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geometric cycles

Journal of K-Theory (1)

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Geometric K-homology with coefficients I: ℤ/kℤ-cycles and Bockstein sequence
Robin J. Deeley
Journal:

Journal of K-Theory / Volume 9 / Issue 3 / June 2012

Published online by Cambridge University Press:

04 November 2011, pp. 537-564

Print publication:

June 2012
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We construct a Baum-Douglas type model for K-homology with coefficients in ℤ/kℤ. The basic geometric object in a cycle is a spinc ℤ/kℤ-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.