Acylindrical hyperbolicity for Artin groups of dimension 2

Nicolas Vaskou

Published 2020-07-31Version 1

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 applying a criterion of Martin to 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.