Computable amenable actions for exact groups

Determine which exact groups admit computable presentations together with computable, amenable actions on computably compact spaces.

Background

The paper establishes that if a computably presented group acts amenably and computably on a computably compact space, then the associated reduced group C-algebra has a computable presentation. It then proves this framework for infinite hyperbolic groups by constructing a computably compact presentation of their boundaries on which the natural group action is computable.

The unresolved question asks for a characterization of the broader class of exact groups for which analogous computable presentations and computable amenable actions exist. Such a characterization would extend the paper’s method beyond hyperbolic groups and identify when exactness can be accompanied by the effective dynamical structure required for computability of reduced group C-algebras.