Continuum of allosteric actions for non-amenable surface groups

Abstract

Let $\Sigma$ be a closed surface other than the sphere, the torus, the projective plane or the Klein bottle. We construct a continuum of p.m.p. ergodic minimal profinite actions for the fundamental group of $\Sigma$, that are topologically free but not essentially free, a property that we call allostery. Moreover, the IRS's we obtain are pairwise distincts.

18 pages, 3 figures

References in corpus (2)

• Non-abelian free groups admit non-essentially free actions on rooted trees
• Hyperfinite actions on countable sets and probability measure spaces

Cited by in corpus (1)

• Amenable wreath products with non almost finite actions of mean dimension zero