2010 Fiscal Year Final Research Report

Geometric research of 2-vector fields

Research Project

Project/Area Number	20540059
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Geometry
Research Institution	Akita University
Principal Investigator	MIKAMI Kentaro Akita University, 工学資源学研究科, 教授 (70006592)
Project Period (FY)	2008 – 2010
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
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".