Geometric K-homology with coefficients I: ?/K?-cycles and Bockstein sequence

摘要

We construct a Baum-Douglas type model for K-homology with coefficients in ?/k?. The basic geometric object in a cycle is a spin ~c ?/k?-manifold. The relationship between these cycles and the topological side of the Freed-Melrose index theorem is discussed in detail. Finally, using inductive limits, we construct geometric models for K-homology with coefficients in any countable abelian group.