A cohomological Seiberg-Witten invariant emerging from the adjunction inequality

2017/04/19 by Hokuto Konno, Konno, Hokuto
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1704.05859

openalex publication_date 2017/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an invariant of closed \rm spin^c 4-manifolds using families of Seiberg-Witten equations. This invariant is formulated as a cohomology class on a certain abstract simplicial complex consisting of embedded surfaces of a 4-manifold. We also give examples of 4-manifolds which admit positive scalar curvature metrics and for which this invariant does not vanish. This non-vanishing result of our invariant provides a new class of adjunction-type genus constraints on configurations of embedded surfaces in a 4-manifold whose Seiberg-Witten invariant vanishes.

Related

• Constraints on embedded spheres and real projective planes in 4-manifolds from Seiberg-Witten theory
• Relative Seiberg-Witten and Ozsvath-Szabo 4-dimensional invariants with respect to embedded surfaces
• A surgery formula for Seiberg-Witten invariants
• Some refined higher type adjunction inequalities on 4-manifolds
• Seiberg-Witten-Floer homology of a surface times a circle for non-torsion spin-c structures