Algebraic invariants for group actions on the Cantor set
type: Item
instance of: scholarly article
title: Algebraic invariants for group actions on the Cantor set
zbMATH Open document ID: 1490.37010
DOI: 10.1007/978-3-030-62497-2_44
publication date: 2021-12-10T00:00:00Z
review text: This is a very condensed survey of a series of results by many authors concerning Cantor systems, i.e., continuous actions of a countable group \(G\) on the Cantor set \(X\). By an algebraic invariant the author means any algebraic structure which either determines some dynamical properties of the action or depends on the dynamics. The group of automorphisms is an example. The \textit{full group} is another example. It is the subgroup \([G]\) of the group of homeomorphisms \(f\) of \(X\) such that for every \(x\in X\) there exists \(g\in G\) such that \(f(x)=T^g(x)\). More than 40 papers are mentioned in the bibliography. For the entire collection see [\textit{D. R. Wood} (ed.) et al., 2019--20 MATRIX annals. Cham: Springer (2021; Zbl 1459.37002)].
reviewed by: Zdzisław Dzedzej
Mathematics Subject Classification ID: 37B02
Mathematics Subject Classification ID: 37B51
Mathematics Subject Classification ID: 37B10
zbMATH DE Number: 7442387
zbMATH Keywords: algebraic invariants
zbMATH Keywords: Cantor set
zbMATH Keywords: group of automorphisms
author: María Isabel Cortez
MaRDI profile type: Publication
full work available at URL: 978-3-030-62497-2 44
OpenAlex ID: W3132669936
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description: scientific article; zbMATH DE number 7442387