Every symplectic four-dimensional small cover is aspherical; symplecticity on polygon-product bases equals factor-compatibility, with a non-product example constructed.
Buchstaber and Taras E
2 Pith papers cite this work. Polarity classification is still indexing.
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Small covers as pullbacks from the simplex are equivalently characterized by torsion-free odd-degree integral cohomology, vanishing of the first Steenrod square on even-degree mod 2 cohomology, and relations among integral and mod 2 Betti numbers.
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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.
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Small covers as pullbacks from the simplex
Small covers as pullbacks from the simplex are equivalently characterized by torsion-free odd-degree integral cohomology, vanishing of the first Steenrod square on even-degree mod 2 cohomology, and relations among integral and mod 2 Betti numbers.