Related papers: Presentations of generalisations of Thompson's gro…

We consider generalisations of Thompson's group $V$, denoted $V_r(\Sigma)$, which also include the groups of Higman, Stein and Brin. We show that, under some mild hypotheses, $V_r(\Sigma)$ is the full automorphism group of a Cantor-algebra.…

In his papers [2], [3] Brin introduced the higher dimensional Thompson groups nV which are generalizations to the Thompson's group V of self-homeomorphisms of the Cantor set and found a finite set of generators and relations in the case n =…

We show that Brin's generalisations $2V$ and $3V$ of the Thompson-Higman group $V$ are of type $FP_\infty$. Our methods also give a new proof that both groups are finitely presented.

We define a family of groups that generalises Thompson's groups $T$ and $G$ and also those of Higman, Stein and Brin. For groups in this family we descrine centralisers of finite subgroups and show, that for a given finite subgroup $Q$,…

We study a class of generalisations of Thompson's group $V$ arising naturally as topological full groups of purely infinite, minimal groupoids. In the process, we show that the derived subgroup of such a group is 2-generated whenever it is…

We show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group $V$, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to…

In a previous paper, we defined a higher dimensional analog of Thompson's group V, and proved that it is simple, infinite, finitely generated, and not isomorphic to any of the known Thompson groups. There are other Thompson groups that are…

Given a group $G$ acting faithfully on a set $S$, we characterize precisely when the twisted Brin-Thompson group $SV_G$ is finitely presented. The answer is that $SV_G$ is finitely presented if and only if we have the following: $G$ is…

We describe a procedure for constructing a generalized Thompson group out of a family of groups that is equipped with what we call a cloning system. The previously known Thompson groups F, V, Vbr and Fbr arise from this procedure using,…

The higher-dimensional Thompson groups $nV$, for $n \geq 2$, were introduced by Brin in 2005. We provide new presentations for each of these infinite simple groups. The first is an infinite presentation, analogous to the Coxeter…

Let n be bigger than 1 and let A be an element in the Higman-Thompson group V_n. We study the structure of the centralizer of a in V_n through a careful analysis of the action of the group generated by A on the Cantor set C. We make use of…

We prove new results about the remarkable infinite simple groups introduced by Richard Thompson in the 1960s. We define the groups as partial transformation groups and we give a faithful representation in the Cuntz C*-algebra. For the…

We study centralisers of finite order automorphisms of generalisations of Thompson's group F and conjugacy classes of finite subgroups in finite extensions of these groups. In particular, we show that centralisers of finite automorphisms in…

We establish {\em{virtual surjection to pairs}} (VSP) as a general criterion for the finite presentability of subdirect products of groups: if $\Gamma_1,...,\Gamma_n$ are finitely presented and $S<\Gamma_1\times...\times\Gamma_n$ projects…

We outline a general procedure that builds classifying spaces for generalized Thompson groups $\Gamma$. The construction depends on a small number of choices: (1) an inverse semigroup $S$ of partial transformations that ``locally determine"…

We construct a family of infinite simple groups that we call \emph{twisted Brin-Thompson groups}, generalizing Brin's higher-dimensional Thompson groups $sV$ ($s\in\mathbb{N}$). We use twisted Brin-Thompson groups to prove a variety of…

This note serves as a short and reader-friendly introduction to twisted Brin-Thompson groups, which were recently constructed by Belk and the author to provide a family of simple groups with a variety of interesting properties. Most…

Let $V_r(\Sigma)$ be the generalised Thompson group defined as the automorphism group of a valid, bounded, and complete Cantor algebra. We show that that for every $n>0$ there is a $k>n,$ such that there exists a $k$-dimensional…

We prove that Thompson's groups $F$ and $V$ are the geometry groups of associativity, and of associativity together with commutativity, respectively. We deduce new presentations of $F$ and $V$. These presentations lead to considering a…

We prove that the Brin-Thompson groups sV, also called higher dimensional Thompson's groups, are of type F_\infty for all natural numbers s. This result was previously shown for s up to 3, by considering the action of sV on a naturally…