2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77276For a compact connected manifold M of dimension n greater than 3 and with no metric of positive scalar curvature, we prove that the Yamabe invariant is unchanged under surgery on spheres of dimension different from 1, n-2 and n-1. We use this result to give new computations of the invariant in dimension four and display new examples of 4-manifolds which do not admit Einstein metrics.10 pages, LatexDifferential Geometry53C25, 53C99text