Work

Paschke duality and assembly maps

Year: 2021

Type: preprint

Abstract: We construct a natural transformation between two versions of $G$-equivariant $K$-homology with coefficients in a $G$-$C^{*}$-category for a countable discrete group $G$. Its domain is a coarse geometric $K$-homology and its target is the usual analytic $K$-homology. Following classical terminology, we call this transformation the Paschke transformation. We show that under certain finiteness assumptions on a $G$-space $X$, the Paschke transformation is an equivalence on $X$. As an application, we provide a direct comparison of the homotopy theoretic Davis-Lück assembly map with Kasparov's analytic assembly map appearing in the Baum-Connes conjecture.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2107.02843

Authors: Bunke, Ulrich, Engel, Alexander, Land, Markus

Institutions: University of Regensburg, University of Münster, Universität Greifswald, University of Copenhagen, Ludwig-Maximilians-Universität München

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, Deutsche Forschungsgemeinschaft, Danmarks Grundforskningsfond

Awards: G1652504919, G1753692188, Neue Methoden in algebraischer Ktheorie, G2418827033, EXC 2044: Mathematik Münster: Dynamik – Geometrie – Struktur, Copenhagen Center for Geometry and Topology (GeoTop), Makroskopische Invarianten von Mannigfaltigkeiten, G6938060324, G93948134

OpenAlex ID: W3181200570

Cites: 32

Cited by: 1

Related to: 20