Geometric $K$-homology with coefficients II

Details Geometric $K$-homology with coefficients II Geometric $K$-homology with coefficients II

2011-01-04

arxiv.org/abs/1101.0703v1

Mathematics

K-Theory and Homology

25 pages, 4 figures

Scientific paper

We discuss the analytic aspects of the geometric model for $K$-homology with coefficients in $\mathbb{Z}/k\mathbb{Z}$ constructed in "Geometric K-homology with coefficients I". 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 $spin^c$ manifolds, geometric K-homology, and Atiyah-Singer index theorem.

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