Abstract
We show that every positive definite closed –manifold with and without –handles has a vanishing stable cohomotopy Seiberg–Witten invariant, and thus admits no symplectic structure. We also show that every closed oriented –manifold with and and without –handles admits no symplectic structure for at least one orientation of the manifold. In fact, relaxing the –handle condition, we prove these results under more general conditions which are much easier to verify.
Citation
Kouichi Yasui. "Geometrically simply connected $4$–manifolds and stable cohomotopy Seiberg–Witten invariants." Geom. Topol. 23 (5) 2685 - 2697, 2019. https://doi.org/10.2140/gt.2019.23.2685
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