Year: 2026
Type: preprint
Abstract: We prove that right-angled Artin groups (RAAGs) are profinitely rigid relative to the class of Artin groups. More precisely, if $A_Γ$ is an arbitrary Artin group and $A_Λ$ is a right-angled Artin group such that their profinite completions are isomorphic, i.e., $\widehat{A_Γ}\cong\widehat{A_Λ},$ then $Γ$ is right-angled and $Γ\congΛ$ as labeled graphs. The proof combines the structure of pro-$p$ completions of Artin groups with finite Coxeter quotients to recover the defining graph.
Source: arXiv (Cornell University)
Author: Liu, Zihao
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213918275