Antoine Poulin

activity

20242026

collaborators

4 papers

math.GR2026

Cost of one-relator groups

Antoine Poulin, Konrad WrÃ³bel

For any infinite one-relator group $I^ = ⟨ S ∣ w^{m} ⟩$ , we prove that $cost (I^) = ∣ S ∣ - \frac{1}{m}$ . For such groups, this gives $Î²^{(2)}_1(Î)=\mathrm{cost}(Î)…

math.GR2026

Exactness and the topology of the space of invariant random equivalence relations

HÃ©ctor JardÃ³n-SÃ¡nchez, Sam Mellick, Antoine Poulin +1

We characterize exactness of a countable group $I^$ in terms of invariant random equivalence relations (IREs) on $I^$ . Specifically, we show that $I^$ is exact if and only if every…

math.LO2025

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…

math.GR2024

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 $I ¨ $ -finite measure, are induced by free actio…