Year: 2026
Type: preprint
Abstract: We prove a range of rigidity results for quasiisometric embeddings between right-angled Artin groups. Among other things, we: (1) classify all self--quasiisometric-embeddings of RAAGs defined on cycles; (2) show that no $n$--dimensional RAAG is a universal receiver for quasiisometric embeddings of $n$--dimensional RAAGs. (3) prove that if the direct product $F_2^n\times A_{C_5}^m$ can be quasiisometrically embedded in a RAAG $A_Γ$ of the same dimension, then the defining graph of $F_2^n\times A_{C_5}^m$ must appear as an induced subgraph of $Γ$; We also establish a strong rigidity theorem for quasiisometrically embedded images of 2--flats in RAAGs defined by triangle-free graphs that are not stars, generalising a theorem of Bestvina--Kleiner--Sageev.
Source: arXiv (Cornell University)
Authors: Bader, Shaked, Bensaid, Oussama, Petyt, Harry
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161054227