Geometric research of 2-vector fields
| Project/Area Number |
20540059
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Akita University |
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Principal Investigator |
MIKAMI Kentaro Akita University, 工学資源学研究科, 教授 (70006592)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | ポアソン / スカウテン括弧 / 同変コホモロジー / ゲルファント / クリフォード代数 / スカウテン括弧積 / コホモロジー / 同変 / ゲルファント・フックス / 自明表現 / 一般複素構造 / ポアソン構造 / ゲルファント・フックスコホモロジー / 群不変コホモロジー / ポアソンコホモロジー群 / 幾何学 / 一般化複素構造 |
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| Research Abstract |
The Schouten bracket is a main tool in Poisson geometry and there are several trials of understanding of meaning of the Schouten bracket. Using some idea of generalized complex geometry, we investigated the essence of the Schouten bracket in the framework of Clifford algebra. Also, we have gotten complete understanding of difference of our Schouten bracket and the other bracket in I. Vaissman's book "Lectures on the geometry of Poisson manifolds"(Birkhauser). Concerning to Gel'fand-Kalinin-Fuks cohomology of formal Hamiltonian vector fields on symplectic 2-plane, we prepared programs of Maple which is a computer software of symbol calculus and also several computers, and made a success in getting more information of Gel'fand-Kalini-Fuks cohomology until weight 18 comparing D.Kotschick and S.Morita's work "The Gel'fand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations".
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Report
(4 results)
Research Products
(7 results)
