  This paper focuses on tools for constructing 4-manifolds that have
fundamental group $G$ isomorphic to a right-angled Artin group and that are
also minimal, in the sense that they minimize $b_2(M)$, the dimension of
$H_2(M;\mathbb{Q})$. For a finitely presented group $G$, define $h(G) = \min\{
b_2(M) | M \in \mathcal M(G) \}$.
  In this paper, we explore the ways in which we can bound $h(G)$ from below
using group cohomology and the tools necessary to build 4-manifolds that
realize these lower bounds. We give solutions for right-angled Artin groups, or
RAAGs, when the graph associated to $G$ has no 4-cliques, and further we reduce
this problem to the case when the graph is connected and contains only
4-cliques. We then give solutions for many infinite families of RAAGs and
provide a conjecture to the solution for all RAAGs.
