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arXiv · 1210.1662

Higher weight Gel'fand-Kalinin-Fuks classes of formal Hamiltonian vector fields of symplectic R^2

Kentaro Mikami·Hiroki Kodama·Yasuharu Nakae
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Abstract

In "The Gel'fand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations", arXiv:0910.3414, (October 2009) by D.Kotschick and S.Morita, the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields without constant vector fields on 2n-plane were characterized by two parameters, one is degree and the other is weight. And they obtained those cohomology groups of the 2-plane while their weight <= 10. In this paper, for those cohomology groups of the 2-plane, we succeeded in determining the dimension of cochain complexes by Sp(2,R)-representation theory for their weight even less than 50, thus, we manipulate the Euler characteristic numbers. We also decide our relative Gel'fand-Kalinin-Fuks cohomology groups until whose weight < 20 by getting a concrete matrix representation of the coboundary operator.

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Kentaro Mikami, Hiroki Kodama, Yasuharu Nakae. 2014-02-19. Higher weight Gel'fand-Kalinin-Fuks classes of formal Hamiltonian vector fields of symplectic R^2. https://arxiv.org/abs/1210.1662

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