Splittings of triangle Artin groups

Abstract

We show that a triangle Artin group ${\text{Art}}_{MNP}$ where $M\le N\le P$ splits as an amalgamated product or an HNN extension of finite rank free groups, provided that either $M>2$, or $N>3$. We also prove that all even three generator Artin groups are residually finite.

15 pages, 7 figures. Comments are welcome!