3 citations · 5 across the 6 of their papers we have counts for
7 papers
Cost of one-relator groups
Antoine Poulin, Konrad Wróbel
For any infinite one-relator group , we prove that . For such groups, this gives ,…
Exactness and the topology of the space of invariant random equivalence relations
Héctor Jardón-Sánchez, Sam Mellick, Antoine Poulin +1
We characterize exactness of a countable group in terms of invariant random equivalence relations (IREs) on . Specifically, we show that is exact if and only if every we…
Elasticity of free type III actions of free groups
Antoine Poulin
We prove that measure-class-preserving non-amenable treeable equivalence relations of type III, meaning not preserving any equivalent -finite measure, are induced by free action…
Borel Complexity of the Isomorphism Relation of Archimedean Orders in Finitely Generated Groups
Antoine Poulin
In 2020, Calderoni, Marker, Motto Ros and Shani asked what the Borel complexity of the isomorphism relation of Archimedean orders on is. We answer this question by p…
Tree-like graphings, wallings, and median graphings of equivalence relations
Ruiyuan Chen, Antoine Poulin, Ran Tao +1
We prove several results showing that every locally finite Borel graph whose large-scale geometry is "tree-like" induces a treeable equivalence relation. In particular, our hypothe…
One-ended spanning trees and definable combinatorics
Matthew Bowen, Antoine Poulin, Jenna Zomback
Let be a Polish space with Borel probability measure and a locally finite one-ended Borel graph on We show that admits a Borel one-ended spanning tree gen…
On Certain Probabilistic Properties of Polynomials over the Ring of -adic Integers
Antonio Lei, Antoine Poulin
In this article, we study several probabilistic properties of polynomials defined over the ring of -adic integers under the Haar measure. First, we calculate the probability tha…