Camille Horbez

activity

20122026

most citedThe Tits alternative for the automorphism group of a free product

27 citations · 195 across the 31 of their papers we have counts for

collaborators

Showing math.GRShow all

29 papers · 1 filter

math.GR2026

Algebraic and measurable embeddings between square-free right-angled Artin groups

Adrien Abgrall, Alexandra Gurieva, Camille Horbez

Let $Γ, Δ$ be finite simplicial graphs, and assume that $Γ$ has no induced squares. We prove that the right-angled Artin group $A (Δ)$ measurably embeds into $A (Γ)$ if and only if $A…

math.GR2025

PolExp growth for automorphisms of toral relatively hyperbolic groups

Rémi Coulon, Arnaud Hilion, Camille Horbez +1

Let $G$ be a toral relatively hyperbolic group, and let $φ \in Aut (G)$ . We prove that, under iteration of $φ$ , the conjugacy length $∣∣ φ^{n} (g) ∣∣$ of every element $g \in G$ gr…

math.GR2024

Measure equivalence classification of right-angled Artin groups: the finite $Out$ classes

Camille Horbez, Jingyin Huang

Given a right-angled Artin group $G$ with finite outer automorphism group, we determine which right-angled Artin groups are measure equivalent (or orbit equivalent) to $G$ .

math.GR2023

Integrable measure equivalence rigidity of right-angled Artin groups via quasi-isometry

Camille Horbez, Jingyin Huang

Let $G$ be a right-angled Artin group with $∣ Out (G) ∣ < + \infty$ . We prove that if a countable group $H$ with bounded torsion is measure equivalent to $G$ , with an $L^{1}$ -inte…

math.GR2022

On the homology growth and the $ℓ^{2}$ -Betti numbers of $Out (W_{n})$

Damien Gaboriau, Yassine Guerch, Camille Horbez

Let $n \geq 3$ , and let $Out (W_{n})$ be the outer automorphism group of a free Coxeter group $W_{n}$ of rank $n$ . We study the growth of the dimension of the homology groups (wi…

math.GR2022★ 1 cited

Measure equivalence rigidity among the Higman groups

Camille Horbez, Jingyin Huang

We prove that all (generalized) Higman groups on at least $5$ generators are superrigid for measure equivalence. More precisely, let $k \geq 5$ , and let $H$ be a group with generator…

math.GR2021

Measure equivalence rigidity of the handlebody groups

Sebastian Hensel, Camille Horbez

Let $V$ be a connected $3$ -dimensional handlebody of finite genus at least $3$ . We prove that the handlebody group $Mod (V)$ is superrigid for measure equivalence, i.e. eve…

math.GR2021

Orbit equivalence rigidity of irreducible actions of right-angled Artin groups

Camille Horbez, Jingyin Huang, Adrian Ioana

Let $G_{Γ} ↷ X$ and $G_{Λ} ↷ Y$ be two free measure-preserving actions of one-ended right-angled Artin groups with trivial center on standard probability sp…

math.GR2021★ 2 cited

Measure equivalence rigidity of $Out (F_{N})$

Vincent Guirardel, Camille Horbez

We prove that for every $N \geq 3$ , the group $Out (F_{N})$ of outer automorphisms of a free group of rank $N$ is superrigid from the point of view of measure equivalence: any…

math.GR2020★ 9 cited

Measure equivalence classification of transvection-free right-angled Artin groups

Camille Horbez, Jingyin Huang

We prove that if two transvection-free right-angled Artin groups are measure equivalent, then they have isomorphic extension graphs. As a consequence, two right-angled Artin groups…

math.GR2020

Proper proximality in non-positive curvature

Camille Horbez, Jingyin Huang, Jean Lécureux

Proper proximality of a countable group is a notion that was introduced by Boutonnet, Ioana and Peterson as a tool to study rigidity properties of certain von Neumann algebras asso…

math.GR2020

Cocycle superrigidity from higher rank lattices to $Out (F_{N})$

Vincent Guirardel, Camille Horbez, Jean Lécureux

We prove a rigidity result for cocycles from higher rank lattices to $Out (F_{N})$ and more generally to the outer automorphism group of a torsion-free hyperbolic group. More…

math.GR2020★ 5 cited

Boundary amenability and measure equivalence rigidity among two-dimensional Artin groups of hyperbolic type

Camille Horbez, Jingyin Huang

We study $2$ -dimensional Artin groups of hyperbolic type from the viewpoint of measure equivalence, and establish rigidity theorems. We first prove that they are boundary amenable.…

math.GR2020★ 6 cited

Acylindrical hyperbolicity of automorphism groups of infinitely-ended groups

Anthony Genevois, Camille Horbez

We prove that the automorphism group of every infinitely-ended finitely generated group is acylindrically hyperbolic. In particular $Aut (F_{n})$ is acylindrically h…

math.GR2019

Rigidity of the Torelli subgroup in $O u t (F_{N})$

Sebastian Hensel, Camille Horbez, Richard D. Wade

Let $N$ be at least 4. We prove that every injective homomorphism from the Torelli subgroup into $O u t (F_{N})$ differs from the inclusion by a conjugation in $O u t (F_{N})$ . This applies…

math.GR2019★ 1 cited

Commensurations of subgroups of $Out (F_{N})$

Camille Horbez, Richard D. Wade

A theorem of Farb and Handel asserts that for $N \geq 4$ , the natural inclusion from $Out (F_{N})$ into its abstract commensurator is an isomorphism. We give a new proof of the…

math.GR2019★ 16 cited

Boundaries of relative factor graphs and subgroup classification for automorphisms of free products

Vincent Guirardel, Camille Horbez

Given a countable group $G$ splitting as a free product $G = G_{1} * \dots * G_{k} * F_{N}$ , we establish classification results for subgroups of the group $O u t (G, F)$ of all…

math.GR2017★ 22 cited

Algebraic laminations for free products and arational trees

Vincent Guirardel, Camille Horbez

This work is the first step towards a description of the Gromov boundary of the free factor graph of a free product, with applications to subgroup classification for outer automorp…

math.GR2017

Boundary amenability of $O u t (F_{N})$

Mladen Bestvina, Vincent Guirardel, Camille Horbez

We prove that $O u t (F_{N})$ is boundary amenable. This also holds more generally for $O u t (G)$ , where $G$ is either a toral relatively hyperbolic group or a finitely generated right-an…

math.GR2016★ 1 cited

On the topological dimension of the Gromov boundaries of some hyperbolic $O u t (F_{N})$ -graphs

Mladen Bestvina, Camille Horbez, Richard D. Wade

We give upper bounds, linear in rank, to the topological dimensions of the Gromov boundaries of the intersection graph, the free factor graph and the cyclic splitting graph of a fi…

math.GR2015★ 17 cited

Central limit theorems for mapping class groups and $Out (F_{N})$

Camille Horbez

We prove central limit theorems for the random walks on either the mapping class group of a closed, connected, orientable, hyperbolic surface, or on $Out (F_{N})$ , each time un…

math.GR2015★ 6 cited

Spectral theorems for random walks on mapping class groups and $Out (F_{N})$

François Dahmani, Camille Horbez

We establish spectral theorems for random walks on mapping class groups of connected, closed, oriented, hyperbolic surfaces, and on $Out (F_{N})$ . In both cases, we relate the…

math.GR2014★ 27 cited

The Tits alternative for the automorphism group of a free product

Camille Horbez

Let $G = G_{1} * \dots * G_{k} * F$ be a countable group which splits as a free product, where all groups $G_{i}$ are freely indecomposable and not isomorphic to $Z$ , and $F$ …

math.GR2014★ 19 cited

Hyperbolic graphs for free products, and the Gromov boundary of the graph of cyclic splittings

Camille Horbez

We define analogues of the graphs of free splittings, of cyclic splittings, and of maximally-cyclic splittings of $F_{N}$ for free products of groups, and show their hyperbolicity. G…

Algebraic and measurable embeddings between square-free right-angled Artin groups

PolExp growth for automorphisms of toral relatively hyperbolic groups

Measure equivalence classification of right-angled Artin groups: the finite Out classes

Integrable measure equivalence rigidity of right-angled Artin groups via quasi-isometry

On the homology growth and the ℓ2-Betti numbers of Out(Wn​)

Measure equivalence rigidity among the Higman groups

Measure equivalence rigidity of the handlebody groups

Orbit equivalence rigidity of irreducible actions of right-angled Artin groups

Measure equivalence rigidity of Out(FN​)

Measure equivalence classification of transvection-free right-angled Artin groups

Proper proximality in non-positive curvature

Cocycle superrigidity from higher rank lattices to Out(FN​)

Boundary amenability and measure equivalence rigidity among two-dimensional Artin groups of hyperbolic type

Acylindrical hyperbolicity of automorphism groups of infinitely-ended groups

Rigidity of the Torelli subgroup in Out(FN​)

Commensurations of subgroups of Out(FN​)

Boundaries of relative factor graphs and subgroup classification for automorphisms of free products

Algebraic laminations for free products and arational trees

Boundary amenability of Out(FN​)

On the topological dimension of the Gromov boundaries of some hyperbolic Out(FN​)-graphs

Central limit theorems for mapping class groups and Out(FN​)

Spectral theorems for random walks on mapping class groups and Out(FN​)

The Tits alternative for the automorphism group of a free product

Hyperbolic graphs for free products, and the Gromov boundary of the graph of cyclic splittings

Measure equivalence classification of right-angled Artin groups: the finite $Out$ classes

On the homology growth and the $ℓ^{2}$ -Betti numbers of $Out (W_{n})$

Measure equivalence rigidity of $Out (F_{N})$

Cocycle superrigidity from higher rank lattices to $Out (F_{N})$

Rigidity of the Torelli subgroup in $O u t (F_{N})$

Commensurations of subgroups of $Out (F_{N})$

Boundary amenability of $O u t (F_{N})$

On the topological dimension of the Gromov boundaries of some hyperbolic $O u t (F_{N})$ -graphs

Central limit theorems for mapping class groups and $Out (F_{N})$

Spectral theorems for random walks on mapping class groups and $Out (F_{N})$