論 |
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| Research Abstract |
The author studied the classification problem of smooth fiber bundles with fiber diffeomorphic to the sphere. He defined "algebraic obstructions" for fiber bundles over 2-sphere with fiber diffeomorphic to odd dimensional sphere and showed that if the fiber dimension is at least 7 and if the obstructions vanish then the fiber bundle is in fact trivial. He also showed that if the fiber dimension is 5 and if the obstructions vanish then the fiber bundle is presentable by a family of embeddings of 2-spheres and an element of some discrete abelian group. Thus the classification of sphere bundles is reduced to an algebraic problem and the classification of families of embeddings.
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