Branched coarse coverings and transfer maps
Ulrich Bunke

TL;DR
This paper introduces branched coarse coverings and transfer maps in coarse homology, demonstrating their structure in coarse K-homology and applying these concepts to Atiyah's L^2-index theorem and Higson's counterexample to the coarse Baum-Connes conjecture.
Contribution
It develops the theory of branched coarse coverings and transfers, extending coarse K-homology with new structures and applying them to important index theorems and conjectures.
Findings
Coarse K-homology theories admit transfer structures.
Established versions of Atiyah's L^2-index theorem in coarse homotopy theory.
Provided a new argument related to Higson's counterexample to the coarse Baum-Connes conjecture.
Abstract
We introduce the concepts of branched coarse coverings and transfers between coarse homology theories along them. We show that various versions of coarse -homology theories admit the additional structure of transfers. We show versions of Atiyah's -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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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology
