2010 Fiscal Year Final Research Report
Localization of Riemann-Roch number via perturbation of Dirac operator and its applications
| Project/Area Number |
21840045
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Gakushuin University |
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Principal Investigator |
HAJIME Fujita Gakushuin University, 理学部, 助教 (50512159)
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| Co-Investigator(Renkei-kenkyūsha) |
FURUTA Iki 東京大学, 大学院・数理科学研究科, 教授 (50181459)
YOSHIDA Takahiko 明治大学, 先端数理科学インスティテュート, 研究員 (70451903)
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| Project Period (FY) |
2009 – 2010
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| Keywords | ディラック作用素 / 指数理論 / 局所化 |
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| Research Abstract |
We developed an analytic index theory with several topological properties and proved the product formula of the indices. We use perturbation of Dirac operators on open manifolds whose ends are covered by torus bundles with an appropriate compatibility conditions. As an applications we gave geometric proofs of Guillemin-Sternberg's quantization conjecture for Hamiltonian torus action and Danilov's theorem for toric manifolds.
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