AI 中文总结
本文证明直角Artin群在Artin群类中具有profinite刚性，即若其profinite完备化同构于某Artin群的，则该Artin群必为直角且定义图同构，方法结合pro-p完备化与有限Coxeter商。
AI 中文摘要
我们证明直角Artin群（RAAGs）在Artin群类中是profinite刚性的。更精确地说，若$A_\Gamma$是任意Artin群且$A_\Lambda$是直角Artin群，使得它们的profinite完备化同构，即$\widehat{A_\Gamma}\cong\widehat{A_\Lambda}$，则$\Gamma$是直角的且$\Gamma\cong\Lambda$作为标记图。证明结合了Artin群的pro-$p$完备化结构与有限Coxeter商来恢复定义图。
英文摘要
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.
Comments21 pages, 3 figures. Comments are welcome!
