Geometric K-homology with coefficients I

Abstract

We construct a Baum-Douglas type model for $K$-homology with coefficients in $\mathbb{Z}/k\mathbb{Z}$. The basic geometric object in a cycle is a $spi{n}^c$ $\mathbb{Z}/k\mathbb{Z}$-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.

22 pages, 2 figures

References in corpus (2)

• On the Equivalence of Geometric and Analytic K-Homology
• Bivariant K-theory via correspondences

Cited by in corpus (1)

• Applying geometric K-cycles to fractional indices