The simple type conjecture for mod 2 Seiberg–Witten invariants
Tsuyoshi Kato
Kyoto University, JapanNobuhiro Nakamura
Fukushima Medical University, JapanKouichi Yasui
Osaka University, Japan
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Abstract
We prove that, under a simple condition on the cohomology ring, every closed 4-manifold has mod 2 Seiberg–Witten simple type. This result shows that there exists a large class of topological 4-manifolds such that all smooth structures have mod 2 simple type, and yet some have non-vanishing (mod 2) Seiberg–Witten invariants. As corollaries, we obtain adjunction inequalities and show that, under a mild topological condition, every geometrically simply connected closed 4-manifold has the vanishing mod 2 Seiberg–Witten invariant for at least one orientation.
Cite this article
Tsuyoshi Kato, Nobuhiro Nakamura, Kouichi Yasui, The simple type conjecture for mod 2 Seiberg–Witten invariants. J. Eur. Math. Soc. 25 (2023), no. 12, pp. 4869–4877
DOI 10.4171/JEMS/1297