Existence of topologically free minimal F_∞-actions on the Cantor set without dynamical comparison (with or without invariant measures), plus separation of strict comparison in the crossed product from dynamical comparison, via monoid construction and embedding into a refinement monoid realized as a
Smallness and Comparison Properties for Minimal Dynamical Systems
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abstract
We introduce the dynamic comparison property for minimal dynamical systems which has applications to the study of crossed product C*-algebras. We demonstrate that this property holds for a large class of systems which includes all examples where the underlying space is finite-dimensional, as well as for an explicit infinite-dimensional example, showing that the it is strictly weaker than finite-dimensionality in general.
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2026 1verdicts
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Topologically free minimal actions without dynamical comparison
Existence of topologically free minimal F_∞-actions on the Cantor set without dynamical comparison (with or without invariant measures), plus separation of strict comparison in the crossed product from dynamical comparison, via monoid construction and embedding into a refinement monoid realized as a