A Going-Down principle for ample groupoids and the Baum-Connes conjecture

Bönicke, C. (2020) A Going-Down principle for ample groupoids and the Baum-Connes conjecture. Advances in Mathematics, 372, 107314. (doi: 10.1016/j.aim.2020.107314)

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Abstract

We study a Going-Down (or restriction) principle for ample groupoids and its applications. The Going-Down principle for locally compact groups was developed by Chabert, Echterhoff and Oyono-Oyono and allows to study certain functors, that arise in the context of the topological K-theory of a locally compact group, in terms of their restrictions to compact subgroups. We extend this principle to the class of ample Hausdorff groupoids using Le Gall's groupoid equivariant version of Kasparov's bivariant KK-theory. Moreover, we provide an application to the Baum-Connes conjecture for ample groupoids which are strongly amenable at infinity. This result in turn is then used to relate the Baum-Connes conjecture for an ample groupoid group bundle which is strongly amenable at infinity to the Baum-Connes conjecture for the fibres.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bonicke, Dr Christian
Authors: Bönicke, C.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
Publisher:Elsevier
ISSN:0001-8708
ISSN (Online):1090-2082
Published Online:28 July 2020
Copyright Holders:Copyright © 2020 Elsevier Inc.
First Published:First published in Advances in Mathematics 372: 107314
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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