14 citations · 29 across the 16 of their papers we have counts for
19 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…
On dense totipotent free subgroups in full groups
Alessandro Carderi, Damien Gaboriau, François Le Maître
We study probability measure preserving (p.m.p.) non-free actions of free groups and the associated IRS's. The perfect kernel of a countable group Gamma is the largest closed subsp…
Quantitative measure equivalence between amenable groups
Thiebout Delabie, Juhani Koivisto, François Le Maître +1
We initiate a quantitative study of measure equivalence (and orbit equivalence) between finitely generated groups, which extends the classical setting of measure equi…
On a measurable analogue of small topological full groups II
François Le Maître
We pursue the study of full groups of graphings and of the closures of their derived groups, which we call derived full groups. Our main result shows th…
On a measurable analogue of small topological full groups
François Le Maître
We initiate the study of a measurable analogue of small topological full groups that we call full groups. These groups are endowed with a Polish group topology which…
Orbit full groups for locally compact groups
Alessandro Carderi, François Le Maître
We show that the topological rank of an orbit full group generated by an ergodic, probability measure-preserving free action of a non-discrete unimodular locally compact Polish gro…
On strongly just infinite profinite branch groups
François Le Maître, Phillip Wesolek
For profinite branch groups, we first demonstrate the equivalence of the Bergman property, uncountable cofinality, Cayley boundedness, the countable index property, and the conditi…
Highly faithful actions and dense free subgroups in full groups
François Le Maître
In this paper, we show that every measure-preserving ergodic equivalence relation of cost less than m comes from a "rich" faithful invariant random subgroup of the free group on m…
Chief factors in Polish groups
Colin D. Reid, Phillip R. Wesolek
In finite group theory, chief factors play an important and well-understood role in the structure theory. We here develop a theory of chief factors for Polish groups. In the develo…
Infinitesimal generators and quasi non-archimedean topological groups
Tsachik Gelander, François Le Maître
We show that connected separable locally compact groups are infinitesimally finitely generated, meaning that there is an integer such that every neighborhood of the identity co…
Connected Polish groups with ample generics
Adriane Kaïchouh, François Le Maître
In this paper, we give the first examples of connected Polish groups that have ample generics, answering a question of Kechris and Rosendal. We show that any Polish group with ampl…
More Polish full groups
Alessandro Carderi, François Le Maître
We associate to every action of a Polish group on a standard probability space a Polish group that we call the orbit full group. For discrete groups, we recover the well-known full…
On full groups of non ergodic probability measure preserving equivalence relations
François Le Maître
We give a formula relating the topological rank of the full group of an aperiodic pmp equivalence relation to the cost of its ergodic components. Furthermore, we obtain examples of…
The number of topological generators for full groups of ergodic equivalence relations
François Le Maître
We completely elucidate the relationship between two invariants associated with an ergodic probability measure-preserving (pmp) equivalence relation, namely its cost and the minima…