Residual finiteness of certain 2-dimensional Artin groups

Abstract

We show that many $2$-dimensional Artin groups are residually finite. This includes $3$-generator Artin groups with labels $\ge 4$ except for $(2m+1,4,4)$ for any $m\ge 2$. As a first step towards residual finiteness we show that these Artin groups, and many more, split as free products with amalgamation or HNN extensions of finite rank free groups. Among others, this holds for all large type Artin groups with defining graph admitting an orientation, where each simple cycle is directed.

arXiv comment29 pages, 18 figures. The mistakes from the previous version have been corrected. The statement of Theorem A has been weakened to exclude some cases