9 papers · 1 filter
Quasiisometric embeddings between right-angled Artin groups: flexibility
Shaked Bader, Oussama Bensaid, Harry Petyt
We give a complete characterisation of when the right-angled Artin group on one cycle graph can be quasiisometrically embedded in the right-angled Artin group on another cycle grap…
Quasiisometric embeddings between right-angled Artin groups: rigidity
Shaked Bader, Oussama Bensaid, Harry Petyt
By introducing branching conditions on the defining graph, we prove a range of rigidity results for quasiisometric embeddings between right-angled Artin groups. The starting point…
From branching quasiflats to flats in CAT(0) cube complexes
Shaked Bader, Oussama Bensaid, Harry Petyt
We study quasiisometric embeddings between finite-dimensional CAT(0) cube complexes. More specifically, we introduce geometric branching conditions under which flats in the domain,…
Virtual splittings of right-angled Artin groups
Oussama Bensaid, Anthony Genevois, Romain Tessera
In this article, we determine, given a finite graph and an integer , when a right-angled Artin group virtually splits over an abelian subgroup of rank . Mor…
Coarse separation and splittings in right-angled Artin groups
Oussama Bensaid, Anthony Genevois, Romain Tessera
In this article, we characterise geometrically when a right-angled Artin group splits over an abelian subgroup. More precisely, given a finite graph , we show that splits…
Coarse separation and splittings in hyperbolic groups
Oussama Bensaid, Anthony Genevois, Romain Tessera
We study coarse separation in one-ended hyperbolic groups from a quantitative point of view, focusing on the volume growth of separating subsets. We prove that a one-ended hyperbol…
Embedding products of trees into higher rank
Oussama Bensaid, Thang Nguyen
We show that there exists a quasi-isometric embedding of the product of copies of into any symmetric space of non-compact type of rank , and ther…
Coarse separation and large-scale geometry of wreath products
Oussama Bensaid, Anthony Genevois, Romain Tessera
In this article, we introduce and study a natural notion of coarse separation for metric spaces, with an emphasis on coarse separation by subspaces of polynomial or subexponential…
Coarse embeddings of symmetric spaces and Euclidean buildings
Oussama Bensaid
Introduced by Gromov in the 80's, coarse embeddings are a generalization of quasi-isometric embeddings when the control functions are not necessarily affine. In this paper, we will…