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Baum–Connes conjecture for singular foliations
Iakovos Androulidakis and Georges Skandalis |
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Vol. 4 (2019), No. 4, 561–620
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Abstract |
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We consider singular foliations whose holonomy groupoid may be nicely decomposed using Lie groupoids (of unequal dimension). We construct a -theory group and a natural assembly type morphism to the -theory of the foliation -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 -theory. |
Keywords
Baum–Connes conjecture, singular foliations, singularity
height
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Mathematical Subject Classification 2010
Primary: 46L87
Secondary: 19K35, 19K56, 22A22, 53C12
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Milestones
Received: 5 February 2018
Revised: 23 April 2019
Accepted: 7 May 2019
Published: 10 January 2020
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Authors |
| Iakovos Androulidakis | |
| Department of Mathematics National and Kapodistrian University of Athens Panepistimiopolis Athens Greece |
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| Georges Skandalis | |
| UFR de Mathématiques Université Paris Diderot Sorbonne Paris Cité Sorbonne Universités UPMC Paris 06, CNRS, IMJ-PRG 75205 Paris CEDEX 13 France |
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