Geometric K-homology with coefficients II: The Analytic Theory and Isomorphism

We discuss the analytic aspects of the geometric model for Khomology with coefficients in Z/kZ constructed in [11]. In particular, using results of Rosenberg and Schochet, we construct a map from this geometric model to its analytic counterpart. Moreover, we show that this map is an isomorphism in the case of a finite CW-complex. The relationship between this map and the Freed-Melrose index theorem is also discussed. Many of these results are analogous to those of Baum and Douglas in the case of spinc manifolds, geometric K-homology, and Atiyah-Singer index theorem.