We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group Diff(D2, ∂D2, vol) of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the L2-norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings...

The goal of this paper is to construct quasi-isometrically embedded subgroups of Thompson’s group F which are isomorphic to F × Zn for all n. A result estimating the norm of an element of Thompson’s group is found. As a corollary, Thompson’s group is seen to be an example of a finitely presented group which has an infinite-dimensional asymptotic cone. The interesting properties of Thompson’s gr...

We show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width and bounded packing. We then use knowledge about intersections of conjugates to characterize finite families of quasimorphisms on hyperbolically embedded subgroups that can be to simultaneously extended to the ambient group.

We show that F has an infinite family of quasi-isometrically embedded subgroups of the form F m × Zn, for integral m, n ≥ 0. These subgroups have simple geometric but more complicated algebraic descriptions We present them to illustrate the intricate geometry of Thompson’s group F as well as the interplay between its standard finite and infinite presentations.

We investigate some product structures in R. Thompson’s group V , primarily by studying the topological dynamics associated with V ’s action on the Cantor set C. We draw attention to the class D(V,C) of groups which have embeddings as demonstrative subgroups of V whose class can be used to assist in forming various products. Note that D(V,C) contains all finite groups, the free group on two gen...

We study some embeddings of finite classical groups defined over field extensions, focusing on their geometry. The embedded groups are subgroups of classical groups lying outside the main Aschbacher classes. We concentrate on PGð8; qÞ where the embedded groups can be seen as automorphism groups of natural geometric objects: Hermitian Veroneseans, Twisted Hermitian Veroneseans and rational curves.