Local Trivializations of Suspended Minimal Cantor Systems and the Stable Orbit-Breaking Subalgebra

Abstract

It is introduced an analogue of the orbit-breaking subalgebra for the case of free flows on locally compact metric spaces, which has a natural approximate structure in terms of a fixed point and any nested sequence of central slices around this point. It is shown that in the case of minimal flows admitting a compact Cantor central slice, the resulting \(C^*\)-algebra is the stabilization of the Putnam orbit-breaking subalgebra associated to the induced homeomorphism on the central slice. This construction provides an alternative characterization (up to stabilization) of the orbit-breaking subalgebra introduced by Putnam for minimal homeomorphisms of Cantor spaces in terms of suspension flows associated to such dynamical systems.