2020/09/14 by Tsuyoshi Kato, Kato, Tsuyoshi, Nobuhiro Nakamura +3 · 1 citation
Mathematics · #57R55 #57R65 #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT #msc:57R55 #msc:57R65
paper · pdf · doi:10.48550/arxiv.2009.06791
8 pages, minor changes, to appear in Journal of the European Mathematical Society
openalex publication_date 2020/09/14 · arxiv created 2021/03/29 · arxiv updated 2021/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.