2011/08/01 by Katsuhiko Kuribayashi, Kuribayashi, Katsuhiko
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AT #math.SG
paper · pdf · doi:10.48550/arxiv.1108.0218
21 pages. To appear in Differential Geometry and its Applications
openalex publication_date 2011/08/01 · arxiv created 2011/08/03 · arxiv updated 2011/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be a fibration on a simply-connected base with symplectic fibre (M, ω). Assume that the fibre is nilpotent and T2k-separable for some integer k or a nilmanifold. Then our main theorem, Theorem 1.8, gives a necessary and sufficient condition for the cohomology class [ω] to extend to a cohomology class of the total space of F. This allows us to describe Thurston's criterion for a symplectic fibration to admit a compatible symplectic form in terms of the classifying map for the underlying fibration. The obstruction due to Lalond and McDuff for a symplectic bundle to be Hamiltonian is also rephrased in the same vein. Furthermore, with the aid of the main theorem, we discuss a global nature of the set of the homotopy equivalence classes of fibrations with symplectic fibre in which the class [ω] is extendable.