Amenable-group Z-stability and the small boundary property

Establish that, for every free minimal action of an amenable group on a compact metrizable space, Z-stability of the crossed product is equivalent to the small boundary property.

Background

The survey identifies Z-stability as the remaining dynamical condition needed for classifiability of crossed products associated to free minimal amenable actions. Although examples show that Z-stability can fail, the conjecture proposes that its precise dynamical characterization is the small boundary property.