2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152088We use rudiments of the Seiberg-Witten gluing theory for trivial circle bundles over a Riemann surface to relate de Seiberg-Witten basic classes of two $4$-manifolds containing Riemann surfaces of the same genus and self-intersection zero with those of the $4$-manifold resulting as a connected sum along the surface. We study examples in which this is enough to describe completely the basic classes.AMSLaTeX, 16 pages, no figuresDifferential Geometrytext