Signatures of foliated surface bundles and the symplectomorphism groups of surfaces
Preprint
Abstract
For any closed oriented surface F of genus at least three, we prove the existence of foliated F-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 on the fiber. We relate the cohomology class represented by the transverse symplectic form to a crossed homomorphism from the symplectomophism group of the fiber to its first real cohomology. This crossed homomorphism extends the flux homomorphism defined on the identity component of the symplectomorphism group.Keywords
All Related Versions
- Version 1, 2003-05-13, ArXiv
- Published version: Topology, 44 (1), 131.
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