2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60454We give a simple proof of the cobordism invariance of the index of an elliptic operator. The proof is based on a study of a Witten-type deformation of an extension of the operator to a complete Riemannian manifold. One of the advantages of our approach is that it allows to treat directly general elliptic operator which are not of Dirac type.Some references are added, some minor changes are made. To appear in Proc. of AMSSpectral TheoryDifferential Geometrytext