Work

Almost Finiteness and Groups of Dynamical Origin

Year: 2025

Type: article

Abstract: We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces and show that it implies comparison when the acting group is amenable. As a consequence, free actions on finite-dimensional spaces of many notable amenable groups of dynamical origin are almost finite. For instance, this applies to topological full groups of Cantor minimal systems and the Basilica group. In particular, minimal such actions give rise to classifiable crossed products.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf016

Authors: Petr Naryshkin, Spyridon Petrakos

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, University of Münster

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Award: SFB 1442: Geometrie: Deformationen und Rigidität