Acylindrical hyperbolicity for Artin groups of dimension 2

TL;DR

This paper proves that all irreducible 2-dimensional Artin groups of rank at least 3 are acylindrically hyperbolic by analyzing their action on the modified Deligne complex, revealing new geometric properties.

Contribution

It establishes acylindrical hyperbolicity for a broad class of 2-dimensional Artin groups using geometric group theory techniques.

Findings

Irreducible 2-dimensional Artin groups of rank ≥ 3 are acylindrically hyperbolic.

Develops new geometric insights into the links of the modified Deligne complex.

Provides tools for studying the geometry of Artin groups via their complexes.

Abstract

In this paper, we show that every irreducible $2$-dimensional Artin group $A_{\Gamma}$ of rank at least $3$ is acylindrically hyperbolic. We do this by studying the action of $A_{\Gamma}$ on its modified Deligne complex. Along the way, we prove results of independent interests on the geometry of links of this complex.