On extensions of a symplectic class

Katsuhiko Kuribayashi

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arXiv · 1108.0218

On extensions of a symplectic class

Katsuhiko Kuribayashi

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Abstract

Let F be a fibration on a simply-connected base with symplectic fibre (M, ω). Assume that the fibre is nilpotent and T^{2k}-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.

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Katsuhiko Kuribayashi. 2011-08-03. On extensions of a symplectic class. https://arxiv.org/abs/1108.0218

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