Finite Stature in Artin groups

TL;DR

This paper establishes criteria for finite stature in graphs of groups, applies it to triangle Artin groups, and demonstrates residual finiteness, thereby expanding the class of known residually finite Artin groups.

Contribution

It provides new criteria for finite stature in graphs of groups and applies these to specific Artin groups to prove residual finiteness.

Findings

Triangle Artin groups have finite stature.

Residual finiteness is established for these groups.

Expands the class of residually finite Artin groups.

Abstract

We give criteria for a graph of groups to have finite stature with respect to its collection of vertex groups, in the sense of Huang-Wise. We apply it to the triangle Artin groups that were previously shown to split as a graph of groups. This allows us to deduce residual finiteness, and expands the list of Artin groups known to be residually finite.