Vol. 7, No. 2, 2022

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An equivariant PPV theorem and Paschke–Higson duality

Moulay-Tahar Benameur and Indrava Roy

Vol. 7 (2022), No. 2, 237–278
Abstract

We state the Paschke–Higson duality theorem for a transformation groupoid. Our proof relies on an equivariant localized and norm-controlled version of the Pimsner–Popa–Voiculescu theorem. The main consequence is the existence of a Higson–Roe exact sequence, involving the Baum–Connes assembly map for such a groupoid.

Keywords
$K\mkern-2mu$-theory, $K\mkern-2mu$-homology, operator algebras, Paschke, Higson–Roe
Mathematical Subject Classification
Primary: 19K33, 19K35, 19K56, 46L05, 46L08
Secondary: 46L80, 46L85
Milestones
Received: 14 April 2021
Revised: 27 March 2022
Accepted: 11 April 2022
Published: 13 September 2022
Authors
Moulay-Tahar Benameur
Institut Montpellierain Alexander Grothendieck
Université Montpellier et CNRS
Campus Triolet
Montpellier
France
Indrava Roy
Institute of Mathematical Sciences (HBNI)
Chennai
India