On Gromov's conjecture for right-angled Artin groups

Abstract

We prove that the universal covering $\Wi M$ of an $n$-dimensional closed spin PSC manifold $M$ whose fundamental group ${\pi }_1(M)$ is a right-angled Artin group has macroscopic dimension $\dim_{mc}\Wi M\le n-2$. This confirms Gromov's conjecture in the case of right-angled Artin groups.