2024/03/28 by Nachi Avraham-Re’em, Emmanuel Roy, Avraham-Re'em, Nachi +1
Mathematics · #Advanced Topology and Set Theory #Mathematics and Applications #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2403.19567
We define and study Poissonian actions of Polish groups as a framework to Poisson suspensions, characterize them spectrally, and provide a complete characterization of their ergodicity. We further construct 'spatial' Poissonian actions, answering partially a question of Glasner, Tsirelson & Weiss about Lévy groups. We also construct for every diffeomorphism group an ergodic free spatial probability preserving actions. This constitutes a new class of Polish groups admitting non-essentially countable orbit equivalence relations, obtaining progress on a problem of Kechris.