An affirmative answer to a conjecture on the Metoki class

摘要

In [6], Kotschick and Morita showed that the Gel'fand-Kalinin-Fuks class in H_(GF)~7(ηam_2,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 H_(GF)~9(ηam_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.