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Existence of symplectic structures on torus bundles over surfaces

Rafal Walczak
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Abstract

Let E be the total space of a locally trivial torus bundle over the surface Σ_g of genus g>1. Using the Seiberg--Witten theory and spectral sequences we prove that E carries a symplectic structure if and only if the homology class of the fiber [T^2] is nonzero in H_2(E,R).

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Rafal Walczak. 2004-04-20. Existence of symplectic structures on torus bundles over surfaces. https://arxiv.org/abs/math/0310261

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