2009 Fiscal Year Final Research Report
Rigidity of partially hyperbolic dynamical systems and actions of solvable Lie groups
| Project/Area Number |
19740085
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
ASAOKA Masayuki Kyoto University, 大学院・理学研究科, 准教授 (10314832)
|
|---|
| Project Period (FY) |
2007 – 2009
|
| Keywords | 群作用 / 双曲力学系 / 葉層構造 |
|---|
| Research Abstract |
I gave a complete classification of locally free actions of the wo-dimensional non-abelian Lie group on three-manifolds, which was a open problem for hirty years. I also constructed the deformation space of the actions. For analogous actions n higher dimension, I conjectured that they are flexible similar to the low-dimensional ase. However, it turned out that the actions exhibits rigidity in higher-dimension. I also ormulated a natural conjecture on parameter rigidity of locally free actions of solvable Lie roups in terms of the leafwise cohomology of the orbit foliations
|
