An affirmative answer to a conjecture on the Metoki class

In [6], Kotschick and Morita showed that the Gel'fand-Kalinin-Fuks class in H-GF(7) (ham(2), sp(2, R))(8) is decomposed as a product eta boolean AND omega of some leaf cohomology class eta and a transverse symplectic class omega. We show that the same formula holds for the Metoki class, which is a non-trivial element in H-GF(9) (ham(2), 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 Grobner Basis theory using computer calculations.