A cohomological Seiberg–Witten invariant emerging from the adjunction inequality. Issue 1 (11th April 2022)

• Record Type: Journal Article
• Authors: Konno, Hokuto
• Is Part Of: Journal of topology. Volume 15:Issue 1(2022)
• Page Start: 108
• Page End: 167
• Publication Date: 2022-04-11
• Subjects: Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12215
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: We construct an invariant of closed spin c $\mathrm{spin}^c$ 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.