Title:
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The type semigroup, comparison, and almost finiteness for ample groupoids
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Author:
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Ara, P.; Bönicke, C.; Bosa, J.; Li, K.
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Abstract:
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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. © The Author(s), 2021. Published by Cambridge University Press. |
Publication date:
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2021-10-27 |
Subject (UDC):
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51 - Matemàtiques |
Subject(s):
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Almost finite groupoids; amenability; dynamical comparison; type semigroup |
Rights:
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L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Pages:
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40 p. |
Document type:
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Article Article - Accepted version |
DOI:
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10.1017/etds.2021.115
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Published by:
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Cambridge University Press
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Publish at:
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Ergodic Theory and Dynamical Systems
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