Geometrically simply connected 4-manifolds and stable cohomotopy Seiberg-Witten invariants
| Autor: | Yasui, Kouichi |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Geom. Topol. 23 (2019) 2685-2697 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/gt.2019.23.2685 |
| Popis: | We show that every positive definite closed 4-manifold with $b_2^+>1$ and without 1-handles has a vanishing stable cohomotopy Seiberg-Witten invariant, and thus admits no symplectic structure. We also show that every closed oriented 4-manifold with $b_2^+\not\equiv 1$ and $b_2^-\not\equiv 1\pmod{4}$ and without 1-handles admits no symplectic structure for at least one orientation of the manifold. In fact, relaxing the 1-handle condition, we prove these results under more general conditions which are much easier to verify. Comment: 9 pages, exposition improved, to appear in Geometry & Topology |
| Databáze: | arXiv |
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