On finite local approximations of isometric actions of residually finite groups

2025/12/16 by В. А. Алексеев, Andreas Thom, Alekseev, Vadim +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2512.14147

Abstract

We show that any isometric action of a residually finite group admits approximate local finite models. As a consequence, if G is residually finite, every isometric G-action embeds isometrically into a metric ultraproduct of finite isometric G-actions.

Citations

• Metric topological groups: their metric approximation and metric\n ultraproducts
• Finitely approximable groups and actions Part I: The Ribes--Zalesski\uı property

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