2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147616We give the definition of the Seiberg-Witten-Floer homology group for a homology 3-sphere. Its Euler characteristic number is a Casson-type invariant. For a four-manifold with boundary a homology sphere, a relative Seiberg-Witten invariant is defined taking values in the Seiberg-Witten-Floer homology group, these relative Seiberg-Witten invariants are applied to certain homology spheres bounding Stein surfaces.LaTex; 30 pages, fix some LaTex problems, cut one subsection, update the relation with equivariant Seiberg-Witten-Floer homology and one application to Stein surface with boundaryDifferential Geometrytext