2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77284We prove that the Yamabe invariant of any simply connected smooth manifold of dimension n greater than four is non-negative. Equivalently that the infimum of the L^{n/2} norm of the scalar curvature, over the space of all Riemannian metrics on the manifold, is zero.10 pages, LatexDifferential Geometry53C99text