An affirmative answer to a conjecture on the Metoki class

Abstract

In [6], Kotschick and Morita showed that the Gel'fand–Kalinin–Fuks class in H⁷_GF ($\mathfrak{ham}$₂, $\mathfrak{sp}$(2,ℝ))₈ is decomposed as a product η ∧ ω of some leaf cohomology class η and a transverse symplectic class ω. We show that the same formula holds for the Metoki class, which is a non-trivial element in H⁹_GF ($\mathfrak{ham}$₂, $\mathfrak{sp}$(2,ℝ))₁₄. The result was conjectured in [6], where they studied characteristic classes of transversely symplectic foliations due to Kontsevich. Our proof depends on Gröbner Basis theory using computer calculations.