Geometric K-homology with coefficients II

2011/01/04 by Robin J. Deeley, Deeley, Robin J.
Computer Science · Mathematics · #19K33 (Primary) 19K56 #46L85 #55N20 (Secondary) #Advanced Operator Algebra Research #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Topological and Geometric Data Analysis #math.KT #msc:19K33 #msc:19K56 #msc:46L85 #msc:55N20

paper · pdf · doi:10.48550/arxiv.1101.0703

16 pages, 2 figures

openalex publication_date 2011/01/04 · arxiv created 2013/02/18 · arxiv updated 2013/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the analytic aspects of the geometric model for K-homology with coefficients in ℤ/kℤ 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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