Joaquín Brum: New examples of allosteric groups and actions.

mardi 16 sept. 2025, 09:45 → 11:45 Europe/Paris

Abstract: Let X be compact Hausdorff space and \mu a probability measure on X. A continuous and \mu-preserving action of a countable group G on X is called Allosteric if it is minimal, \mu-ergodic and the set of points in X with free orbit is a residual set of measure 0. Several groups are known to admit Allosteric actions such as non-trivial free products of residually finite groups, hyperbolic surface groups and some amenable wreath products.  

 

We will show new families of groups (including hyperbolic 3-manifold groups) admitting allosteric actions. The construction relies on using (elementary) combinatorial topology to construct towers of finite coverings over CW-complex realizations of the (allosteric) groups. Also we will give an example of an allosteric action of the free group on two generators admitting no profinite factor. 

 

This is a work in progress with Sebastièn Alvarez, Matilde Martínez and Rafael Potrie.