THE GROUP ACTIONS ON MANIFOLDS AND THE EQUIVARIANT DETERMINANT OF ELLIPTIC OPERATORS.
| Project/Area Number |
25400084
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Tokyo University of Marine Science and Technology |
|---|
Principal Investigator |
TSUBOI KENJI 東京海洋大学, 学術研究院, 教授 (50180047)
|
|---|
| Project Period (FY) |
2013-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
|---|
| Keywords | 概複素多様体 / 向き付けられた多様体 / 有限群作用 / 楕円型作用素 / 同変行列式 / 変換群 / 向きづけられた多様体 / 作用の回転角 / Atiyah-Singer 指数 / 同変指数 / Zagier の公式 / Eisenstein の公式 / 符号作用素 / 写像類群 / 非可換有限群 / コンパクト・リーマン面 / 群作用 |
|---|
| Outline of Final Research Achievements |
Firstly we obtain a necessary condition for the existence of finite group actions on alomost complex manifolds, where the action is assumed to preserve the almost complex structure and the fixed points of the action is assumed to be isolated. The condition above contains the condition of Harvey for compact Riemann surfaces. This result is published in J.Math.Soc.Japan, vol.65-3, p.797-827 at June, 2013. Secondly we show that the C-p groups can act on Riemann surfaces of genus r for some p,r, where C-p group is a finite group such that the order of the commutator subgroup is a multiple of the prime number p. Thirdly we obtain a necessary condition for the existence of finite group actions on oriented manifolds, where the action is assumed to preserve the orientation and the fixed points of the action is assumed to be isolated. The condition above contains the condition of Harvey for compact Riemann surfaces.
|
Report
(6 results)
Research Products
(1 results)
