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arXiv · 2608.23424

Explicit construction of orbit equivalence for rank-one actions

Alexandre I. Danilenko·Mykyta I. Vieprik
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Abstract

Let $G$ be a discrete countable infinite group. Given two rank-one measure-preserving $G$-actions whose invariant measures are either both finite or both infinite, we give a direct explicit construction, from their cutting-and-stacking parameters, of a Borel orbit equivalence on invariant conull subsets. We also prove a topological counterpart of this assertion, under additional compatibility assumptions, for continuous $(C,F)$-actions of $G$ on non-compact locally compact Cantor spaces.

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Alexandre I. Danilenko, Mykyta I. Vieprik. 2026-08-24. Explicit construction of orbit equivalence for rank-one actions. https://arxiv.org/abs/2608.23424

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