Flexibilities of finite group actions on manifolds
Project/Area Number |
24540083
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Kyushu University |
Principal Investigator |
SUMI Toshio 九州大学, 基幹教育院, 准教授 (50258513)
|
Project Period (FY) |
2012-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
|
Keywords | 有限群作用 / スミス集合 / 実表現 / 接表現 |
Outline of Final Research Achievements |
I studied representation spaces induced by smooth actions on manifolds of finite groups. In particular, I studied finite group smooth actions on spheres. The Smith problem, whether tangential representation spaces over fixed points of a sphere with just two fixed points are isomorphic?, is fundamental one for transformation group theory. I determinied the Smith set which consists of the differences of tangential representative spaces over such a sphere for some class of finite groups. I also gave a sufficient and necessary condition for a finite group to be a gap group by viewing centralizers and normalizers.
|
Report
(4 results)
Research Products
(11 results)