11 papers
A torsion-free non-sofic group
Francesco Fournier-Facio
OpenAI announced the existence of a non-sofic group: the unit group of the binary Leavitt algebra. We exhibit a different source of examples (relying on the same technical criterio…
Finiteness properties and Higman's rope trick
Francesco Fournier-Facio, Matthew C. B. Zaremsky
In 1961 Higman proved that every finitely generated recursively presented group embeds into a finitely presented group. In 2018 Leary proved that every finitely generated group emb…
The Local Lifting Property, Property FD, and stability of approximate representations
Francesco Fournier-Facio, Rufus Willett
We establish Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for classes of finitely generated groups of central importance in geometric and combinatorial gro…
Abstract twisted Brin--Thompson groups
Francesco Fournier-Facio, Xiaolei Wu, Matthew C. B. Zaremsky
Given a group acting faithfully on a set , one gets a simple group denoted , called a twisted Brin--Thompson group. In this paper we drop the faithfulness assumption,…
Profinite isomorphisms, stable commutator length, and fixed point properties
Francesco Fournier-Facio
We construct Grothendieck pairs witnessing that the following are not profinite invariants: stable commutator length, quasimorphisms (answering a question of Echtler and Kammeyer),…
First-order theory of torsion-free Tarski monsters
Rémi Coulon, Francesco Fournier-Facio, Meng-Che "Turbo" Ho
We develop methods to control the first-order theory of groups arising as certain direct limits of torsion-free hyperbolic groups, answering several questions in the literature. We…