On the Poincaré isomorphism in \(K\)-theory on manifolds with edges (Q461769)

Manifolds with edges are a class of manifolds with a specific kind of nonisolated singularities. They are obtained by collapsing the fibers of the smooth bundle with a smooth closed base whose total space is the boundary of the manifold \(M\). The authors construct the Poincaré isomorphism between the \(K\)-group of a certain noncommutative algebra \(A\) and the group of analytic \(K\)-cohomologies of the algebra of continuous functions on \(M\). This is a generalization of the classical Poincaré isomorphism as the algebra \(A\) is the algebra of continuous functions when \(M\) is a smooth manifold.