6 papers
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 . M…
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 spli…
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…