The relative Mishchenko--Fomenko higher index and almost flat bundles II: Almost flat index pairing

2019/08/28 by Yosuke Kubota, Kubota, Yosuke · 1 citation
Mathematics · #46L80 #58J32 #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Primary 19K56 #Secondary 19K35

paper · pdf · doi:10.48550/arxiv.1908.10733

openalex publication_date 2019/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the second part of a series of papers which bridges the Chang--Weinberger--Yu relative higher index and geometry of almost flat hermitian vector bundles on manifolds with boundary. In this paper we apply the description of the relative higher index given in Part I to provide the relative version of the Hanke--Schick theorem, which relates the relative higher index with index pairing of a K-homology cycle with almost flat relative vector bundles. We also deal with the quantitative version and the dual problem of this theorem.

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