10 papers
Spaces of UCP maps and subalgebras of von Neumann algebras
Pierre Fima, François Le Maître, Kunal Mukherjee +1
In this paper, we establish that several natural topologies on the space of state-preserving unital completely positive maps coincide and that make it a Polish space. We then focus…
Spatial models for boolean actions in the infinite measure-preserving setup
Fabien Hoareau, François Le Maître
We show that up to a null set, every infinite measure-preserving action of a locally compact Polish group can be turned into a continuous measure-preserving action on a locally com…
On dense orbits in the space of subequivalence relations
François Le Maître
We first explain how to endow the space of subequivalence relations of any non-singular countable equivalence relation with a Polish topology, extending the framework of Kechris' r…
Classification of non-free p.m.p. boolean actions of ergodic full groups and applications
Alessandro Carderi, Alice Giraud, François Le Maître
We extend Dye's reconstruction theorem, which classifies isomorphisms between full groups, to a classification of homomorphisms between full groups. For full groups of ergodic p.m.…
On the space of subgroups of Baumslag-Solitar groups I: perfect kernel and phenotype
Alessandro Carderi, Damien Gaboriau, François Le Maître +1
Given a Baumslag-Solitar group, we study its space of subgroups from a topological and dynamical perspective. We first determine its perfect kernel (the largest closed subset witho…
Polish topologies on groups of non-singular transformations
François Le Maître
In this paper, we prove several results concerning Polish group topologies on groups of non-singular transformation. We first prove that the group of measure-preserving transformat…