2003/05/13 by D. Kotschick, S. Morita
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Geometry and complex manifolds #math.GT #math.SG #msc:57R17 #msc:57R30 #msc:57R50
paper · pdf · doi:10.1016/j.top.2004.05.002
published as Topology 44 (2005), 131--149 · 23 pages
arxiv created 2003/05/13 · openalex publication_date 2004/07/30 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.