New York Journal of Mathematics
Volume 21 (2015) 1371-1387


Aimee S. A. Johnson and David M. McClendon

Speedups and orbit equivalence of finite extensions of ergodic Zd-actions

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Published: December 18, 2015
Keywords: ergodic Zd action; finite extension; cocycle; speedup; relative isomorphism
Subject: Primary 37A20, Secondary 37A15, 37A35

We classify n-point extensions of ergodic Zd-actions up to relative orbit equivalence and establish criteria under which one n-point extension of an ergodic Zd-action can be sped up to be relatively isomorphic to an n-point extension of another ergodic Zd-action. Both results are characterized in terms of an algebraic object associated to each n-point extension which is a conjugacy class of subgroups of the symmetric group on n elements.

Author information

Aimee S. A. Johnson:
Department of Mathematics and Statistics, Swarthmore College, 500 College Ave. Swarthmore, PA 19081

David M. McClendon:
Department of Mathematics and Computer Science, Ferris State University, ASC 2021, Big Rapids, MI 49307