Poincare isomorphism in K-theory on manifolds with edges

TL;DR

This paper constructs a Poincare isomorphism in K-theory for manifolds with edges using noncommutative geometry, linking algebraic and topological K-theory groups.

Contribution

It introduces a novel framework for the Poincare isomorphism on manifolds with edges within noncommutative geometry, connecting algebraic and topological K-theory.

Findings

Established a noncommutative algebra associated with manifolds with edges

Constructed an isomorphism between K-groups of the algebra and K-homology of the manifold

Demonstrated the naturality of the Poincare isomorphism in this setting

Abstract

The aim of this paper is to construct the Poincare isomorphism in K-theory on manifolds with edges. We show that the Poincare 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.