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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.
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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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