Nonfree almost finite actions for locally finite-by-virtually Z groups

Li K, Ma X (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Journal of the London Mathematical Society-Second Series London Mathematical Society

Book Volume: 110

Article Number: e12959

Journal Issue: 1

DOI: 10.1112/jlms.12959

Abstract

In this paper, we study almost finiteness and almost finiteness in measure of nonfree actions. Let (Formula presented.) be a minimal action of a locally finite-by-virtually (Formula presented.) group (Formula presented.) on the Cantor set (Formula presented.). We prove that under certain assumptions, the action (Formula presented.) is almost finite in measure if and only if (Formula presented.) is essentially free. As an application, we obtain that any minimal topologically free action of a virtually (Formula presented.) group on an infinite compact metrizable space with the small boundary property is almost finite. This is the first general result, assuming only topological freeness, in this direction, and these lead to new results on uniform property (Formula presented.) and (Formula presented.) -stability for their crossed product (Formula presented.) -algebras. Some concrete examples of minimal topological free (but nonfree) subshifts are provided.

Authors with CRIS profile

Kang Li Juniorprofessur für Mathematik (Darstellungstheorie und Operatoralgebren)

Involved external institutions

York University CA Canada (CA)

How to cite

APA:

Li, K., & Ma, X. (2024). Nonfree almost finite actions for locally finite-by-virtually Z groups. Journal of the London Mathematical Society-Second Series, 110(1). https://doi.org/10.1112/jlms.12959

MLA:

Li, Kang, and Xin Ma. "Nonfree almost finite actions for locally finite-by-virtually Z groups." Journal of the London Mathematical Society-Second Series 110.1 (2024).

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