Almost finiteness for allosteric actions

Determine whether there is a version of almost finiteness applicable to allosteric actions and whether such a version implies Z-stability in the minimal case.

Background

Almost finiteness is a principal mechanism for proving Z-stability, but the standard framework is most effective for free or essentially free actions. Since allosteric actions are topologically free but not essentially free, the survey asks whether an adapted notion can treat them systematically.

References

Question 6.1.3. Is there a version of almost finiteness that applies to allosteric actions? Does this version of almost finiteness imply Z-stability in the minimal case?

— Classifiability of crossed products  (2610.06586 - Gardella, 5 Oct 2026) in Question 6.1.3, Section 6.1, p. 47

Question 6.1.6. Is there a version of almost finiteness that does not incorporate amenability of G into the definition but rather amenability of G ↷ X? Do amenable dynamical systems (with dynamical comparison) of paradoxical groups satisfy this property? Does this version of almost finiteness imply Z-stability in the minimal case?

— Classifiability of crossed products  (2610.06586 - Gardella, 5 Oct 2026) in Question 6.1.6, Section 6.1, p. 48