2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70523It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered boundary. The main ingredients of the proof of these results are: an analog of the Atiyah-Singer difference construction in the noncommutative case and an analog of Poincare isomorphism in K-theory for our singular manifolds. As applications we give a formula in topological terms for the obstruction to Fredholm problems on manifolds with singularities and a formula for K-groups of algebras of pseudodifferential operators.revised version; 25 pages; section with applications expandedOperator AlgebrasAnalysis of PDEsK-Theory and Homology58J05 19K33 35S35 47L15text