Francesco Fournier-Facio

activity

20202026

most citedBounded cohomology and binate groups

17 citations · 33 across the 32 of their papers we have counts for

collaborators

34 papers

quant-ph2026

Non-Hermitian Cooperation Induced Chern Insulator

Weiwei Zhu, Bingbing Wang, Mengxiang Xie +5

Conventional Chern insulators rely on breaking time-reversal symmetry via magnetic fields or synthetic gauge fields. Here we introduce a fundamentally different paradigm: a static…

math.GR2026

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…

math.GR2026

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…

math.GR2026

An improved characterisation of inner automorphisms of groups

Francesco Fournier-Facio

We show that every group $G$ embeds malnormally into a simple, complete co-Hopfian group $H$ . This implies that a non-trivial endomorphism of $G$ extends to $H$ if and only if it i…

math.GR2026

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…

math.GR2026

Abstract twisted Brin--Thompson groups

Francesco Fournier-Facio, Xiaolei Wu, Matthew C. B. Zaremsky

Given a group $G$ acting faithfully on a set $S$ , one gets a simple group denoted $S V_{G}$ , called a twisted Brin--Thompson group. In this paper we drop the faithfulness assumption,…

math.GR2026

Profinite isomorphisms, stable commutator length, and fixed point properties

Francesco Fournier-Facio

We construct Grothendieck pairs witnessing that stable commutator length and quasimorphisms are not profinite invariants, answering a question of Echtler and Kammeyer. Moreover, we…

math.GR2026

Kazhdan groups of dimension $16$ with prescribed second $ℓ^{2}$ -Betti number

Francesco Fournier-Facio, Roman Sauer

We construct a family of simple, lacunary hyperbolic groups with property $(T)$ that have rational cohomological dimension~ $16$ and whose second $ℓ^{2}$ -Betti number can be prescr…

math.GR2025

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…

math.GR2025

Stable commutator length on free $Q$ -groups

Francesco Fournier-Facio

We study stable commutator length on free $Q$ -groups. We prove that every non-identity element has positive stable commutator length, and that the corresponding free group…

math.GR2025

Finiteness properties of stabilisers of oligomorphic actions

Francesco Fournier-Facio, Peter H. Kropholler, Robert Alonzo Lyman +1

An action of a group on a set is oligomorphic if it has finitely many orbits of $n$ -element subsets for all $n$ . We prove that for a large class of groups (including all groups of…

math.GR2025

Bounded cohomology, quotient extensions, and hierarchical hyperbolicity

Francesco Fournier-Facio, Giorgio Mangioni, Alessandro Sisto

We call a central extension bounded if its Euler class is represented by a bounded cocycle. We prove that a bounded central extension of a hierarchically hyperbolic group (HHG) is…

math.GR2025

Boone-Higman embeddings of $Aut (F_{n})$ and mapping class groups of punctured surfaces

James Belk, Francesco Fournier-Facio, James Hyde +1

We prove that the groups $Aut (F_{n})$ satisfy the Boone-Higman conjecture for all $n$ , meaning each $Aut (F_{n})$ embeds in a finitely presented simple group. In fact,…

math.GR2025

Dimensions of finitely generated simple groups and their subgroups

Francesco Fournier-Facio, Bin Sun

We construct finitely generated simple torsion-free groups with strong homological control. Our main result is that every subset of $N \cup {\infty}$ , with some obvious…

math.GR2025

Property $R_{\infty}$ for groups with infinitely many ends

Francesco Fournier-Facio, Harry Iveson, Armando Martino +2

We show that an accessible group with infinitely many ends has property $R_{\infty}$ . That is, it has infinitely many twisted conjugacy classes for any twisting automorphism. We de…

math.GR2024

A note on separability in outer automorphism groups

Francesco Fournier-Facio

We give a criterion for separability of subgroups of certain outer automorphism groups. This answers questions of Hagen and Sisto, by strengthening and generalizing a result of the…

math.GR2024

Hyperbolic actions of Thompson's group $F$ and generalizations

Sahana Balasubramanya, Francesco Fournier-Facio, Matthew C. B. Zaremsky

We study the poset of hyperbolic structures on Thompson's group $F$ and its generalizations $F_{n}$ for $n \geq 2$ . The global structure of this poset is as simple as one would expec…

math.GT2024

The bounded cohomology of transformation groups of Euclidean spaces and discs

Francesco Fournier-Facio, Nicolas Monod, Sam Nariman +1

We prove that the groups of orientation-preserving homeomorphisms and diffeomorphisms of $R^{n}$ are boundedly acyclic, in all regularities. This is the first full computati…

math.GR2024★ 1 cited

Displacement techniques in bounded cohomology

Caterina Campagnolo, Francesco Fournier-Facio, Yash Lodha +1

Several algebraic criteria, reflecting displacement properties of transformation groups, have been used in the past years to prove vanishing of bounded cohomology and stable commut…

math.GR2023★ 1 cited

An algebraic criterion for the vanishing of bounded cohomology

Caterina Campagnolo, Francesco Fournier-Facio, Yash Lodha +1

We prove the vanishing of bounded cohomology with separable dual coefficients for many groups of interest in geometry, dynamics, and algebra. These include compactly supported stru…

math.GR2023

Local Hilbert--Schmidt stability

Francesco Fournier-Facio, Maria Gerasimova, Pieter Spaas

We introduce a notion of local Hilbert--Schmidt stability, motivated by the recent definition by Bradford of local permutation stability, and give examples of (non-residually finit…

math.GR2023

Ulam stability of lamplighters and Thompson groups

Francesco Fournier-Facio, Bharatram Rangarajan

We show that a large family of groups is uniformly stable relative to unitary groups equipped with submultiplicative norms, such as the operator, Frobenius, and Schatten $p$ -norms.…

math.GR2022

Property (NL) for group actions on hyperbolic spaces

Sahana Balasubramanya, Francesco Fournier-Facio, Anthony Genevois +1

We introduce Property (NL), which indicates that a group does not admit any (isometric) action on a hyperbolic space with loxodromic elements. In other words, such a group $G$ can…

math.GR2022★ 1 cited

Finitely presented left orderable monsters

Francesco Fournier-Facio, Yash Lodha, Matthew C. B. Zaremsky

A left orderable monster is a finitely generated left orderable group all of whose fixpoint-free actions on the line are proximal: the action is semiconjugate to a minimal action s…

Non-Hermitian Cooperation Induced Chern Insulator

A torsion-free non-sofic group

Finiteness properties and Higman's rope trick

An improved characterisation of inner automorphisms of groups

The Local Lifting Property, Property FD, and stability of approximate representations

Abstract twisted Brin--Thompson groups

Profinite isomorphisms, stable commutator length, and fixed point properties

Kazhdan groups of dimension 16 with prescribed second ℓ2-Betti number

First-order theory of torsion-free Tarski monsters

Stable commutator length on free Q-groups

Finiteness properties of stabilisers of oligomorphic actions

Bounded cohomology, quotient extensions, and hierarchical hyperbolicity

Boone-Higman embeddings of Aut(Fn​) and mapping class groups of punctured surfaces

Dimensions of finitely generated simple groups and their subgroups

Property R∞​ for groups with infinitely many ends

A note on separability in outer automorphism groups

Hyperbolic actions of Thompson's group F and generalizations

The bounded cohomology of transformation groups of Euclidean spaces and discs

Displacement techniques in bounded cohomology

An algebraic criterion for the vanishing of bounded cohomology

Local Hilbert--Schmidt stability

Ulam stability of lamplighters and Thompson groups

Property (NL) for group actions on hyperbolic spaces

Finitely presented left orderable monsters

Kazhdan groups of dimension $16$ with prescribed second $ℓ^{2}$ -Betti number

Stable commutator length on free $Q$ -groups

Boone-Higman embeddings of $Aut (F_{n})$ and mapping class groups of punctured surfaces

Property $R_{\infty}$ for groups with infinitely many ends

Hyperbolic actions of Thompson's group $F$ and generalizations