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.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/2911 |
| Date | 28 July 2010 |
| Creators | Deeley, Robin |
| Contributors | Emerson, Heath |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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