An affirmative answer to a conjecture for Metoki class

Abstract

In "The {G}el'fand-{K}alinin-{F}uks class and characteristic classes of transversely symplectic foliations" arXiv:0910.3414, Kotschick and Morita showed that the Gel'fand-Kalinin-Fuks class in $\ds\HGF{7}{2}{}{8}$ is decomposed as a product $\eta \wedge \omega$ of some leaf cohomology class $\eta$ and a transverse symplectic class $\omega$. We show that the same formula holds for Metoki class, which is a non-trivial element in $\ds \HGF{9}{2}{}{14}$. The result was conjectured by Kotschick and Morita, where they studied characteristic classes of symplectic foliations due to Kontsevich. Our proof depends on Groebner Basis theory using computer calculations.

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References in corpus (5)

• The Gelfand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations
• Higher weight Gel'fand-Kalinin-Fuks classes of formal Hamiltonian vector fields of symplectic R^2
• The relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on 6-dimensional plane
• Another proof to Kotschick-Morita's Theorem of Kontsevich homomorphism
• A Groebner-bases algorithm for the computation of the cohomology of Lie (super) algebras

Cited by in corpus (2)

• Cohomology groups of homogeneous Poisson structures
• Another proof to Kotschick-Morita's Theorem of Kontsevich homomorphism