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Geometric K-homology with coefficients II: The Analytic Theory and Isomorphism

Published online by Cambridge University Press:  28 August 2013

Robin J. Deeley
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Abstract

We discuss the analytic aspects of the geometric model for K-homology with coefficients in ℤ/kℤ constructed in [12]. 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 spinc manifolds, geometric K-homology, and Atiyah-Singer index theorem.

Keywords

K-homologyℤ/kℤ-manifoldsthe Freed-Melrose index theoremPrimary: 19K33Secondary: 19K5646L8555N20

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Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 2 , October 2013 , pp. 235 - 256
Copyright
Copyright © ISOPP 2013 

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