Vol. 4, No. 4, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
Ethics Statement
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Author Index
To Appear
 
Other MSP Journals
A Baum–Connes conjecture for singular foliations

Iakovos Androulidakis and Georges Skandalis

Vol. 4 (2019), No. 4, 561–620
Abstract

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.

Keywords
Baum–Connes conjecture, singular foliations, singularity height
Mathematical Subject Classification 2010
Primary: 46L87
Secondary: 19K35, 19K56, 22A22, 53C12
Milestones
Received: 5 February 2018
Revised: 23 April 2019
Accepted: 7 May 2019
Published: 10 January 2020
Authors
Iakovos Androulidakis
Department of Mathematics
National and Kapodistrian University of Athens
Panepistimiopolis
Athens
Greece
Georges Skandalis
UFR de Mathématiques
Université Paris Diderot
Sorbonne Paris Cité Sorbonne Universités
UPMC Paris 06, CNRS, IMJ-PRG
75205 Paris CEDEX 13
France