Strong ergodicity for the Gamma-jump operator and for actions of Polish wreath products

2022/03/28 by Assaf Shani, Shani, Assaf
Mathematics · #03E15 #03E40 #03E75 #37A20 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Logic (math.LO) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2203.14427

openalex publication_date 2022/03/28 · openalex created_date 2022/04/27 · openalex updated_date 2026/07/28

Abstract

Let Γ and Δ be sufficiently distinct countable groups. We show that there is an orbit equivalence relation E, induced by an action of the Polish wreath product group Γ\wrΓ, so that E is generically F-ergodic for any orbit equivalence relation F induced by an action of Δ\wrΔ. More generally, we establish generic ergodicity between Γ-jumps and the iterated Δ-jumps, answering a question of Clemens and Coskey. The proofs follow a translation between Borel homomorphisms and definable pins.

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