Geometric K-homology with coefficients

Date

2010-07-28T16:13:45Z

Authors

Deeley, Robin

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Abstract

We construct geometric models for K-homology with coefficients based on the theory of Z/k-manifolds. To do so, we generalize the operations and relations Baum and Douglas put on spinc-manifolds to spinc Z/kZ-manifolds. We then de fine a model for K-homology with coefficients in Z/k using cycles of the form ((Q,P), (E,F), f) where (Q, P) is a spinc Z/k-manifold, (E, F) is a Z/k-vector bundle over (Q, P) and f is a continuous map from (Q, P) into the space whose K-homology we are modelling. Using results of Rosenberg and Schochet, we then construct an analytic model for K-homology with coefficients in Z/k and a natural map from our geometric model to this analytic model. We show that this map is an isomorphism in the case of finite CW-complexes. Finally, using direct limits, we produced geometric models for K-homology with coefficients in any countable abelian group.

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Keywords

K-homology, index theory, z/k-manifolds

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