Branched coarse coverings and transfer maps

2025/02/03 by Ulrich Bunke, Bunke, Ulrich
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2502.01497

openalex publication_date 2025/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the concepts of branched coarse coverings and transfers between coarse homology theories along them. We show that various versions of coarse K-homology theories admit the additional structure of transfers. We show versions of Atiyah's L²-index theorem in coarse homotopy theory and apply them to give a new argument for the corresponding step in Higson's counterexample to the coarse Baum-Connes conjecture.

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