On the Poincaré isomorphism in K-theory on manifolds with edges

In this paper, the Poincaré isomorphism in K -theory on manifolds with edges is constructed. It is shown that the Poincaré isomorphism can be naturally constructed in terms of noncommutative geometry. More precisely, we obtain a correspondence between a manifold with edges and a noncommutative algebra and establish an isomorphism between the K -group of this algebra and the K -homology group of the manifold with edges, which is considered as a compact topological space.