Finite odometer factors of rank one ℤ^d-actions

2023/06/15 by Aimee Johnson, Johnson, Aimee S. A., David M. McClendon +1
Mathematics · #37A15 #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2306.09477

openalex publication_date 2023/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give explicit conditions characterizing the Følner rank one ℤ^d-actions that factor onto a finite odometer; those that factor onto an arbitrary, but specified ℤ^d-odometer, and those that factor onto an unspecified ℤ^d-odometer. We also give explicit conditions describing the Følner rank one ℤ^d-actions that are conjugate to a specific ℤ^d-odometer, and those that are conjugate to some ℤ^d-odometer. These conditions are based on cutting and stacking procedures used to generate the action, and generalize results given in \citeFGHSW for rank one ℤ-actions.

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