Vol. 4, No. 4, 2019

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A Baum–Connes conjecture for singular foliations

Iakovos Androulidakis and Georges Skandalis

Vol. 4 (2019), No. 4, 561–620

We consider singular foliations whose holonomy groupoid may be nicely decomposed using Lie groupoids (of unequal dimension). We construct a K-theory group and a natural assembly type morphism to the K-theory of the foliation C-algebra generalizing to the singular case the Baum–Connes assembly map. This map is shown to be an isomorphism under assumptions of amenability. We examine some simple examples that can be described in this way and make explicit computations of their K-theory.

Baum–Connes conjecture, singular foliations, singularity height
Mathematical Subject Classification 2010
Primary: 46L87
Secondary: 19K35, 19K56, 22A22, 53C12
Received: 5 February 2018
Revised: 23 April 2019
Accepted: 7 May 2019
Published: 10 January 2020
Iakovos Androulidakis
Department of Mathematics
National and Kapodistrian University of Athens
Georges Skandalis
UFR de Mathématiques
Université Paris Diderot
Sorbonne Paris Cité Sorbonne Universités
75205 Paris CEDEX 13