The type semigroup, comparison and almost finiteness for ample groupoids

Autor:	Ara, Pere, Bönicke, Christian, Bosa, Joan, Li, Kang
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems Mathematics - Metric Geometry Mathematics - Operator Algebras 22A22
Druh dokumentu:	Working Paper
Popis:	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. Comment: Revised version. To appear in Ergodic Theory and Dynamical Systems
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.00376 Zobrazit plný text záznamu View this record from Arxiv