Property $R_{\infty }$ for some spherical and affine Artin-Tits groups

Abstract

Let $n\ge 2$. In this note we give a short uniform proof of property $R_{\infty }$ for the Artin-Tits groups of spherical types $A_n$, $B_n$, $D_4$, $I_2(m)$ ($m\ge 3$), their pure subgroups, and for the Artin-Tits groups of affine types ${\tilde{A}}_{n-1}$ and ${\tilde{C}}_n$. In particular, we provide an alternative proof of a recent result of Dekimpe, Gonçalves and Ocampo, who established property $R_{\infty }$ for pure Artin braid groups.

v2: minor changes to implement referee's comments. To appear in Journal of Group Theory. 6 pages, 1 figure

References in corpus (4)

• Artin groups of type B and D
• The $R_{\infty }$-property for right-angled Artin groups
• Artin groups of types $F_4$ and $H_4$ are not commensurable with that of type $D_4$
• Curve graphs for Artin-Tits groups of type $B$, $\tilde{A}$ and $\tilde{C}$ are hyperbolic