The space of actions, partition metric and combinatorial rigidity
Abstract
We introduce a natural pseudometric on the space of actions of d-generated groups. In this pseudometric, the zero classes correspond to the weak equivalence classes defined by Kechris, and the metric identification is compact. We achieve this by employing symbolic dynamics and an ultraproduct construction which also facilitates the extension of our results to unitary representations. As a byproduct, we show that the weak equivalence class of every free non-amenable action contains an action that satisfies the measurable von Neumann problem.
Fields of Study & Subjects
Advanced Operator Algebra Research
Computability
Logic
AI Algorithms
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Groups Geometry and Dynamics
- Volume
- 20
- Issue
- 1
- Pages
- 1–20
- Publication date
- 9 January 2026