Bounded topological orbit equivalence and \(C^*\)-algebras
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.
scientific article; zbMATH DE number 1185902