Bounded topological orbit equivalence and \(C^*\)-algebras
type: Item
instance of: scholarly article
title: Bounded topological orbit equivalence and \(C^*\)-algebras
zbMATH Open document ID: 0940.37004
author: Mike Boyle
author: Jun Tomiyama
published in: Journal of the Mathematical Society of Japan
publication date: 2000-04-26T00:00:00Z
review text: This paper has two main results. A purely topological result is the Bounded Orbit Equivalence (Theorem 2.3): if \(S\) and \(T\) are topologically free homeomorphisms of a compact Hausdorff space with the same orbits, and \(Tx=S^{n(x)} x\) where the cocycle \(n\) is bounded, then the complement of a closed nowhere dense set of periodic points is the union of disjoint open invariant sets \(A\) and \(B\), with \(T{|}_A=S{|}_A\) and \(T{|}_B=S^{-1}{|}_A\). The cocycle is cohomologous to \(1\) on \(A\) and to \(-1\) on \(B\). The second main result (Theorem 3.6), is a complete characterization of restricted isomorphisms for the crossed product \(C^*\)-algebras of topologically free homeomorphisms \(S\), \(T\) of compact Hausdorff spaces.
reviewed by: Zvonko Čerin
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37A55
zbMATH DE Number: 1185902
zbMATH Keywords: measurable dynamics
zbMATH Keywords: orbit equivalence
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: \(K\)-theory
zbMATH Keywords: periodic points
zbMATH Keywords: invariant sets
zbMATH Keywords: cocycle
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/05020317
OpenAlex ID: W2050902539
DOI: 10.2969/JMSJ/05020317
description: scientific article; zbMATH DE number 1185902