Some virtually poly-free Artin groups

TL;DR

This paper proves that certain classes of Artin groups of affine and complex types are virtually poly-free, advancing understanding of their algebraic structure and partially answering whether all Artin groups share this property.

Contribution

It establishes that specific Artin groups of affine and complex types are virtually poly-free, providing new insights into their algebraic properties.

Findings

Certain affine Artin groups are virtually poly-free

Certain complex Artin groups are virtually poly-free

Partial progress on the general question of Artin groups being virtually poly-free

Abstract

In this short note we prove that a class of Artin groups of affine and complex types are virtually poly-free, answering partially the question if all Artin groups are virtually poly-free.