2013 Fiscal Year Final Research Report
Localization of Riemann-Roch number via torus bundles and its application
| Project/Area Number |
23740059
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Japan Women's University (2012-2013)
Gakushuin University (2011) |
|---|
Principal Investigator |
FUJITA Hajime 日本女子大学, 理学部, 講師 (50512159)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
FURUTA Mikio 東京大学, 大学院・数理科学研究科, 教授 (50181459)
YOSHIDA Takahiko 明治大学, 理工学部・数学科, 講師 (70451903)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Keywords | Dirac型作用素の指数 / 指数の局所化 / シンプレクティック幾何 / 同変指数 |
|---|
| Research Abstract |
Main results of this research are the following three.
1. We substantially revised the paper concerning a formulation of local index theory via torus bundles and a perturbation along the fibers. We also revised the paper concerning its application to a geometric proof of the quantization conjecture for Hamiltonian torus action. Both papers are accepted to Comm. Math. Phys.. 2. We computed the local index arising from the geodesic flow on the cotangent bundle of the standard sphere. In the computation we used the description of a compactification of the cotangent bundle and behavior of the local index under the symplectic cutting. 3. We gave a formulation of a kind of circle equivariant index. We investigated difference and similarity between our equivariant index and the theory of transverse index due to Braverman, Ma-Zhang, and we wrote a paper on the subject.
|
