Related papers: Action graphs, semiconjugacy, and non-embedding in…

In a recent paper, we showed that groups admitting "veelike actions" on a finite language embed in mapping class groups of certain two-sided subshifts. In this note, we illustrate this theorem for the embedding of Thompson's $V$ by…

We show that the canonical actions of the Thompson group V and its generalizations on the Cantor set are not strongly ergodic. This implies that the associated crossed product von Neumann algebras are not full. This also yields a…

We study actions of groups by homeomorphisms on $\mathbf{R}$ (or an interval) that are minimal, have solvable germs at $\pm \infty$ and contain a pair of elements of a certain type. We call such actions coherent. We establish that such an…

Given a bounded valence, bushy tree T, we prove that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T'. This theorem has many applications: quasi-isometric rigidity…

We construct a "higher dimensional" version 2V of Thompson's group V. Like V it is an infinite, finitely presented, simple subgroup of the homeomorphism group of the Cantor set, but we show that it is not isomorphic to V by showing that the…

The main result of this article is that any braided (resp. annular, planar) diagram group $D$ splits as a short exact sequence $1 \to R \to D \to S \to 1$ where $R$ is a subgroup of some right-angled Artin group and $S$ a subgroup of…

We study the bounded cohomology of certain groups acting on the Cantor set. More specifically, we consider the full group of homeomorphisms of the Cantor set as well as Thompson's group $V$. We prove that both of these groups are boundedly…

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 main result applies to its possible homomorphisms into other…

We prove that the tree almost automorphism groups admit exactly three commensurability classes of closed commensurated subgroups. Our proof utilizes an independently interesting characterization of subgroups of the tree almost automorphism…

We construct an action of the Thompson group F on a compact space built from pairs of infinite, binary rooted trees. The action arises as an F-equivariant compactification of the action of F by translations on one of its homogeneous spaces,…

One way to show that Thompson's group F is non-amenable is to exhibit an action of F on a locally compact CAT(0) space X containing no F-invariant flats and having no global fixed points in its boundary-at-infinity. We study the actions of…

We obtain a characterisation of confined subgroups of Thompson's group $F$. As a result, we deduce that orbital graph of a point under action of $F$ has uniformly subexponential growth if and only if this point is fixed by the commutator…

Schreier graphs of the actions of Thompson's group $F$ on the orbits of all points of the unit interval and of the Cantor set with respect to the standard generating set $\{x_0,x_1\}$ are explicitly constructed. The closure of the space of…

We embed Thompson's group $V$ in the mapping class group of a mixing subshift of finite type. Question~6.3 in [Boyle-Chuysurichay, 17] asks whether these mapping class groups are sofic. Our result suggests that this question is difficult to…

We use geometric techniques to investigate several examples of quasi-isometrically embedded subgroups of Thompson's group F. Many of these are explored using the metric properties of the shift map phi in F. These subgroups have simple…

We consider a finitely generated group acting minimally on a compact space by homeomorphsims, and assume that the Schreier graph of at least one orbit is quasi-isometric to a line. We show that the topological full group of such an action…

Hughes defined a class of groups that act as local similarities on compact ultrametric spaces. Guba and Sapir had previously defined braided diagram groups over semigroup presentations. The two classes of groups share some common…

We determine the abstract commensurator com(F) of Thompson's group F and describe it in terms of piecewise linear homeomorphisms of the real line and in terms of tree pair diagrams. We show com (F) is not finitely generated and determine…

We show that Thompson's group $F$ has a topological action on a compact metric space that is proximal and has no fixed points.

This paper deals with the extension of partial actions of topological groups on topological spaces. Within this framework, we introduce a class of topological embeddings defined via the inverse semigroup of homeomorphisms between open…