Research of non-commutative geometry, singular point, and geometric asymptotics
| Project/Area Number |
22540095
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Keio University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2010-04-01 – 2015-03-31
|
| Project Status |
Completed (Fiscal Year 2014)
|
| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
|---|
| Keywords | 非可換幾何学 / シンプレクティック幾何学 / 一般複素幾何学 / 量子化 / 指数定理 / フーリエ積分作用素 / quantization / poisson structure / Kaehler structure / noncommutative geometry / poisson geometry / 一般複素幾何 / 一般ケーラー幾何 / Courant algebroid / symplectic geometry / bi-Hermitian structure / 非可換幾何 / 幾何学的漸近解析 / 微分幾何 / 特異点論 / 局所指数定理 / 変形量子化 / Poisson幾何 / symplectic幾何 / asymptoric analysis / index theorem / ディラック作用素 / ポアソン構造 / エータ関数 / 圏 |
|---|
| Outline of Final Research Achievements |
First, I introduced non-commutative deformation of structure sheaves of schemes, and I cnstructed a concrete example via complex projective spaces. Furthermore, I computed exponential map with respect to a new product. Second, with Hideki Omori, Yoshiaki Maeda, Akira Yoshioka, we studied the ordering problem on a flat space, and convergent problem with respect to a parameter h. Third, with Yasushi Homma, Tatsuya Tate, we sudy eta functions for Dirac operators on 3-manifolds (e.g. Heisenberg manifold, Lenz spaces etc.). Fourth, with Tadashi Taniguchi, we study quantization of super Calabi-Yau twistor spaces endowed with super Poisson structure via Penrose double fibration.
|
Report
(6 results)
Research Products
(9 results)
