Analytic and topological index maps with values in the K-theory of\n mapping cones

2013/02/18 by Robin J. Deeley, Deeley, Robin J.
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1302.4296

openalex publication_date 2013/02/18 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Index maps taking values in the K-theory of a mapping cone are defined and\ndiscussed. The resulting index theorem can be viewed in analogy with the\nFreed-Melrose index theorem. The framework of geometric K-homology is used in\na fundamental way. In particular, an explicit isomorphism from a geometric\nmodel for K-homology with coefficients in a mapping cone, C_\φ, to\nKK(C(X),C_\φ) is constructed.\n

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