On morphisms between pseudogroups and applications to their topological full groups

Nicolás Matte Bon (Université Lyon 1 )

Thursday 15th October, 2020 16:00-17:00 Contact the organisers for Zoom info


Pseudogroups of partial homeomorphisms (equivalently, étale groupoids) defined over a totally disconnected space are a rich source of cexamples of countable groups, namely their topological full group, which consists of invertible elements in the pseudogroups.
I will discuss a notion of morphism between pseudogroups (and a counterpart for étale groupoids) which naturally induces a group homomorphism between the topological full groups. The main object of the talk will be a result that goes in the converse directions, showing that under suitable conditions an abstract homomorphism of the topological full group to another group of homeomorphisms is induced by a morphism of pseudogroups.
This criterion is based on a more general framework to prove rigidity theorem for groups given by sufficiently rich actions by homeomorphisms, via the study of the possible stabilisers of their continuous actions on compact spaces (also called "confined subgroups"). If time permits I will explain other results in this setting obtained in joint work with Adrien Le Boudec.

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