Geodesic
Homotopy classification of~elliptic~operators on stratified manifolds
Izvestiya. Mathematics , Tome 71 (2007) no. 6, pp. 1167-1192

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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. 
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     author = {V. E. Nazaikinskii and A. Yu. Savin and B. Yu. Sternin},
     title = {Homotopy classification of~elliptic~operators on stratified manifolds},
     journal = {Izvestiya. Mathematics },
     pages = {1167--1192},
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     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2007_71_6_a4/}
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V. E. Nazaikinskii; A. Yu. Savin; B. Yu. Sternin. Homotopy classification of~elliptic~operators on stratified manifolds. Izvestiya. Mathematics , Tome 71 (2007) no. 6, pp. 1167-1192. http://geodesic.mathdoc.fr/item/IM2_2007_71_6_a4/