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For any closed oriented surface Σg of genus g?3, we prove the existence of foliatedΣg-bundles over surfaces such that the signatures of the total spaces are non-zero. We can arrange that the total holonomy of the horizontal foliations preserve a prescribed symplectic form ω on the fiber. We relate the cohomology class represented by the transverse symplectic form to a crossed homomorphism which is an extension of the flux homomorphism from the identity component to the whole group of symplectomorphisms of Σg with respect to the symplectic form ω. 相似文献
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