Abstract
Let E be the total space of a locally trivial torus bundle over a surface Σ g of genus g > 1. Using Seiberg–Witten theory and spectral sequences, we prove that E carries a symplectic structure if and only if the homology class of the fiber [T2] is nonzero in H2(E, ℝ).
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Mathematics Subject Classifications (2000): 53D05, 57R57, 55R20.
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Walczak, R. Existence of Symplectic Structures on Torus Bundles Over Surfaces. Ann Glob Anal Geom 28, 211–231 (2005). https://doi.org/10.1007/s10455-005-8500-z
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DOI: https://doi.org/10.1007/s10455-005-8500-z