Related papers: Higher dimensional Thompson groups have Serre's pr…

A few years ago the so-called oriented subgroup $\vec F$ of the Thompson group $F$ was introduced by V. Jones while investigating the connections between subfactors and conformal field theories. In the coding of links and knots by elements…

Dimension growth functions of groups have been introduced by Gromov in 1999. We prove that every solvable finitely generated subgroups of the R. Thompson group $F$ has polynomial dimension growth while the group $F$ itself, and some…

We prove a variety of results about subgroups of Thompson's group $V$. First we prove that every action graph of a finitely generated subgroup of $V$ acting on an orbit in Cantor space is quasi-isometric to a tree. Then we prove that for a…

We complete the program begun by Brin and Squier of characterising conjugacy in Thompson's group $F$ using the standard action of $F$ as a group of piecewise linear homeomorphisms of the unit interval.

This paper studies when a pair of elements in F are the images of the standard generators of F under a self monomorphism.

We describe, through the use of Rubin's theorem, the automorphism groups of the Higman-Thompson groups $G_{n,r}$ as groups of specific homeomorphisms of Cantor spaces $\mathfrak{C}_{n,r}$. This continues a thread of research begun by Brin,…

In the binomial $\ell$-gonal model for random groups, where the random relations all have fixed length $\ell\geq 3$ and the number of generators goes to infinity, we establish a double threshold near density $d=\frac{1}{\ell}$ where the…

We show that Thompson's group F occurs with great frequency in the group of PL homeomorphisms of the unit interval.

We show that for a large class $\mathcal{C}$ of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group $G$ of rank $k$ in $\mathcal{C}$, there is a sequence of $k$-markings…

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 prove that the braided Thompson's groups $V_{\rm br}$ and $F_{\rm br}$ are of type $F_\infty$, confirming a conjecture by John Meier. The proof involves showing that matching complexes of arcs on surfaces are highly connected. In an…

We study global fixed points for actions of Coxeter groups on nonpositively curved singular spaces. In particular, we consider property FA_n, an analogue of Serre's property FA for actions on CAT(0) complexes. Property FA_n has implications…

Following a procedure due to V. Jones, using suitably normalized elements in a Temperley-Lieb-Jones (planar) algebra we introduce a 3-parametric family of unitary representations of the Thompson's group $F$ equipped with canonical (vacuum)…

The aim of the paper is to give a full classification of factorizations of groups in terms of descent cohomology (pointed) sets introduced in [5]. We show that descent cohomology includes Serre's non-abelian group cohomology as a special…

We describe some of the geometric properties of the automorphism group Aut(F) of Thompson's group F. We give realizations of Aut(F) geometrically via periodic tree pair diagrams, which lead to natural presentations and give effective…

We show that the \s{\phi}-labeled Thompson groups and the twisted Brin--Thompson groups are boundedly acyclic. This allows us to prove several new embedding results for groups. First, every group of type $F_n$ embeds quasi-isometrically…

In this paper we consider the $T$- and $V$- versions, $T_{\tau}$ and $V_{\tau}$ , of the irrational slope Thompson group $F_{\tau}$ considered in [3]. We give infinite presentations for these groups and show how they can be represented by…

Braided Thompson's groups are finitely presented groups introduced by Brin and Dehornoy which contain the ordinary braid groups $B_n$, the finitary braid group $B_{\infty}$ and Thompson's group $F$ as subgroups. We describe some of the…

We provide a new characterization of amenability for countable groups, based on frame representations admitting almost invariant vectors. By relaxing the frame inequalities, thereby weakening amenability, we obtain a large class of…

In this second article, we continue to study classes of groups constructed from a functorial method due to Vaughan Jones. A key observation of the author shows that these groups have remarkable diagrammatic properties that can be used to…