Negative curvature in locally reducible Artin groups

TL;DR

This paper introduces the 2-complete Artin complex for locally reducible Artin groups, demonstrating its systolic properties and implications for subgroup structure and hyperbolicity.

Contribution

It defines the 2-complete Artin complex and proves its systolicity, revealing new geometric properties and subgroup behaviors in locally reducible Artin groups.

Findings

The 2-complete Artin complex is systolic for these groups.

Parabolic subgroups with proper 2-completions are weakly malnormal.

Many locally reducible Artin groups are acylindrically hyperbolic.

Abstract

In this paper, we define the 2-complete Artin complex and show that it is systolic for locally reducible Artin groups. The stabilizers of simplices in this complex are exactly the proper parabolic subgroups which are "2-complete." We use this systolicity to show that parabolic subgroups, with 2-completions that are not the whole Artin group, are weakly malnormal. This allows us to conclude that many locally reducible Artin groups are acylindrically hyperbolic.