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

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.

20 pages

References in corpus (1)

• The Gelfand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations

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• Another proof to Kotschick-Morita's Theorem of Kontsevich homomorphism
• Lower weight Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R^4
• First Betti number of weighted homology group of Hamiltonian vector fields on symplectic tori