Every symplectic four-dimensional small cover is aspherical; symplecticity on polygon-product bases equals factor-compatibility, with a non-product example constructed.
van der Blij,An invariant of quadratic forms mod8, Indag
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Symplectic small covers in dimension four
Every symplectic four-dimensional small cover is aspherical; symplecticity on polygon-product bases equals factor-compatibility, with a non-product example constructed.