10 citations · 37 across the 18 of their papers we have counts for
19 papers
-free subgroups of Thompson's are virtually free
Nicolás Matte Bon, Michele Triestino
It is an open problem to determine whether surface groups can embed in Thompson's group . We prove that any finitely generated subgroup of Thompson's group without abelian g…
Commensurating actions and self-similar groups
Nicolás Matte Bon, Volodymyr Nekrashevych, Tianyi Zheng
Commensurating actions govern how a group can act on non-positively curved cube complexes. We obtain a complete picture of them for a class of finitely generated groups acting on r…
Groups with classifiable actions on the line
Joaquín Brum, Martín Gilabert Vio, Nicolás Matte Bon
We motivate and study the class of countable groups such that the conjugacy relation between minimal actions of on by orientation-preserving home…
Subexponential growth and actions on one-manifolds
Sang-hyun Kim, Nicolás Matte Bon, Mikael de la Salle +1
Let be a countable group with no finitely generated subgroup of exponential growth. We show that every action of on a countable set preserving a linear (respectively, circu…
GAGTA 2023 Problem Session
Henry Bradford, Christopher H. Cashen, Francesco Fournier-Facio +2
The conference `Geometric and Asymptotic Group Theory with Applications (GAGTA) 2023: Groups and Dynamics' took place at the Erwin Schrödinger Institute on July 17-21. These are th…
A realisation result for moduli spaces of group actions on the line
Joaquín Brum, Nicolás Matte Bon, Cristóbal Rivas +1
Given a finitely generated group , the possible actions of on the real line (without global fixed points), considered up to semi-conjugacy, can be encoded by the space of or…
Solvable Groups and Affine Actions on the Line
Joaquín Brum, Nicolás Matte Bon, Cristóbal Rivas +1
We prove a structural result for orientation-preserving actions of finitely generated solvable groups on real intervals, considered up to semi-conjugacy. As applications we obtain…
Growth of actions of solvable groups
Adrien Le Boudec, Nicolás Matte Bon
Given a finitely generated group , we are interested in common geometric properties of all graphs of faithful actions of . In this article we focus on their growth. We say th…
Piecewise strongly proximal actions, free boundaries and the Neretin groups
Pierre-Emmanuel Caprace, Adrien Le Boudec, Nicolás Matte Bon
A closed subgroup of a locally compact group is confined if the closure of the conjugacy class of in the Chabauty space of does not contain the trivial subgroup. We…
Locally moving groups and laminar actions on the line
Joaquín Brum, Nicolás Matte Bon, Cristóbal Rivas +1
We prove various results that, given a sufficiently rich subgroup of the group of homeomorphisms on the real line, describe the structure of the other possible actions of o…
Confined subgroups and high transitivity
Adrien Le Boudec, Nicolás Matte Bon
An action of a group is highly transitive if acts transitively on -tuples of distinct points for all . Many examples of groups with a rich geometric or dynamic…
A commutator lemma for confined subgroups and applications to groups acting on rooted trees
Adrien Le Boudec, Nicolás Matte Bon
A subgroup of a group is confined if the -orbit of under conjugation is bounded away from the trivial subgroup in the space of subgroups of $…
Triple transitivity and non-free actions in dimension one
Adrien Le Boudec, Nicolás Matte Bon
The transitivity degree of a group is the supremum of all integers such that admits a faithful -transitive action. Few obstructions are known to impose an upper boun…
Rigidity properties of full groups of pseudogroups over the Cantor set
Nicolás Matte Bon
We show that the (topological) full group of a minimal pseudogroup over the Cantor set satisfies various rigidity phenomena of topological dynamical and combinatorial nature. Our m…
Locally compact groups whose ergodic or minimal actions are all free
Adrien Le Boudec, Nicolas Matte Bon
We construct locally compact groups with no non-trivial Invariant Random Subgroups and no non-trivial Uniformly Recurrent Subgroups.
Subgroup dynamics and -simplicity of groups of homeomorphisms
Adrien Le Boudec, Nicolás Matte Bon
We study the uniformly recurrent subgroups of groups acting by homeomorphisms on a topological space. We prove a general result relating uniformly recurrent subgroups to rigid stab…
Full groups of bounded automaton groups
Nicolás Matte Bon
We show that every bounded automaton group can be embedded in a finitely generated, simple amenable group. The proof is based on the study of the topological full groups associated…
Topological full groups of minimal subshifts with subgroups of intermediate growth
Nicolás Matte Bon
We show that every Grigorchuk group embeds in (the commutator subgroup of) the topological full group of a minimal subshift. In particular, the topological full group of a Ca…
The Liouville property for groups acting on rooted trees
Gideon Amir, Omer Angel, Nicolás Matte Bon +1
We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for e…