| 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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| 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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