Study of stability of fixed point sets in equivariant manifolds
| Project/Area Number |
26400090
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Okayama University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2014-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
|---|
| Keywords | 同変多様体 / 変換群論 / 不動点集合 / 同変手術理論 / 同変コボルディズム / 変換群 / 群作用 / 多様体 / 同変手術 / s－同境 / バーンサイド環 / 有限群 / 手術理論 / Mackey 関手 / ギャップ条件 / 国際研究者交流 / ヨーロッパ |
|---|
| Outline of Final Research Achievements |
Let G be a finite group and let F be a closed manifold satisfying a certain condition such as one of G-fixed point sets of smooth G-actions on disks or spheres. The purpose of this research project was to construct smooth G-actions with fixed point set F on a specified sequence X(1), X(2), X(3), ... of closed manifolds X(n), for example complex projective spaces, real projective spaces, and lens spaces. In the period of the present research project, we constructed smooth G-actions with fixed point set F for the group G being the alternating group of degree 5 or 6, on sequences of complex projective spaces, real projective spaces, and lens spaces, by means of the reflection method of G-framed maps and equivariant cobordisms, equivariant surgery theory, and s-cobordism theory.
|
Report
(5 results)
Research Products
(23 results)
