Ara, P., Bonicke, C. , Bosa, J. and Li, K. (2023) The type semigroup, comparison and almost finiteness for ample groupoids. Ergodic Theory and Dynamical Systems, 43(2), pp. 361-400. (doi: 10.1017/etds.2021.115)
Text
252055.pdf - Accepted Version Available under License Creative Commons Attribution Non-commercial No Derivatives. 680kB |
Abstract
We prove that a minimal second countable ample groupoid has dynamical comparison if and only if its type semigroup is almost unperforated. Moreover, we investigate to what extent a not necessarily minimal almost finite groupoid has an almost unperforated type semigroup. Finally, we build a bridge between coarse geometry and topological dynamics by characterizing almost finiteness of the coarse groupoid in terms of a new coarsely invariant property for metric spaces, which might be of independent interest in coarse geometry. As a consequence, we are able to construct new examples of almost finite principal groupoids lacking other desirable properties, such as amenability or even a-T-menability. This behaviour is in stark contrast to the case of principal transformation groupoids associated to group actions.
Item Type: | Articles |
---|---|
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Bonicke, Dr Christian and Bosa, Dr Joan |
Authors: | Ara, P., Bonicke, C., Bosa, J., and Li, K. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Ergodic Theory and Dynamical Systems |
Publisher: | Cambridge University Press |
ISSN: | 0143-3857 |
ISSN (Online): | 1469-4417 |
Published Online: | 27 October 2021 |
Copyright Holders: | Copyright © 2021 The Authors |
First Published: | First published in Ergodic Theory and Dynamical Systems 43(2): 361-400 |
Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
University Staff: Request a correction | Enlighten Editors: Update this record