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Continuum of allosteric actions for non-amenable surface groups

Part of: Structure and classification of infinite or finite groups Topological dynamics Ergodic theory

Published online by Cambridge University Press:  19 July 2023

MATTHIEU JOSEPH Open the ORCID record for MATTHIEU JOSEPH [Opens in a new window]
MATTHIEU JOSEPH*
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d’Orsay, Orsay 91405, France
*
e-mail: [email protected]
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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 probability measure preserving 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 invariant random subgroups we obtain are pairwise distincts.

Keywords

measure-preserving actionsminimal actionsinvariant random subgroupsuniformly recurrent subgroupsspace of subgroups

MSC classification

Primary: 37A15: General groups of measure-preserving transformations 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Secondary: 20E08: Groups acting on trees 20E26: Residual properties and generalizations; residually finite groups 20E15: Chains and lattices of subgroups, subnormal subgroups
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 6 , June 2024 , pp. 1581 - 1596
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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