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

Abstract

The aim of this paper is to construct the Poincaré isomorphism in K-theory on manifolds with edges. We show that the Poincaré isomorphism can naturally be constructed in the framework of noncommutative geometry. More precisely, to a manifold with edges we assign a noncommutative algebra and construct an isomorphism between the K-group of this algebra and the K-homology group of the manifold with edges viewed as a compact topological space.