Homotopy classification of elliptic operators on stratified manifolds

Abstract

We give a homotopy classification of elliptic operators on a stratified manifold. Namely, we establish an isomorphism between the set of elliptic operators modulo stable homotopy and the K-homology group of the manifold. By way of application, we obtain an explicit formula for the obstruction of Atiyah-Bott type to the existence of Fredholm problems in the case of stratified manifolds.