Topology of the group of diffeomorphisms and the spaces of embeddings of manifolds
| Project/Area Number |
21840002
|
|---|
| Research Category |
Grant-in-Aid for Research Activity Start-up
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Hokkaido University |
|---|
Principal Investigator |
WATANABE Tadayuki Hokkaido University, 大学院・理学研究院, 助教 (70467447)
|
|---|
| Project Period (FY) |
2009 – 2010
|
| Project Status |
Completed (Fiscal Year 2010)
|
| Budget Amount *help |
¥2,015,000 (Direct Cost: ¥1,550,000、Indirect Cost: ¥465,000)
Fiscal Year 2010: ¥1,105,000 (Direct Cost: ¥850,000、Indirect Cost: ¥255,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
|---|
| Keywords | ファイバー束 / 微分同相 / 埋め込み / Morse / 理論 / 代数的K理論 / 微分同相群 / Morse理論 / 有理ホモトピー群 / 擬アイソトピー |
|---|
| 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.
|
Report
(3 results)
Research Products
(16 results)
