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Kotschick and Morita recently discovered factorisations of characteristicclasses of transversally symplectic foliations that yield new characteristicclasses in foliated cohomology. We describe an alternative construction of suchfactorisations and construct examples of topologically trivial foliated vectorbundles for which these characteristic classes are non-trivial. This shows thatthe foliated cohomology classes of Kotschick and Morita carry information thatis not merely topological.

On foliated characteristic classes of transversally symplectic foliations