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On the dynamic asymptotic dimension of étale groupoids

Lookup NU author(s): Dr Christian BönickeORCiD

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

Abstract

We investigate the dynamic asymptotic dimension for étale groupoids introduced by Guentner, Willett and Yu. In particular, we establish several permanence properties, including estimates for products and unions of groupoids. We also establish invariance of the dynamic asymptotic dimension under Morita equivalence. In the second part of the article, we consider a canonical coarse structure on an étale groupoid and compare the asymptotic dimension of the resulting coarse space with the dynamic asymptotic dimension of the underlying groupoid.

Publication metadata

Author(s): Bönicke C

Publication type: Article

Publication status: Published

Journal: Mathematische Zeitschrift

Year: 2024

Volume: 307

Online publication date: 26/04/2024

Acceptance date: 15/03/2024

Date deposited: 21/03/2024

ISSN (print): 0025-5874

ISSN (electronic): 1432-1823

Publisher: Springer Nature

URL: https://doi.org/10.1007/s00209-024-03492-x

DOI: 10.1007/s00209-024-03492-x

Data Access Statement: Not applicable.

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