A study of representations appeared as the tangential spaces of manifilds at fixed points
| Project/Area Number |
17540084
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kyushu University |
|---|
Principal Investigator |
SUMI Toshio Kyushu University, Faculty of Design, Associate Professor (50258513)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
IWASE Norio KYUSHU UNIVERSITY, Faculty of Mathematics, Associate Professor (60213287)
|
|---|
| Project Period (FY) |
2005 – 2007
|
| Project Status |
Completed (Fiscal Year 2007)
|
| Budget Amount *help |
¥3,040,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
|
|---|
| Keywords | gap modules / gap group / finite group actions / Smith equivalent / 実表現 / ライティネン予想 / 表現 |
|---|
| Research Abstract |
I studied about tangential spaces at the fixed point of a finite group action on a sphere. Smith posted a problem whether tangential spaces are isomorphic for an action on a sphere with exactly two fixed points. Many colleague studied the corresponding problem. I used the technique by Solomon and Pawalowski and obtained a sufficient condition to have two or more real conjugacy classes of elements not of prime power order. I completely determine nilpotent groups which have two or more real conjugacy classes of elements not of prime power order. By another approach combining the above I showed that there is a smooth action on a sphere with exactly two fixed points such that two tangencial spaces are not isomorphic, if the number of real conjugacy classes of elements not of prime power order is greater than 1, for a finite non-solvable groups except the automorphic group of the alternating group on six letters and the field automorphism extension for the projective special linear group PSL (2, 27). Furthermore, I studied the case of solvable groups and showed that the sufficient condition can be applied for some classes of solvable groups.
|
Report
(4 results)
Research Products
(26 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Presentation] Smith問題について2006
Author(s)
T.Sumi
Organizer
変換群論の手法
Place of Presentation
京都大学数理解析研究所
Year and Date
2006-05-26
Description
「研究成果報告書概要(和文)」より
Related Report
-
-
-
-
-
