2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68889Let 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).Changed content; Latex; Comments are welcomeSymplectic Geometry53D05, 57R57, 55R20text